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26 Hypothesis and Variables – Meaning, Classification and Uses

C. Parvathi

INTRODUCTION

Today, we are going to see the meaning of the hypothesis, steps involved to write a hypothesis, its characteristics, types and errors in formulating hypothesis. It involves different errors of hypothesis for which we have to identify the variables which will enable the research scholars to justify the area of research and design of the research work under taken by the investigator.

Hypothesis is usually considered as the principal instrument in research. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate objective of testing hypotheses. Decision-makers often face situations wherein they are interested in testing hypotheses on the basis of available information and then take decisions on the basis of such testing. In social science, where direct knowledge of population parameter(s) is rare, hypothesis testing is often used strategy for deciding whether a sample data offers such support for a hypothesis from which generalization can be made. Thus hypothesis testing enables us to make probability statements about population parameter(s). The hypothesis may not be proved absolutely, but in practice it is accepted if it has withstood a critical testing. Before we explain how hypotheses are tested through different tests meant for this purpose, it will be appropriate to explain clearly the meaning of a hypothesis and the related concepts for better understanding of the hypothesis testing techniques.

WHAT IS HYPOTHESIS?

Generally, when one talks about hypothesis, one simply means mere assumption or some supposition to be proved or disproved. Thus a hypothesis may be defined as a proposition or a set of proposition set forth as an explanation for the occurrence of some specified group of phenomena either asserted merely as a provisional conjecture to guide some investigation or accepted a highly probable in the light of established facts. Research hypothesis is a predictive  statement, capable of being tested by scientific methods that relate an independent variable to some dependant variable. For example, consider statement like the following ones:

“Students who receive counseling will show better performance increase in creativity than students not receiving counseling” or “the automobile  A is performing better than automobile B .”

The above hypothesis is capable of being objectively verified and tested. It is a proposition which can be put to a test to determine its validity.

Here, we are examining the truth or otherwise of the hypothesis (guess, claim or assumptions, etc.) about some feature about one or more populations on the basis of samples drawn from these populations. Testing plays a major role in statistical investigation. Generally, a statistical hypothesis is a statement or a conclusion or an assumption about certain characteristic populations which is drawn on a logical basis and it can be tested based on the sample evidences. Test of hypothesis means either accept or reject the hypothesis under a valid reason. The test of significance enables a researcher to decide either to accept or reject the statistical hypothesis. For example, a manufacturing company producing bolts of different sizes and claims that not more than 2 per cent bolts are defective. In order to verify the claim as true or not, we have to check it on the basis of sample of bolts. A company wants to verify the effectiveness of advertisement given through print media is less effective than audio-visual media or not. There are wide ranges of areas in business where we have to come across situations of arriving at a decision of accepting or rejecting hypothesis. So, it is very much important to have knowledge about the logical basis of such decisions and it is provided by hypothesis testing, which is the objective of this chapter.

It is a usual procedure that sample is drawn from the population an estimate of population parameter which is in other words, called sample statistic. Estimate of population parameters thus obtained may or may not exactly match with true values. To take the sample statistic as the estimate of population parameter is involved with risk. So, it is worthwhile to find whether the  difference between the estimated value of the parameter or the true value is significantly different or it could have arisen due to fluctuation of sampling. For this reason only, a hypothesis is formulated and then tested for validity.

Meaning of Hypothesis:

Hypothesis simply means a mere assumption to be proved or disproved. But for a researcher hypothesis is a formal question that he intends to resolve. It is a testable statement; hypotheses are generally either derived theory of from direct observation of data

Types of Hypothesis

Null hypothesis

Null hypothesis is the statement about the parameters, which is usually a hypothesis of no difference and is denoted by Ho.

Alternative Hypothesis

Any hypothesis, which is complementary to the null hypothesis, is called an alternative hypothesis, usually denoted by H1.

BASIC CONCEPTS ON TESTING OF HYPOTHESES

a) NULL HYPOTHESIS

In the context of statistical analysis, we often talk about null hypothesis and alternative hypothesis. If we are to compare method A with method B about its superiority and if we proceed on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis. The null hypothesis is generally symbolized as Ho and the alternative hypothesis as Ha.

In the choice of null hypothesis, the following considerations are usually kept in view:

Alternative hypothesis is usually the one which one wishes to prove and the null hypothesis is the one which one wishes to disprove. Thus, a null hypothesis represents the hypothesis we are trying to reject, and the alternative hypothesis represents all other possibilities.

  If the rejection of a certain hypothesis when it actually true involves great risk, it is taken as null hypothesis.

Null hypothesis should always be specific hypothesis i.e., it should not state about or approximately a certain value.

b)   THE LEVEL OF SIGNIFICANCE

This is a very important concept in the context of hypothesis testing. It is always some percentage (usually 5%) which should be chosen with great care. In case we take the significance level at 5 percent, then this implies that Ho will be rejected when the sampling result (i.e., observed evidence) has a less than 0.05 probability of occurring if Ho is true. In other words, the 5 percent level of significance means that researcher is willing to take as much as 5 percent risk of rejecting the null hypothesis when it (Ho) happens to be true.

c) DECISION RULE OF TEST OF HYPOTHESIS

Given a hypothesis Ho and an alternative hypothesis Ha, we make a rule which is known as decision rule according to which we accept Ho (i.e., reject Ha) or reject Ho (i.e., accept Ha).

d) TYPE I ERROR AND TYPE II ERRORS

In the context of testing of hypotheses, there are basically two types of errors. We may reject Ho when Ho is true and we may accept Ho when Ho is not true. The former is known as Type I error and the latter as Type II error. In other words, Type I error means rejection of hypothesis which should have been accepted and Type II error means accepting the hypothesis which should have been rejected. Type I error is denoted by α (alpha) known as α error, also called as the level of significance of test; and Type II error is denoted by β (beta) known as β error.

e) TWO-TAILED AND ONE-TAILED TESTS

In the content of hypothesis testing, these two terms are quite important and must be clearly understood. A two-tailed test rejects the null hypothesis if, say, the sample mean is significantly higher or lower than the hypothesized value of the mean of the population. Such a test is appropriate when the null hypothesis is some specified value and the alternative hypothesis is a value not equal to the specified value of the null hypothesis.

ERRORS IN TESTING OF HYPOTHESIS

In the procedure of testing of hypothesis, a decision is taken about the acceptance or rejection of null hypothesis. The possible decisions can be written in a tabular form.

There is always some possibility of committing the following two types of errors in taking such as decision as

Type I Error: Reject the null hypothesis Ho when it is true.

Type II Error: Accept the null hypothesis Ho when it is false.

Now, we write α = Probability of committing Type I error

And β = Probability of committing Type II error

The compliment of Type II error is called as the power of the test and is given by (1- β) and the size of Type I error (α) is also called as level of significance . The level of significance is  the quantity of risk, which can be readily tolerated in making a decision Ho. Usually the value of α, is chosen depending upon the desired degree of precession and it and its value varies between 0.05 (for moderate precision) to 0.01 (for high precision).

PROCEDURE FOR HYPOTHESIS TESTING

In hypothesis testing the main question is: whether to accept the null hypothesis or not. Procedure for hypothesis testing refers to all those steps that we undertake for making a choice between the two actions i.e., rejection and acceptance of a null hypothesis.

The various steps involved in hypothesis testing are stated below:

(i)  Selection of Variables

DEPENDENT VARIABLE

The variable that depends on other factors is called dependent variable. These variables are expected to change a result of an experimental manipulation of the independent variable or variables. The outcome variable measured in each subject, who may be influenced by manipulation of the independent variable, is termed the dependent variable.

INDEPENDENT VARIABLE

The variable that is stable and unaffected by other variables is called independent variable. It refers to the condition of an experiment that is systematically manipulated by the investigator. In experimental research, an investigator manipulates one variable and measures the effect of that manipulation on another variable. For example, let’s take a study in which the investigators want to determine how often an exercise must be done to increase strength.

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Fill in the blanks

F  Hypothesis is usually considered as the principal instrument of _________________

F   The null hypothesis is generally symbolized as_________

F   The variable that depends on other factor is called _____________ Variable.

IDENTIFYING THE KEY VARIABLES FOR ANALYSIS

• The key variables provide focus when writing the Introduction section
• The key variables are the major terms to be used in methodology.
• The key variables are the terms to be operationally defined if an Operational Definition of Terms section is necessary.
• The key variables must be directly measured or manipulated for the research study to be valid

     (ii)   Making a formal statement

(iii) Selecting a significance level

(iv) Deciding the distribution to use

(v) Selecting a random sample and computing an appropriate value

(vi) Calculation of the probability; and

(vii) Comparing the probability

FLOW DIAGRAM FOR HYPOTHESIS TESTING

TEST OF HYPOTHESIS

Statisticians have developed several tests of hypotheses (also known as the tests of significance) for the purpose of testing of hypotheses which can be classified as: (a) Parametric tests or standard test of hypothesis and (b) Non-parametric tests or distribution-free test of hypotheses.

Parametric tests are usually assuming certain properties of the parent population from which we draw samples. Assumptions like observations come from a normal population, sample size is large, assumptions about the population parameters like mean, variance, etc., must hold good before parametric tests can be used.

Non-parametric tests assume only nominal or ordinal data, whereas parameters tests require measurement equivalent to at least an interval scale.

IMPORTANT PARAMETRIC TESTS

The important parametric tests are:

(i)   Z-test

Z-test is based on the normal probability distribution and is used for judging the significance of several statistical measures, particularly the mean.

(ii)   t-test

t-test is based on t-distribution and is considered an appropriate test for judging the significance of an sample mean or for judging the significance of difference between the means of two samples in case of small sample(s) when population variance is not known (in which we use variance of the samples as an estimate of the population variance).

(iii)   X 2 -test

X2-test is also used as a test of goodness of fit and also as a test of independence in which case it is a non-parametric test. X2-test is based on chi-square distribution and as a parametric test is used for comparing a sample variance to a theoretical population variance.

(iv)   F-test

F-test is based on F-distribution and is used to compare the variance of the two-independent samples.

LIMITATIONS OF THE TESTS OF HYPOTHESES

Limitations of test of hypothesis are as follows:

i) The tests should not be used in a mechanical fashion. It should be kept in view that testing is not decision- making itself; the tests are only useful aids for decision-making.

ii) Tests do not explain the reasons as to why does the difference exist, like between the means of the two samples. They simply indicate whether the difference is due to fluctuations of sampling or because of other reasons.

 iii) Results of test of significance are based on probabilities which cannot be expressed with full certainty. When a test shows that a difference is statistically significant, then it simply suggests that the difference is probably not due to chance.

iv) Statistical inferences based on the significance tests cannot be said to be entirely correct evidences concerning the truth of the hypotheses. This is specially so in case of small samples where the probability of drawing inferences happens to be generally higher. For greater reliability, the size of samples is sufficiently enlarged.

To conclude, we have seen the meaning, steps, and characteristics of hypothesis in a detailed manner. Framing and testing of the hypothesis is the major part of the research work with which investigator will be able to test by scientific method(s), to apply econometric models to establish a strong relationship between the theory and the analysis of the research work which will strengthen the findings of the study. Therefore, in social science, framing the hypothesis occupies a significant place to proceed with the research work. Hence, the present E-module will be very useful for the project investigators and thereby conclusions drawn will enable the government to take decision at policy level.

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Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

Principles of Research Methodology pp 31–53 Cite as

The Research Hypothesis: Role and Construction

• Phyllis G. Supino EdD 3  
• First Online: 01 January 2012

5958 Accesses

A hypothesis is a logical construct, interposed between a problem and its solution, which represents a proposed answer to a research question. It gives direction to the investigator’s thinking about the problem and, therefore, facilitates a solution. There are three primary modes of inference by which hypotheses are developed: deduction (reasoning from a general propositions to specific instances), induction (reasoning from specific instances to a general proposition), and abduction (formulation/acceptance on probation of a hypothesis to explain a surprising observation).

A research hypothesis should reflect an inference about variables; be stated as a grammatically complete, declarative sentence; be expressed simply and unambiguously; provide an adequate answer to the research problem; and be testable. Hypotheses can be classified as conceptual versus operational, single versus bi- or multivariable, causal or not causal, mechanistic versus nonmechanistic, and null or alternative. Hypotheses most commonly entail statements about “variables” which, in turn, can be classified according to their level of measurement (scaling characteristics) or according to their role in the hypothesis (independent, dependent, moderator, control, or intervening).

A hypothesis is rendered operational when its broadly (conceptually) stated variables are replaced by operational definitions of those variables. Hypotheses stated in this manner are called operational hypotheses, specific hypotheses, or predictions and facilitate testing.

• Attention Deficit Hyperactivity Disorder
• Operational Definition
• Moderator Variable
• Ventricular Performance
• Attention Deficit Hyperactivity Disorder Group

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Wrong hypotheses, rightly worked from, have produced more results than unguided observation

—Augustus De Morgan, 1872[ 1 ]—

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Supino, P.G. (2012). The Research Hypothesis: Role and Construction. In: Supino, P., Borer, J. (eds) Principles of Research Methodology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3360-6_3

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Frequently asked questions

What is a hypothesis.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Frequently asked questions: Methodology

Attrition refers to participants leaving a study. It always happens to some extent—for example, in randomized controlled trials for medical research.

Differential attrition occurs when attrition or dropout rates differ systematically between the intervention and the control group . As a result, the characteristics of the participants who drop out differ from the characteristics of those who stay in the study. Because of this, study results may be biased .

Action research is conducted in order to solve a particular issue immediately, while case studies are often conducted over a longer period of time and focus more on observing and analyzing a particular ongoing phenomenon.

Action research is focused on solving a problem or informing individual and community-based knowledge in a way that impacts teaching, learning, and other related processes. It is less focused on contributing theoretical input, instead producing actionable input.

Action research is particularly popular with educators as a form of systematic inquiry because it prioritizes reflection and bridges the gap between theory and practice. Educators are able to simultaneously investigate an issue as they solve it, and the method is very iterative and flexible.

A cycle of inquiry is another name for action research . It is usually visualized in a spiral shape following a series of steps, such as “planning → acting → observing → reflecting.”

To make quantitative observations , you need to use instruments that are capable of measuring the quantity you want to observe. For example, you might use a ruler to measure the length of an object or a thermometer to measure its temperature.

Criterion validity and construct validity are both types of measurement validity . In other words, they both show you how accurately a method measures something.

While construct validity is the degree to which a test or other measurement method measures what it claims to measure, criterion validity is the degree to which a test can predictively (in the future) or concurrently (in the present) measure something.

Construct validity is often considered the overarching type of measurement validity . You need to have face validity , content validity , and criterion validity in order to achieve construct validity.

Convergent validity and discriminant validity are both subtypes of construct validity . Together, they help you evaluate whether a test measures the concept it was designed to measure.

• Convergent validity indicates whether a test that is designed to measure a particular construct correlates with other tests that assess the same or similar construct.
• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related. This type of validity is also called divergent validity .

You need to assess both in order to demonstrate construct validity. Neither one alone is sufficient for establishing construct validity.

• Discriminant validity indicates whether two tests that should not be highly related to each other are indeed not related

Content validity shows you how accurately a test or other measurement method taps  into the various aspects of the specific construct you are researching.

In other words, it helps you answer the question: “does the test measure all aspects of the construct I want to measure?” If it does, then the test has high content validity.

The higher the content validity, the more accurate the measurement of the construct.

If the test fails to include parts of the construct, or irrelevant parts are included, the validity of the instrument is threatened, which brings your results into question.

Face validity and content validity are similar in that they both evaluate how suitable the content of a test is. The difference is that face validity is subjective, and assesses content at surface level.

When a test has strong face validity, anyone would agree that the test’s questions appear to measure what they are intended to measure.

For example, looking at a 4th grade math test consisting of problems in which students have to add and multiply, most people would agree that it has strong face validity (i.e., it looks like a math test).

On the other hand, content validity evaluates how well a test represents all the aspects of a topic. Assessing content validity is more systematic and relies on expert evaluation. of each question, analyzing whether each one covers the aspects that the test was designed to cover.

A 4th grade math test would have high content validity if it covered all the skills taught in that grade. Experts(in this case, math teachers), would have to evaluate the content validity by comparing the test to the learning objectives.

Snowball sampling is a non-probability sampling method . Unlike probability sampling (which involves some form of random selection ), the initial individuals selected to be studied are the ones who recruit new participants.

Because not every member of the target population has an equal chance of being recruited into the sample, selection in snowball sampling is non-random.

Snowball sampling is a non-probability sampling method , where there is not an equal chance for every member of the population to be included in the sample .

This means that you cannot use inferential statistics and make generalizations —often the goal of quantitative research . As such, a snowball sample is not representative of the target population and is usually a better fit for qualitative research .

Snowball sampling relies on the use of referrals. Here, the researcher recruits one or more initial participants, who then recruit the next ones.

Participants share similar characteristics and/or know each other. Because of this, not every member of the population has an equal chance of being included in the sample, giving rise to sampling bias .

Snowball sampling is best used in the following cases:

• If there is no sampling frame available (e.g., people with a rare disease)
• If the population of interest is hard to access or locate (e.g., people experiencing homelessness)
• If the research focuses on a sensitive topic (e.g., extramarital affairs)

The reproducibility and replicability of a study can be ensured by writing a transparent, detailed method section and using clear, unambiguous language.

Reproducibility and replicability are related terms.

• Reproducing research entails reanalyzing the existing data in the same manner.
• Replicating (or repeating ) the research entails reconducting the entire analysis, including the collection of new data . 
• A successful reproduction shows that the data analyses were conducted in a fair and honest manner.
• A successful replication shows that the reliability of the results is high.

Stratified sampling and quota sampling both involve dividing the population into subgroups and selecting units from each subgroup. The purpose in both cases is to select a representative sample and/or to allow comparisons between subgroups.

The main difference is that in stratified sampling, you draw a random sample from each subgroup ( probability sampling ). In quota sampling you select a predetermined number or proportion of units, in a non-random manner ( non-probability sampling ).

Purposive and convenience sampling are both sampling methods that are typically used in qualitative data collection.

A convenience sample is drawn from a source that is conveniently accessible to the researcher. Convenience sampling does not distinguish characteristics among the participants. On the other hand, purposive sampling focuses on selecting participants possessing characteristics associated with the research study.

The findings of studies based on either convenience or purposive sampling can only be generalized to the (sub)population from which the sample is drawn, and not to the entire population.

Random sampling or probability sampling is based on random selection. This means that each unit has an equal chance (i.e., equal probability) of being included in the sample.

On the other hand, convenience sampling involves stopping people at random, which means that not everyone has an equal chance of being selected depending on the place, time, or day you are collecting your data.

Convenience sampling and quota sampling are both non-probability sampling methods. They both use non-random criteria like availability, geographical proximity, or expert knowledge to recruit study participants.

However, in convenience sampling, you continue to sample units or cases until you reach the required sample size.

In quota sampling, you first need to divide your population of interest into subgroups (strata) and estimate their proportions (quota) in the population. Then you can start your data collection, using convenience sampling to recruit participants, until the proportions in each subgroup coincide with the estimated proportions in the population.

A sampling frame is a list of every member in the entire population . It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.

Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous , so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous , as units share characteristics.

Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population .

A systematic review is secondary research because it uses existing research. You don’t collect new data yourself.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

An observational study is a great choice for you if your research question is based purely on observations. If there are ethical, logistical, or practical concerns that prevent you from conducting a traditional experiment , an observational study may be a good choice. In an observational study, there is no interference or manipulation of the research subjects, as well as no control or treatment groups .

It’s often best to ask a variety of people to review your measurements. You can ask experts, such as other researchers, or laypeople, such as potential participants, to judge the face validity of tests.

While experts have a deep understanding of research methods , the people you’re studying can provide you with valuable insights you may have missed otherwise.

Face validity is important because it’s a simple first step to measuring the overall validity of a test or technique. It’s a relatively intuitive, quick, and easy way to start checking whether a new measure seems useful at first glance.

Good face validity means that anyone who reviews your measure says that it seems to be measuring what it’s supposed to. With poor face validity, someone reviewing your measure may be left confused about what you’re measuring and why you’re using this method.

Face validity is about whether a test appears to measure what it’s supposed to measure. This type of validity is concerned with whether a measure seems relevant and appropriate for what it’s assessing only on the surface.

Statistical analyses are often applied to test validity with data from your measures. You test convergent validity and discriminant validity with correlations to see if results from your test are positively or negatively related to those of other established tests.

You can also use regression analyses to assess whether your measure is actually predictive of outcomes that you expect it to predict theoretically. A regression analysis that supports your expectations strengthens your claim of construct validity .

When designing or evaluating a measure, construct validity helps you ensure you’re actually measuring the construct you’re interested in. If you don’t have construct validity, you may inadvertently measure unrelated or distinct constructs and lose precision in your research.

Construct validity is often considered the overarching type of measurement validity ,  because it covers all of the other types. You need to have face validity , content validity , and criterion validity to achieve construct validity.

Construct validity is about how well a test measures the concept it was designed to evaluate. It’s one of four types of measurement validity , which includes construct validity, face validity , and criterion validity.

There are two subtypes of construct validity.

• Convergent validity : The extent to which your measure corresponds to measures of related constructs
• Discriminant validity : The extent to which your measure is unrelated or negatively related to measures of distinct constructs

Naturalistic observation is a valuable tool because of its flexibility, external validity , and suitability for topics that can’t be studied in a lab setting.

The downsides of naturalistic observation include its lack of scientific control , ethical considerations , and potential for bias from observers and subjects.

Naturalistic observation is a qualitative research method where you record the behaviors of your research subjects in real world settings. You avoid interfering or influencing anything in a naturalistic observation.

You can think of naturalistic observation as “people watching” with a purpose.

A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.

In statistics, dependent variables are also called:

• Response variables (they respond to a change in another variable)
• Outcome variables (they represent the outcome you want to measure)
• Left-hand-side variables (they appear on the left-hand side of a regression equation)

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.

Independent variables are also called:

• Explanatory variables (they explain an event or outcome)
• Predictor variables (they can be used to predict the value of a dependent variable)
• Right-hand-side variables (they appear on the right-hand side of a regression equation).

As a rule of thumb, questions related to thoughts, beliefs, and feelings work well in focus groups. Take your time formulating strong questions, paying special attention to phrasing. Be careful to avoid leading questions , which can bias your responses.

Overall, your focus group questions should be:

• Open-ended and flexible
• Impossible to answer with “yes” or “no” (questions that start with “why” or “how” are often best)
• Unambiguous, getting straight to the point while still stimulating discussion
• Unbiased and neutral

A structured interview is a data collection method that relies on asking questions in a set order to collect data on a topic. They are often quantitative in nature. Structured interviews are best used when: 

• You already have a very clear understanding of your topic. Perhaps significant research has already been conducted, or you have done some prior research yourself, but you already possess a baseline for designing strong structured questions.
• You are constrained in terms of time or resources and need to analyze your data quickly and efficiently.
• Your research question depends on strong parity between participants, with environmental conditions held constant.

More flexible interview options include semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias is the tendency for interview participants to give responses that will be viewed favorably by the interviewer or other participants. It occurs in all types of interviews and surveys , but is most common in semi-structured interviews , unstructured interviews , and focus groups .

Social desirability bias can be mitigated by ensuring participants feel at ease and comfortable sharing their views. Make sure to pay attention to your own body language and any physical or verbal cues, such as nodding or widening your eyes.

This type of bias can also occur in observations if the participants know they’re being observed. They might alter their behavior accordingly.

The interviewer effect is a type of bias that emerges when a characteristic of an interviewer (race, age, gender identity, etc.) influences the responses given by the interviewee.

There is a risk of an interviewer effect in all types of interviews , but it can be mitigated by writing really high-quality interview questions.

A semi-structured interview is a blend of structured and unstructured types of interviews. Semi-structured interviews are best used when:

• You have prior interview experience. Spontaneous questions are deceptively challenging, and it’s easy to accidentally ask a leading question or make a participant uncomfortable.
• Your research question is exploratory in nature. Participant answers can guide future research questions and help you develop a more robust knowledge base for future research.

An unstructured interview is the most flexible type of interview, but it is not always the best fit for your research topic.

Unstructured interviews are best used when:

• You are an experienced interviewer and have a very strong background in your research topic, since it is challenging to ask spontaneous, colloquial questions.
• Your research question is exploratory in nature. While you may have developed hypotheses, you are open to discovering new or shifting viewpoints through the interview process.
• You are seeking descriptive data, and are ready to ask questions that will deepen and contextualize your initial thoughts and hypotheses.
• Your research depends on forming connections with your participants and making them feel comfortable revealing deeper emotions, lived experiences, or thoughts.

The four most common types of interviews are:

• Structured interviews : The questions are predetermined in both topic and order. 
• Semi-structured interviews : A few questions are predetermined, but other questions aren’t planned.
• Unstructured interviews : None of the questions are predetermined.
• Focus group interviews : The questions are presented to a group instead of one individual.

Deductive reasoning is commonly used in scientific research, and it’s especially associated with quantitative research .

In research, you might have come across something called the hypothetico-deductive method . It’s the scientific method of testing hypotheses to check whether your predictions are substantiated by real-world data.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

There are many different types of inductive reasoning that people use formally or informally.

Here are a few common types:

• Inductive generalization : You use observations about a sample to come to a conclusion about the population it came from.
• Statistical generalization: You use specific numbers about samples to make statements about populations.
• Causal reasoning: You make cause-and-effect links between different things.
• Sign reasoning: You make a conclusion about a correlational relationship between different things.
• Analogical reasoning: You make a conclusion about something based on its similarities to something else.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

In inductive research , you start by making observations or gathering data. Then, you take a broad scan of your data and search for patterns. Finally, you make general conclusions that you might incorporate into theories.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

Triangulation can help:

• Reduce research bias that comes from using a single method, theory, or investigator
• Enhance validity by approaching the same topic with different tools
• Establish credibility by giving you a complete picture of the research problem

But triangulation can also pose problems:

• It’s time-consuming and labor-intensive, often involving an interdisciplinary team.
• Your results may be inconsistent or even contradictory.

There are four main types of triangulation :

• Data triangulation : Using data from different times, spaces, and people
• Investigator triangulation : Involving multiple researchers in collecting or analyzing data
• Theory triangulation : Using varying theoretical perspectives in your research
• Methodological triangulation : Using different methodologies to approach the same topic

Many academic fields use peer review , largely to determine whether a manuscript is suitable for publication. Peer review enhances the credibility of the published manuscript.

However, peer review is also common in non-academic settings. The United Nations, the European Union, and many individual nations use peer review to evaluate grant applications. It is also widely used in medical and health-related fields as a teaching or quality-of-care measure. 

Peer assessment is often used in the classroom as a pedagogical tool. Both receiving feedback and providing it are thought to enhance the learning process, helping students think critically and collaboratively.

Peer review can stop obviously problematic, falsified, or otherwise untrustworthy research from being published. It also represents an excellent opportunity to get feedback from renowned experts in your field. It acts as a first defense, helping you ensure your argument is clear and that there are no gaps, vague terms, or unanswered questions for readers who weren’t involved in the research process.

Peer-reviewed articles are considered a highly credible source due to this stringent process they go through before publication.

In general, the peer review process follows the following steps: 

• First, the author submits the manuscript to the editor.
• Reject the manuscript and send it back to author, or 
• Send it onward to the selected peer reviewer(s) 
• Next, the peer review process occurs. The reviewer provides feedback, addressing any major or minor issues with the manuscript, and gives their advice regarding what edits should be made. 
• Lastly, the edited manuscript is sent back to the author. They input the edits, and resubmit it to the editor for publication.

Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.

You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.

Exploratory research is a methodology approach that explores research questions that have not previously been studied in depth. It is often used when the issue you’re studying is new, or the data collection process is challenging in some way.

Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.

Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.

Explanatory research is a research method used to investigate how or why something occurs when only a small amount of information is available pertaining to that topic. It can help you increase your understanding of a given topic.

Clean data are valid, accurate, complete, consistent, unique, and uniform. Dirty data include inconsistencies and errors.

Dirty data can come from any part of the research process, including poor research design , inappropriate measurement materials, or flawed data entry.

Data cleaning takes place between data collection and data analyses. But you can use some methods even before collecting data.

For clean data, you should start by designing measures that collect valid data. Data validation at the time of data entry or collection helps you minimize the amount of data cleaning you’ll need to do.

After data collection, you can use data standardization and data transformation to clean your data. You’ll also deal with any missing values, outliers, and duplicate values.

Every dataset requires different techniques to clean dirty data , but you need to address these issues in a systematic way. You focus on finding and resolving data points that don’t agree or fit with the rest of your dataset.

These data might be missing values, outliers, duplicate values, incorrectly formatted, or irrelevant. You’ll start with screening and diagnosing your data. Then, you’ll often standardize and accept or remove data to make your dataset consistent and valid.

Data cleaning is necessary for valid and appropriate analyses. Dirty data contain inconsistencies or errors , but cleaning your data helps you minimize or resolve these.

Without data cleaning, you could end up with a Type I or II error in your conclusion. These types of erroneous conclusions can be practically significant with important consequences, because they lead to misplaced investments or missed opportunities.

Data cleaning involves spotting and resolving potential data inconsistencies or errors to improve your data quality. An error is any value (e.g., recorded weight) that doesn’t reflect the true value (e.g., actual weight) of something that’s being measured.

In this process, you review, analyze, detect, modify, or remove “dirty” data to make your dataset “clean.” Data cleaning is also called data cleansing or data scrubbing.

Research misconduct means making up or falsifying data, manipulating data analyses, or misrepresenting results in research reports. It’s a form of academic fraud.

These actions are committed intentionally and can have serious consequences; research misconduct is not a simple mistake or a point of disagreement but a serious ethical failure.

Anonymity means you don’t know who the participants are, while confidentiality means you know who they are but remove identifying information from your research report. Both are important ethical considerations .

You can only guarantee anonymity by not collecting any personally identifying information—for example, names, phone numbers, email addresses, IP addresses, physical characteristics, photos, or videos.

You can keep data confidential by using aggregate information in your research report, so that you only refer to groups of participants rather than individuals.

Research ethics matter for scientific integrity, human rights and dignity, and collaboration between science and society. These principles make sure that participation in studies is voluntary, informed, and safe.

Ethical considerations in research are a set of principles that guide your research designs and practices. These principles include voluntary participation, informed consent, anonymity, confidentiality, potential for harm, and results communication.

Scientists and researchers must always adhere to a certain code of conduct when collecting data from others .

These considerations protect the rights of research participants, enhance research validity , and maintain scientific integrity.

In multistage sampling , you can use probability or non-probability sampling methods .

For a probability sample, you have to conduct probability sampling at every stage.

You can mix it up by using simple random sampling , systematic sampling , or stratified sampling to select units at different stages, depending on what is applicable and relevant to your study.

Multistage sampling can simplify data collection when you have large, geographically spread samples, and you can obtain a probability sample without a complete sampling frame.

But multistage sampling may not lead to a representative sample, and larger samples are needed for multistage samples to achieve the statistical properties of simple random samples .

These are four of the most common mixed methods designs :

• Convergent parallel: Quantitative and qualitative data are collected at the same time and analyzed separately. After both analyses are complete, compare your results to draw overall conclusions. 
• Embedded: Quantitative and qualitative data are collected at the same time, but within a larger quantitative or qualitative design. One type of data is secondary to the other.
• Explanatory sequential: Quantitative data is collected and analyzed first, followed by qualitative data. You can use this design if you think your qualitative data will explain and contextualize your quantitative findings.
• Exploratory sequential: Qualitative data is collected and analyzed first, followed by quantitative data. You can use this design if you think the quantitative data will confirm or validate your qualitative findings.

Triangulation in research means using multiple datasets, methods, theories and/or investigators to address a research question. It’s a research strategy that can help you enhance the validity and credibility of your findings.

Triangulation is mainly used in qualitative research , but it’s also commonly applied in quantitative research . Mixed methods research always uses triangulation.

In multistage sampling , or multistage cluster sampling, you draw a sample from a population using smaller and smaller groups at each stage.

This method is often used to collect data from a large, geographically spread group of people in national surveys, for example. You take advantage of hierarchical groupings (e.g., from state to city to neighborhood) to create a sample that’s less expensive and time-consuming to collect data from.

No, the steepness or slope of the line isn’t related to the correlation coefficient value. The correlation coefficient only tells you how closely your data fit on a line, so two datasets with the same correlation coefficient can have very different slopes.

To find the slope of the line, you’ll need to perform a regression analysis .

Correlation coefficients always range between -1 and 1.

The sign of the coefficient tells you the direction of the relationship: a positive value means the variables change together in the same direction, while a negative value means they change together in opposite directions.

The absolute value of a number is equal to the number without its sign. The absolute value of a correlation coefficient tells you the magnitude of the correlation: the greater the absolute value, the stronger the correlation.

These are the assumptions your data must meet if you want to use Pearson’s r :

• Both variables are on an interval or ratio level of measurement
• Data from both variables follow normal distributions
• Your data have no outliers
• Your data is from a random or representative sample
• You expect a linear relationship between the two variables

Quantitative research designs can be divided into two main categories:

• Correlational and descriptive designs are used to investigate characteristics, averages, trends, and associations between variables.
• Experimental and quasi-experimental designs are used to test causal relationships .

Qualitative research designs tend to be more flexible. Common types of qualitative design include case study , ethnography , and grounded theory designs.

A well-planned research design helps ensure that your methods match your research aims, that you collect high-quality data, and that you use the right kind of analysis to answer your questions, utilizing credible sources . This allows you to draw valid , trustworthy conclusions.

The priorities of a research design can vary depending on the field, but you usually have to specify:

• Your research questions and/or hypotheses
• Your overall approach (e.g., qualitative or quantitative )
• The type of design you’re using (e.g., a survey , experiment , or case study )
• Your sampling methods or criteria for selecting subjects
• Your data collection methods (e.g., questionnaires , observations)
• Your data collection procedures (e.g., operationalization , timing and data management)
• Your data analysis methods (e.g., statistical tests  or thematic analysis )

A research design is a strategy for answering your   research question . It defines your overall approach and determines how you will collect and analyze data.

Questionnaires can be self-administered or researcher-administered.

Self-administered questionnaires can be delivered online or in paper-and-pen formats, in person or through mail. All questions are standardized so that all respondents receive the same questions with identical wording.

Researcher-administered questionnaires are interviews that take place by phone, in-person, or online between researchers and respondents. You can gain deeper insights by clarifying questions for respondents or asking follow-up questions.

You can organize the questions logically, with a clear progression from simple to complex, or randomly between respondents. A logical flow helps respondents process the questionnaire easier and quicker, but it may lead to bias. Randomization can minimize the bias from order effects.

Closed-ended, or restricted-choice, questions offer respondents a fixed set of choices to select from. These questions are easier to answer quickly.

Open-ended or long-form questions allow respondents to answer in their own words. Because there are no restrictions on their choices, respondents can answer in ways that researchers may not have otherwise considered.

A questionnaire is a data collection tool or instrument, while a survey is an overarching research method that involves collecting and analyzing data from people using questionnaires.

The third variable and directionality problems are two main reasons why correlation isn’t causation .

The third variable problem means that a confounding variable affects both variables to make them seem causally related when they are not.

The directionality problem is when two variables correlate and might actually have a causal relationship, but it’s impossible to conclude which variable causes changes in the other.

Correlation describes an association between variables : when one variable changes, so does the other. A correlation is a statistical indicator of the relationship between variables.

Causation means that changes in one variable brings about changes in the other (i.e., there is a cause-and-effect relationship between variables). The two variables are correlated with each other, and there’s also a causal link between them.

While causation and correlation can exist simultaneously, correlation does not imply causation. In other words, correlation is simply a relationship where A relates to B—but A doesn’t necessarily cause B to happen (or vice versa). Mistaking correlation for causation is a common error and can lead to false cause fallacy .

Controlled experiments establish causality, whereas correlational studies only show associations between variables.

• In an experimental design , you manipulate an independent variable and measure its effect on a dependent variable. Other variables are controlled so they can’t impact the results.
• In a correlational design , you measure variables without manipulating any of them. You can test whether your variables change together, but you can’t be sure that one variable caused a change in another.

In general, correlational research is high in external validity while experimental research is high in internal validity .

A correlation is usually tested for two variables at a time, but you can test correlations between three or more variables.

A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables.

Different types of correlation coefficients might be appropriate for your data based on their levels of measurement and distributions . The Pearson product-moment correlation coefficient (Pearson’s r ) is commonly used to assess a linear relationship between two quantitative variables.

A correlational research design investigates relationships between two variables (or more) without the researcher controlling or manipulating any of them. It’s a non-experimental type of quantitative research .

A correlation reflects the strength and/or direction of the association between two or more variables.

• A positive correlation means that both variables change in the same direction.
• A negative correlation means that the variables change in opposite directions.
• A zero correlation means there’s no relationship between the variables.

Random error  is almost always present in scientific studies, even in highly controlled settings. While you can’t eradicate it completely, you can reduce random error by taking repeated measurements, using a large sample, and controlling extraneous variables .

You can avoid systematic error through careful design of your sampling , data collection , and analysis procedures. For example, use triangulation to measure your variables using multiple methods; regularly calibrate instruments or procedures; use random sampling and random assignment ; and apply masking (blinding) where possible.

Systematic error is generally a bigger problem in research.

With random error, multiple measurements will tend to cluster around the true value. When you’re collecting data from a large sample , the errors in different directions will cancel each other out.

Systematic errors are much more problematic because they can skew your data away from the true value. This can lead you to false conclusions ( Type I and II errors ) about the relationship between the variables you’re studying.

Random and systematic error are two types of measurement error.

Random error is a chance difference between the observed and true values of something (e.g., a researcher misreading a weighing scale records an incorrect measurement).

Systematic error is a consistent or proportional difference between the observed and true values of something (e.g., a miscalibrated scale consistently records weights as higher than they actually are).

On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.

• If you have quantitative variables , use a scatterplot or a line graph.
• If your response variable is categorical, use a scatterplot or a line graph.
• If your explanatory variable is categorical, use a bar graph.

The term “ explanatory variable ” is sometimes preferred over “ independent variable ” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.

Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.

The difference between explanatory and response variables is simple:

• An explanatory variable is the expected cause, and it explains the results.
• A response variable is the expected effect, and it responds to other variables.

In a controlled experiment , all extraneous variables are held constant so that they can’t influence the results. Controlled experiments require:

• A control group that receives a standard treatment, a fake treatment, or no treatment.
• Random assignment of participants to ensure the groups are equivalent.

Depending on your study topic, there are various other methods of controlling variables .

There are 4 main types of extraneous variables :

• Demand characteristics : environmental cues that encourage participants to conform to researchers’ expectations.
• Experimenter effects : unintentional actions by researchers that influence study outcomes.
• Situational variables : environmental variables that alter participants’ behaviors.
• Participant variables : any characteristic or aspect of a participant’s background that could affect study results.

An extraneous variable is any variable that you’re not investigating that can potentially affect the dependent variable of your research study.

A confounding variable is a type of extraneous variable that not only affects the dependent variable, but is also related to the independent variable.

In a factorial design, multiple independent variables are tested.

If you test two variables, each level of one independent variable is combined with each level of the other independent variable to create different conditions.

Within-subjects designs have many potential threats to internal validity , but they are also very statistically powerful .

Advantages:

• Only requires small samples
• Statistically powerful
• Removes the effects of individual differences on the outcomes

Disadvantages:

• Internal validity threats reduce the likelihood of establishing a direct relationship between variables
• Time-related effects, such as growth, can influence the outcomes
• Carryover effects mean that the specific order of different treatments affect the outcomes

While a between-subjects design has fewer threats to internal validity , it also requires more participants for high statistical power than a within-subjects design .

• Prevents carryover effects of learning and fatigue.
• Shorter study duration.
• Needs larger samples for high power.
• Uses more resources to recruit participants, administer sessions, cover costs, etc.
• Individual differences may be an alternative explanation for results.

Yes. Between-subjects and within-subjects designs can be combined in a single study when you have two or more independent variables (a factorial design). In a mixed factorial design, one variable is altered between subjects and another is altered within subjects.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

“Controlling for a variable” means measuring extraneous variables and accounting for them statistically to remove their effects on other variables.

Researchers often model control variable data along with independent and dependent variable data in regression analyses and ANCOVAs . That way, you can isolate the control variable’s effects from the relationship between the variables of interest.

Control variables help you establish a correlational or causal relationship between variables by enhancing internal validity .

If you don’t control relevant extraneous variables , they may influence the outcomes of your study, and you may not be able to demonstrate that your results are really an effect of your independent variable .

A control variable is any variable that’s held constant in a research study. It’s not a variable of interest in the study, but it’s controlled because it could influence the outcomes.

Including mediators and moderators in your research helps you go beyond studying a simple relationship between two variables for a fuller picture of the real world. They are important to consider when studying complex correlational or causal relationships.

Mediators are part of the causal pathway of an effect, and they tell you how or why an effect takes place. Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds.

If something is a mediating variable :

• It’s caused by the independent variable .
• It influences the dependent variable
• When it’s taken into account, the statistical correlation between the independent and dependent variables is higher than when it isn’t considered.

A confounder is a third variable that affects variables of interest and makes them seem related when they are not. In contrast, a mediator is the mechanism of a relationship between two variables: it explains the process by which they are related.

A mediator variable explains the process through which two variables are related, while a moderator variable affects the strength and direction of that relationship.

There are three key steps in systematic sampling :

• Define and list your population , ensuring that it is not ordered in a cyclical or periodic order.
• Decide on your sample size and calculate your interval, k , by dividing your population by your target sample size.
• Choose every k th member of the population as your sample.

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .

Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.

For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.

You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.

Using stratified sampling will allow you to obtain more precise (with lower variance ) statistical estimates of whatever you are trying to measure.

For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.

In stratified sampling , researchers divide subjects into subgroups called strata based on characteristics that they share (e.g., race, gender, educational attainment).

Once divided, each subgroup is randomly sampled using another probability sampling method.

Cluster sampling is more time- and cost-efficient than other probability sampling methods , particularly when it comes to large samples spread across a wide geographical area.

However, it provides less statistical certainty than other methods, such as simple random sampling , because it is difficult to ensure that your clusters properly represent the population as a whole.

There are three types of cluster sampling : single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.

• In single-stage sampling , you collect data from every unit within the selected clusters.
• In double-stage sampling , you select a random sample of units from within the clusters.
• In multi-stage sampling , you repeat the procedure of randomly sampling elements from within the clusters until you have reached a manageable sample.

Cluster sampling is a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample.

The clusters should ideally each be mini-representations of the population as a whole.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.

Quasi-experimental design is most useful in situations where it would be unethical or impractical to run a true experiment .

Quasi-experiments have lower internal validity than true experiments, but they often have higher external validity  as they can use real-world interventions instead of artificial laboratory settings.

A quasi-experiment is a type of research design that attempts to establish a cause-and-effect relationship. The main difference with a true experiment is that the groups are not randomly assigned.

Blinding is important to reduce research bias (e.g., observer bias , demand characteristics ) and ensure a study’s internal validity .

If participants know whether they are in a control or treatment group , they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.

• In a single-blind study , only the participants are blinded.
• In a double-blind study , both participants and experimenters are blinded.
• In a triple-blind study , the assignment is hidden not only from participants and experimenters, but also from the researchers analyzing the data.

Blinding means hiding who is assigned to the treatment group and who is assigned to the control group in an experiment .

A true experiment (a.k.a. a controlled experiment) always includes at least one control group that doesn’t receive the experimental treatment.

However, some experiments use a within-subjects design to test treatments without a control group. In these designs, you usually compare one group’s outcomes before and after a treatment (instead of comparing outcomes between different groups).

For strong internal validity , it’s usually best to include a control group if possible. Without a control group, it’s harder to be certain that the outcome was caused by the experimental treatment and not by other variables.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

Individual Likert-type questions are generally considered ordinal data , because the items have clear rank order, but don’t have an even distribution.

Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.

The type of data determines what statistical tests you should use to analyze your data.

A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.

To use a Likert scale in a survey , you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.

In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).

The process of turning abstract concepts into measurable variables and indicators is called operationalization .

There are various approaches to qualitative data analysis , but they all share five steps in common:

• Prepare and organize your data.
• Review and explore your data.
• Develop a data coding system.
• Assign codes to the data.
• Identify recurring themes.

The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .

There are five common approaches to qualitative research :

• Grounded theory involves collecting data in order to develop new theories.
• Ethnography involves immersing yourself in a group or organization to understand its culture.
• Narrative research involves interpreting stories to understand how people make sense of their experiences and perceptions.
• Phenomenological research involves investigating phenomena through people’s lived experiences.
• Action research links theory and practice in several cycles to drive innovative changes.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Operationalization means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalize the variables that you want to measure.

When conducting research, collecting original data has significant advantages:

• You can tailor data collection to your specific research aims (e.g. understanding the needs of your consumers or user testing your website)
• You can control and standardize the process for high reliability and validity (e.g. choosing appropriate measurements and sampling methods )

However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.

In restriction , you restrict your sample by only including certain subjects that have the same values of potential confounding variables.

In matching , you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable .

In statistical control , you include potential confounders as variables in your regression .

In randomization , you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.

A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.

Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.

To ensure the internal validity of your research, you must consider the impact of confounding variables. If you fail to account for them, you might over- or underestimate the causal relationship between your independent and dependent variables , or even find a causal relationship where none exists.

Yes, but including more than one of either type requires multiple research questions .

For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.

You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .

To ensure the internal validity of an experiment , you should only change one independent variable at a time.

No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!

You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .

• The type of soda – diet or regular – is the independent variable .
• The level of blood sugar that you measure is the dependent variable – it changes depending on the type of soda.

Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.

In non-probability sampling , the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.

Common non-probability sampling methods include convenience sampling , voluntary response sampling, purposive sampling , snowball sampling, and quota sampling .

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

Using careful research design and sampling procedures can help you avoid sampling bias . Oversampling can be used to correct undercoverage bias .

Some common types of sampling bias include self-selection bias , nonresponse bias , undercoverage bias , survivorship bias , pre-screening or advertising bias, and healthy user bias.

Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.

A sampling error is the difference between a population parameter and a sample statistic .

A statistic refers to measures about the sample , while a parameter refers to measures about the population .

Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

There are seven threats to external validity : selection bias , history, experimenter effect, Hawthorne effect , testing effect, aptitude-treatment and situation effect.

The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).

The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.

Cross-sectional studies cannot establish a cause-and-effect relationship or analyze behavior over a period of time. To investigate cause and effect, you need to do a longitudinal study or an experimental study .

Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.

Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.

Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.

The 1970 British Cohort Study , which has collected data on the lives of 17,000 Brits since their births in 1970, is one well-known example of a longitudinal study .

Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.

Longitudinal studies and cross-sectional studies are two different types of research design . In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.

There are eight threats to internal validity : history, maturation, instrumentation, testing, selection bias , regression to the mean, social interaction and attrition .

Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts and meanings, use qualitative methods .
• If you want to analyze a large amount of readily-available data, use secondary data. If you want data specific to your purposes with control over how it is generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

• The  independent variable  is the amount of nutrients added to the crop field.
• The  dependent variable is the biomass of the crops at harvest time.

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

I nternal validity is the degree of confidence that the causal relationship you are testing is not influenced by other factors or variables .

External validity is the extent to which your results can be generalized to other contexts.

The validity of your experiment depends on your experimental design .

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research, you also have to consider the internal and external validity of your experiment.

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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Theories, Hypotheses, and Laws: Definitions, examples, and their roles in science

by Anthony Carpi, Ph.D., Anne E. Egger, Ph.D.

Listen to this reading

Did you know that the idea of evolution had been part of Western thought for more than 2,000 years before Charles Darwin was born? Like many theories, the theory of evolution was the result of the work of many different scientists working in different disciplines over a period of time.

A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and is logical, testable, and predictive.

As new evidence comes to light, or new interpretations of existing data are proposed, theories may be revised and even change; however, they are not tenuous or speculative.

A scientific hypothesis is an inferred explanation of an observation or research finding; while more exploratory in nature than a theory, it is based on existing scientific knowledge.

A scientific law is an expression of a mathematical or descriptive relationship observed in nature.

Imagine yourself shopping in a grocery store with a good friend who happens to be a chemist. Struggling to choose between the many different types of tomatoes in front of you, you pick one up, turn to your friend, and ask her if she thinks the tomato is organic . Your friend simply chuckles and replies, "Of course it's organic!" without even looking at how the fruit was grown. Why the amused reaction? Your friend is highlighting a simple difference in vocabulary. To a chemist, the term organic refers to any compound in which hydrogen is bonded to carbon. Tomatoes (like all plants) are abundant in organic compounds – thus your friend's laughter. In modern agriculture, however, organic has come to mean food items grown or raised without the use of chemical fertilizers, pesticides, or other additives.

So who is correct? You both are. Both uses of the word are correct, though they mean different things in different contexts. There are, of course, lots of words that have more than one meaning (like bat , for example), but multiple meanings can be especially confusing when two meanings convey very different ideas and are specific to one field of study.

• Scientific theories

The term theory also has two meanings, and this double meaning often leads to confusion. In common language, the term theory generally refers to speculation or a hunch or guess. You might have a theory about why your favorite sports team isn't playing well, or who ate the last cookie from the cookie jar. But these theories do not fit the scientific use of the term. In science, a theory is a well-substantiated and comprehensive set of ideas that explains a phenomenon in nature. A scientific theory is based on large amounts of data and observations that have been collected over time. Scientific theories can be tested and refined by additional research , and they allow scientists to make predictions. Though you may be correct in your hunch, your cookie jar conjecture doesn't fit this more rigorous definition.

All scientific disciplines have well-established, fundamental theories . For example, atomic theory describes the nature of matter and is supported by multiple lines of evidence from the way substances behave and react in the world around us (see our series on Atomic Theory ). Plate tectonic theory describes the large scale movement of the outer layer of the Earth and is supported by evidence from studies about earthquakes , magnetic properties of the rocks that make up the seafloor , and the distribution of volcanoes on Earth (see our series on Plate Tectonic Theory ). The theory of evolution by natural selection , which describes the mechanism by which inherited traits that affect survivability or reproductive success can cause changes in living organisms over generations , is supported by extensive studies of DNA , fossils , and other types of scientific evidence (see our Charles Darwin series for more information). Each of these major theories guides and informs modern research in those fields, integrating a broad, comprehensive set of ideas.

So how are these fundamental theories developed, and why are they considered so well supported? Let's take a closer look at some of the data and research supporting the theory of natural selection to better see how a theory develops.

Comprehension Checkpoint

• The development of a scientific theory: Evolution and natural selection

The theory of evolution by natural selection is sometimes maligned as Charles Darwin 's speculation on the origin of modern life forms. However, evolutionary theory is not speculation. While Darwin is rightly credited with first articulating the theory of natural selection, his ideas built on more than a century of scientific research that came before him, and are supported by over a century and a half of research since.

• The Fixity Notion: Linnaeus

Figure 1: Cover of the 1760 edition of Systema Naturae .

Research about the origins and diversity of life proliferated in the 18th and 19th centuries. Carolus Linnaeus , a Swedish botanist and the father of modern taxonomy (see our module Taxonomy I for more information), was a devout Christian who believed in the concept of Fixity of Species , an idea based on the biblical story of creation. The Fixity of Species concept said that each species is based on an ideal form that has not changed over time. In the early stages of his career, Linnaeus traveled extensively and collected data on the structural similarities and differences between different species of plants. Noting that some very different plants had similar structures, he began to piece together his landmark work, Systema Naturae, in 1735 (Figure 1). In Systema , Linnaeus classified organisms into related groups based on similarities in their physical features. He developed a hierarchical classification system , even drawing relationships between seemingly disparate species (for example, humans, orangutans, and chimpanzees) based on the physical similarities that he observed between these organisms. Linnaeus did not explicitly discuss change in organisms or propose a reason for his hierarchy, but by grouping organisms based on physical characteristics, he suggested that species are related, unintentionally challenging the Fixity notion that each species is created in a unique, ideal form.

• The age of Earth: Leclerc and Hutton

Also in the early 1700s, Georges-Louis Leclerc, a French naturalist, and James Hutton , a Scottish geologist, began to develop new ideas about the age of the Earth. At the time, many people thought of the Earth as 6,000 years old, based on a strict interpretation of the events detailed in the Christian Old Testament by the influential Scottish Archbishop Ussher. By observing other planets and comets in the solar system , Leclerc hypothesized that Earth began as a hot, fiery ball of molten rock, mostly consisting of iron. Using the cooling rate of iron, Leclerc calculated that Earth must therefore be at least 70,000 years old in order to have reached its present temperature.

Hutton approached the same topic from a different perspective, gathering observations of the relationships between different rock formations and the rates of modern geological processes near his home in Scotland. He recognized that the relatively slow processes of erosion and sedimentation could not create all of the exposed rock layers in only a few thousand years (see our module The Rock Cycle ). Based on his extensive collection of data (just one of his many publications ran to 2,138 pages), Hutton suggested that the Earth was far older than human history – hundreds of millions of years old.

While we now know that both Leclerc and Hutton significantly underestimated the age of the Earth (by about 4 billion years), their work shattered long-held beliefs and opened a window into research on how life can change over these very long timescales.

• Fossil studies lead to the development of a theory of evolution: Cuvier

Figure 2: Illustration of an Indian elephant jaw and a mammoth jaw from Cuvier's 1796 paper.

With the age of Earth now extended by Leclerc and Hutton, more researchers began to turn their attention to studying past life. Fossils are the main way to study past life forms, and several key studies on fossils helped in the development of a theory of evolution . In 1795, Georges Cuvier began to work at the National Museum in Paris as a naturalist and anatomist. Through his work, Cuvier became interested in fossils found near Paris, which some claimed were the remains of the elephants that Hannibal rode over the Alps when he invaded Rome in 218 BCE . In studying both the fossils and living species , Cuvier documented different patterns in the dental structure and number of teeth between the fossils and modern elephants (Figure 2) (Horner, 1843). Based on these data , Cuvier hypothesized that the fossil remains were not left by Hannibal, but were from a distinct species of animal that once roamed through Europe and had gone extinct thousands of years earlier: the mammoth. The concept of species extinction had been discussed by a few individuals before Cuvier, but it was in direct opposition to the Fixity of Species concept – if every organism were based on a perfectly adapted, ideal form, how could any cease to exist? That would suggest it was no longer ideal.

While his work provided critical evidence of extinction , a key component of evolution , Cuvier was highly critical of the idea that species could change over time. As a result of his extensive studies of animal anatomy, Cuvier had developed a holistic view of organisms , stating that the

number, direction, and shape of the bones that compose each part of an animal's body are always in a necessary relation to all the other parts, in such a way that ... one can infer the whole from any one of them ...

In other words, Cuvier viewed each part of an organism as a unique, essential component of the whole organism. If one part were to change, he believed, the organism could not survive. His skepticism about the ability of organisms to change led him to criticize the whole idea of evolution , and his prominence in France as a scientist played a large role in discouraging the acceptance of the idea in the scientific community.

• Studies of invertebrates support a theory of change in species: Lamarck

Jean Baptiste Lamarck, a contemporary of Cuvier's at the National Museum in Paris, studied invertebrates like insects and worms. As Lamarck worked through the museum's large collection of invertebrates, he was impressed by the number and variety of organisms . He became convinced that organisms could, in fact, change through time, stating that

... time and favorable conditions are the two principal means which nature has employed in giving existence to all her productions. We know that for her time has no limit, and that consequently she always has it at her disposal.

This was a radical departure from both the fixity concept and Cuvier's ideas, and it built on the long timescale that geologists had recently established. Lamarck proposed that changes that occurred during an organism 's lifetime could be passed on to their offspring, suggesting, for example, that a body builder's muscles would be inherited by their children.

As it turned out, the mechanism by which Lamarck proposed that organisms change over time was wrong, and he is now often referred to disparagingly for his "inheritance of acquired characteristics" idea. Yet despite the fact that some of his ideas were discredited, Lamarck established a support for evolutionary theory that others would build on and improve.

• Rock layers as evidence for evolution: Smith

In the early 1800s, a British geologist and canal surveyor named William Smith added another component to the accumulating evidence for evolution . Smith observed that rock layers exposed in different parts of England bore similarities to one another: These layers (or strata) were arranged in a predictable order, and each layer contained distinct groups of fossils . From this series of observations , he developed a hypothesis that specific groups of animals followed one another in a definite sequence through Earth's history, and this sequence could be seen in the rock layers. Smith's hypothesis was based on his knowledge of geological principles , including the Law of Superposition.

The Law of Superposition states that sediments are deposited in a time sequence, with the oldest sediments deposited first, or at the bottom, and newer layers deposited on top. The concept was first expressed by the Persian scientist Avicenna in the 11th century, but was popularized by the Danish scientist Nicolas Steno in the 17th century. Note that the law does not state how sediments are deposited; it simply describes the relationship between the ages of deposited sediments.

Figure 3: Engraving from William Smith's 1815 monograph on identifying strata by fossils.

Smith backed up his hypothesis with extensive drawings of fossils uncovered during his research (Figure 3), thus allowing other scientists to confirm or dispute his findings. His hypothesis has, in fact, been confirmed by many other scientists and has come to be referred to as the Law of Faunal Succession. His work was critical to the formation of evolutionary theory as it not only confirmed Cuvier's work that organisms have gone extinct , but it also showed that the appearance of life does not date to the birth of the planet. Instead, the fossil record preserves a timeline of the appearance and disappearance of different organisms in the past, and in doing so offers evidence for change in organisms over time.

• The theory of evolution by natural selection: Darwin and Wallace

It was into this world that Charles Darwin entered: Linnaeus had developed a taxonomy of organisms based on their physical relationships, Leclerc and Hutton demonstrated that there was sufficient time in Earth's history for organisms to change, Cuvier showed that species of organisms have gone extinct , Lamarck proposed that organisms change over time, and Smith established a timeline of the appearance and disappearance of different organisms in the geological record .

Figure 4: Title page of the 1859 Murray edition of the Origin of Species by Charles Darwin.

Charles Darwin collected data during his work as a naturalist on the HMS Beagle starting in 1831. He took extensive notes on the geology of the places he visited; he made a major find of fossils of extinct animals in Patagonia and identified an extinct giant ground sloth named Megatherium . He experienced an earthquake in Chile that stranded beds of living mussels above water, where they would be preserved for years to come.

Perhaps most famously, he conducted extensive studies of animals on the Galápagos Islands, noting subtle differences in species of mockingbird, tortoise, and finch that were isolated on different islands with different environmental conditions. These subtle differences made the animals highly adapted to their environments .

This broad spectrum of data led Darwin to propose an idea about how organisms change "by means of natural selection" (Figure 4). But this idea was not based only on his work, it was also based on the accumulation of evidence and ideas of many others before him. Because his proposal encompassed and explained many different lines of evidence and previous work, they formed the basis of a new and robust scientific theory regarding change in organisms – the theory of evolution by natural selection .

Darwin's ideas were grounded in evidence and data so compelling that if he had not conceived them, someone else would have. In fact, someone else did. Between 1858 and 1859, Alfred Russel Wallace , a British naturalist, wrote a series of letters to Darwin that independently proposed natural selection as the means for evolutionary change. The letters were presented to the Linnean Society of London, a prominent scientific society at the time (see our module on Scientific Institutions and Societies ). This long chain of research highlights that theories are not just the work of one individual. At the same time, however, it often takes the insight and creativity of individuals to put together all of the pieces and propose a new theory . Both Darwin and Wallace were experienced naturalists who were familiar with the work of others. While all of the work leading up to 1830 contributed to the theory of evolution , Darwin's and Wallace's theory changed the way that future research was focused by presenting a comprehensive, well-substantiated set of ideas, thus becoming a fundamental theory of biological research.

• Expanding, testing, and refining scientific theories
• Genetics and evolution: Mendel and Dobzhansky

Since Darwin and Wallace first published their ideas, extensive research has tested and expanded the theory of evolution by natural selection . Darwin had no concept of genes or DNA or the mechanism by which characteristics were inherited within a species . A contemporary of Darwin's, the Austrian monk Gregor Mendel , first presented his own landmark study, Experiments in Plant Hybridization, in 1865 in which he provided the basic patterns of genetic inheritance , describing which characteristics (and evolutionary changes) can be passed on in organisms (see our Genetics I module for more information). Still, it wasn't until much later that a "gene" was defined as the heritable unit.

In 1937, the Ukrainian born geneticist Theodosius Dobzhansky published Genetics and the Origin of Species , a seminal work in which he described genes themselves and demonstrated that it is through mutations in genes that change occurs. The work defined evolution as "a change in the frequency of an allele within a gene pool" ( Dobzhansky, 1982 ). These studies and others in the field of genetics have added to Darwin's work, expanding the scope of the theory .

• Evolution under a microscope: Lenski

More recently, Dr. Richard Lenski, a scientist at Michigan State University, isolated a single Escherichia coli bacterium in 1989 as the first step of the longest running experimental test of evolutionary theory to date – a true test meant to replicate evolution and natural selection in the lab.

After the single microbe had multiplied, Lenski isolated the offspring into 12 different strains , each in their own glucose-supplied culture, predicting that the genetic make-up of each strain would change over time to become more adapted to their specific culture as predicted by evolutionary theory . These 12 lines have been nurtured for over 40,000 bacterial generations (luckily bacterial generations are much shorter than human generations) and exposed to different selective pressures such as heat , cold, antibiotics, and infection with other microorganisms. Lenski and colleagues have studied dozens of aspects of evolutionary theory with these genetically isolated populations . In 1999, they published a paper that demonstrated that random genetic mutations were common within the populations and highly diverse across different individual bacteria . However, "pivotal" mutations that are associated with beneficial changes in the group are shared by all descendants in a population and are much rarer than random mutations, as predicted by the theory of evolution by natural selection (Papadopoulos et al., 1999).

• Punctuated equilibrium: Gould and Eldredge

While established scientific theories like evolution have a wealth of research and evidence supporting them, this does not mean that they cannot be refined as new information or new perspectives on existing data become available. For example, in 1972, biologist Stephen Jay Gould and paleontologist Niles Eldredge took a fresh look at the existing data regarding the timing by which evolutionary change takes place. Gould and Eldredge did not set out to challenge the theory of evolution; rather they used it as a guiding principle and asked more specific questions to add detail and nuance to the theory. This is true of all theories in science: they provide a framework for additional research. At the time, many biologists viewed evolution as occurring gradually, causing small incremental changes in organisms at a relatively steady rate. The idea is referred to as phyletic gradualism , and is rooted in the geological concept of uniformitarianism . After reexamining the available data, Gould and Eldredge came to a different explanation, suggesting that evolution consists of long periods of stability that are punctuated by occasional instances of dramatic change – a process they called punctuated equilibrium .

Like Darwin before them, their proposal is rooted in evidence and research on evolutionary change, and has been supported by multiple lines of evidence. In fact, punctuated equilibrium is now considered its own theory in evolutionary biology. Punctuated equilibrium is not as broad of a theory as natural selection . In science, some theories are broad and overarching of many concepts, such as the theory of evolution by natural selection; others focus on concepts at a smaller, or more targeted, scale such as punctuated equilibrium. And punctuated equilibrium does not challenge or weaken the concept of natural selection; rather, it represents a change in our understanding of the timing by which change occurs in organisms , and a theory within a theory. The theory of evolution by natural selection now includes both gradualism and punctuated equilibrium to describe the rate at which change proceeds.

• Hypotheses and laws: Other scientific concepts

One of the challenges in understanding scientific terms like theory is that there is not a precise definition even within the scientific community. Some scientists debate over whether certain proposals merit designation as a hypothesis or theory , and others mistakenly use the terms interchangeably. But there are differences in these terms. A hypothesis is a proposed explanation for an observable phenomenon. Hypotheses , just like theories , are based on observations from research . For example, LeClerc did not hypothesize that Earth had cooled from a molten ball of iron as a random guess; rather, he developed this hypothesis based on his observations of information from meteorites.

A scientist often proposes a hypothesis before research confirms it as a way of predicting the outcome of study to help better define the parameters of the research. LeClerc's hypothesis allowed him to use known parameters (the cooling rate of iron) to do additional work. A key component of a formal scientific hypothesis is that it is testable and falsifiable. For example, when Richard Lenski first isolated his 12 strains of bacteria , he likely hypothesized that random mutations would cause differences to appear within a period of time in the different strains of bacteria. But when a hypothesis is generated in science, a scientist will also make an alternative hypothesis , an explanation that explains a study if the data do not support the original hypothesis. If the different strains of bacteria in Lenski's work did not diverge over the indicated period of time, perhaps the rate of mutation was slower than first thought.

So you might ask, if theories are so well supported, do they eventually become laws? The answer is no – not because they aren't well-supported, but because theories and laws are two very different things. Laws describe phenomena, often mathematically. Theories, however, explain phenomena. For example, in 1687 Isaac Newton proposed a Theory of Gravitation, describing gravity as a force of attraction between two objects. As part of this theory, Newton developed a Law of Universal Gravitation that explains how this force operates. This law states that the force of gravity between two objects is inversely proportional to the square of the distance between those objects. Newton 's Law does not explain why this is true, but it describes how gravity functions (see our Gravity: Newtonian Relationships module for more detail). In 1916, Albert Einstein developed his theory of general relativity to explain the mechanism by which gravity has its effect. Einstein's work challenges Newton's theory, and has been found after extensive testing and research to more accurately describe the phenomenon of gravity. While Einstein's work has replaced Newton's as the dominant explanation of gravity in modern science, Newton's Law of Universal Gravitation is still used as it reasonably (and more simply) describes the force of gravity under many conditions. Similarly, the Law of Faunal Succession developed by William Smith does not explain why organisms follow each other in distinct, predictable ways in the rock layers, but it accurately describes the phenomenon.

Theories, hypotheses , and laws drive scientific progress

Theories, hypotheses , and laws are not simply important components of science, they drive scientific progress. For example, evolutionary biology now stands as a distinct field of science that focuses on the origins and descent of species . Geologists now rely on plate tectonics as a conceptual model and guiding theory when they are studying processes at work in Earth's crust . And physicists refer to atomic theory when they are predicting the existence of subatomic particles yet to be discovered. This does not mean that science is "finished," or that all of the important theories have been discovered already. Like evolution , progress in science happens both gradually and in short, dramatic bursts. Both types of progress are critical for creating a robust knowledge base with data as the foundation and scientific theories giving structure to that knowledge.

Table of Contents

• Theories, hypotheses, and laws drive scientific progress

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How to Develop a Good Research Hypothesis

The story of a research study begins by asking a question. Researchers all around the globe are asking curious questions and formulating research hypothesis. However, whether the research study provides an effective conclusion depends on how well one develops a good research hypothesis. Research hypothesis examples could help researchers get an idea as to how to write a good research hypothesis.

This blog will help you understand what is a research hypothesis, its characteristics and, how to formulate a research hypothesis

Table of Contents

What is Hypothesis?

Hypothesis is an assumption or an idea proposed for the sake of argument so that it can be tested. It is a precise, testable statement of what the researchers predict will be outcome of the study.  Hypothesis usually involves proposing a relationship between two variables: the independent variable (what the researchers change) and the dependent variable (what the research measures).

What is a Research Hypothesis?

Research hypothesis is a statement that introduces a research question and proposes an expected result. It is an integral part of the scientific method that forms the basis of scientific experiments. Therefore, you need to be careful and thorough when building your research hypothesis. A minor flaw in the construction of your hypothesis could have an adverse effect on your experiment. In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment).

Characteristics of a Good Research Hypothesis

As the hypothesis is specific, there is a testable prediction about what you expect to happen in a study. You may consider drawing hypothesis from previously published research based on the theory.

A good research hypothesis involves more effort than just a guess. In particular, your hypothesis may begin with a question that could be further explored through background research.

To help you formulate a promising research hypothesis, you should ask yourself the following questions:

• Is the language clear and focused?
• What is the relationship between your hypothesis and your research topic?
• Is your hypothesis testable? If yes, then how?
• What are the possible explanations that you might want to explore?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate your variables without hampering the ethical standards?
• Does your research predict the relationship and outcome?
• Is your research simple and concise (avoids wordiness)?
• Is it clear with no ambiguity or assumptions about the readers’ knowledge
• Is your research observable and testable results?
• Is it relevant and specific to the research question or problem?

The questions listed above can be used as a checklist to make sure your hypothesis is based on a solid foundation. Furthermore, it can help you identify weaknesses in your hypothesis and revise it if necessary.

Source: Educational Hub

How to formulate a research hypothesis.

A testable hypothesis is not a simple statement. It is rather an intricate statement that needs to offer a clear introduction to a scientific experiment, its intentions, and the possible outcomes. However, there are some important things to consider when building a compelling hypothesis.

1. State the problem that you are trying to solve.

Make sure that the hypothesis clearly defines the topic and the focus of the experiment.

2. Try to write the hypothesis as an if-then statement.

Follow this template: If a specific action is taken, then a certain outcome is expected.

3. Define the variables

Independent variables are the ones that are manipulated, controlled, or changed. Independent variables are isolated from other factors of the study.

Dependent variables , as the name suggests are dependent on other factors of the study. They are influenced by the change in independent variable.

4. Scrutinize the hypothesis

Evaluate assumptions, predictions, and evidence rigorously to refine your understanding.

Types of Research Hypothesis

The types of research hypothesis are stated below:

1. Simple Hypothesis

It predicts the relationship between a single dependent variable and a single independent variable.

2. Complex Hypothesis

It predicts the relationship between two or more independent and dependent variables.

3. Directional Hypothesis

It specifies the expected direction to be followed to determine the relationship between variables and is derived from theory. Furthermore, it implies the researcher’s intellectual commitment to a particular outcome.

4. Non-directional Hypothesis

It does not predict the exact direction or nature of the relationship between the two variables. The non-directional hypothesis is used when there is no theory involved or when findings contradict previous research.

5. Associative and Causal Hypothesis

The associative hypothesis defines interdependency between variables. A change in one variable results in the change of the other variable. On the other hand, the causal hypothesis proposes an effect on the dependent due to manipulation of the independent variable.

6. Null Hypothesis

Null hypothesis states a negative statement to support the researcher’s findings that there is no relationship between two variables. There will be no changes in the dependent variable due the manipulation of the independent variable. Furthermore, it states results are due to chance and are not significant in terms of supporting the idea being investigated.

7. Alternative Hypothesis

It states that there is a relationship between the two variables of the study and that the results are significant to the research topic. An experimental hypothesis predicts what changes will take place in the dependent variable when the independent variable is manipulated. Also, it states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Research Hypothesis Examples of Independent and Dependent Variables

Research Hypothesis Example 1 The greater number of coal plants in a region (independent variable) increases water pollution (dependent variable). If you change the independent variable (building more coal factories), it will change the dependent variable (amount of water pollution).

Research Hypothesis Example 2 What is the effect of diet or regular soda (independent variable) on blood sugar levels (dependent variable)? If you change the independent variable (the type of soda you consume), it will change the dependent variable (blood sugar levels)

You should not ignore the importance of the above steps. The validity of your experiment and its results rely on a robust testable hypothesis. Developing a strong testable hypothesis has few advantages, it compels us to think intensely and specifically about the outcomes of a study. Consequently, it enables us to understand the implication of the question and the different variables involved in the study. Furthermore, it helps us to make precise predictions based on prior research. Hence, forming a hypothesis would be of great value to the research. Here are some good examples of testable hypotheses.

More importantly, you need to build a robust testable research hypothesis for your scientific experiments. A testable hypothesis is a hypothesis that can be proved or disproved as a result of experimentation.

Importance of a Testable Hypothesis

To devise and perform an experiment using scientific method, you need to make sure that your hypothesis is testable. To be considered testable, some essential criteria must be met:

• There must be a possibility to prove that the hypothesis is true.
• There must be a possibility to prove that the hypothesis is false.
• The results of the hypothesis must be reproducible.

Without these criteria, the hypothesis and the results will be vague. As a result, the experiment will not prove or disprove anything significant.

What are your experiences with building hypotheses for scientific experiments? What challenges did you face? How did you overcome these challenges? Please share your thoughts with us in the comments section.

Frequently Asked Questions

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a ‘if-then’ structure. 3. Defining the variables: Define the variables as Dependent or Independent based on their dependency to other factors. 4. Scrutinizing the hypothesis: Identify the type of your hypothesis

Hypothesis testing is a statistical tool which is used to make inferences about a population data to draw conclusions for a particular hypothesis.

Hypothesis in statistics is a formal statement about the nature of a population within a structured framework of a statistical model. It is used to test an existing hypothesis by studying a population.

Research hypothesis is a statement that introduces a research question and proposes an expected result. It forms the basis of scientific experiments.

The different types of hypothesis in research are: • Null hypothesis: Null hypothesis is a negative statement to support the researcher’s findings that there is no relationship between two variables. • Alternate hypothesis: Alternate hypothesis predicts the relationship between the two variables of the study. • Directional hypothesis: Directional hypothesis specifies the expected direction to be followed to determine the relationship between variables. • Non-directional hypothesis: Non-directional hypothesis does not predict the exact direction or nature of the relationship between the two variables. • Simple hypothesis: Simple hypothesis predicts the relationship between a single dependent variable and a single independent variable. • Complex hypothesis: Complex hypothesis predicts the relationship between two or more independent and dependent variables. • Associative and casual hypothesis: Associative and casual hypothesis predicts the relationship between two or more independent and dependent variables. • Empirical hypothesis: Empirical hypothesis can be tested via experiments and observation. • Statistical hypothesis: A statistical hypothesis utilizes statistical models to draw conclusions about broader populations.

Wow! You really simplified your explanation that even dummies would find it easy to comprehend. Thank you so much.

Thanks a lot for your valuable guidance.

I enjoy reading the post. Hypotheses are actually an intrinsic part in a study. It bridges the research question and the methodology of the study.

Useful piece!

This is awesome.Wow.

It very interesting to read the topic, can you guide me any specific example of hypothesis process establish throw the Demand and supply of the specific product in market

Nicely explained

It is really a useful for me Kindly give some examples of hypothesis

It was a well explained content ,can you please give me an example with the null and alternative hypothesis illustrated

clear and concise. thanks.

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Explained well and in simple terms. Quick read! Thank you

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Module 9: Hypothesis Testing With One Sample

Basics of hypothesis testing, learning outcomes.

• Describe hypothesis testing in general and in practice
• Differentiate between Type I and Type II Errors
• Conduct and interpret hypothesis tests for a single population mean, population standard deviation known
• Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown

The actual test begins by considering two  hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

H a : The alternative hypothesis : It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a  decision . They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” or “fail to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in  H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30

H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

H 0 : μ = 2.0

H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66

H 0 : μ = 66

H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ ≥ 5

H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45

H 0 : μ ≥ 45

H a : μ < 45

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

H 0 : p ≤ 0.066

H a : p > 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40

H 0 : p = 0.40

H a : p > 0.40

When you perform a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis  H 0 and the decision to reject or not. The outcomes are summarized in the following table:

The four possible outcomes in the table are: The decision is  not to reject H 0 when H 0 is true (correct decision) . The decision is to reject H 0 when H 0 is true (incorrect decision known as a Type I error ). The decision is not to reject H 0 when, in fact, H 0 is false (incorrect decision known as a Type II error ). The decision is to reject H 0 when H 0 is false ( correct decision whose probability is called the Power of the Test ).

Each of the errors occurs with a particular probability. The Greek letters α and β represent the probabilities.

α = probability of a Type I error = P (Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

β = probability of a Type II error = P (Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

α and β should be as small as possible because they are probabilities of errors. They are rarely zero.

The Power of the Test is 1 – β . Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test.

Suppose the null hypothesis,  H 0 , is: Frank’s rock climbing equipment is safe.

• Ty pe I error: Frank thinks that his rock climbing equipment may not be safe when, in fact, it really is safe.
• Type II error: Frank thinks that his rock climbing equipment may be safe when, in fact, it is not safe.

α = probability that Frank thinks his rock climbing equipment may not be safe when, in fact, it really is safe. β = probability that Frank thinks his rock climbing equipment may be safe when, in fact, it is not safe.

Notice that, in this case, the error with the greater consequence is the Type II error. (If Frank thinks his rock climbing equipment is safe, he will go ahead and use it.)

Suppose the null hypothesis,  H0 , is: the blood cultures contain no traces of pathogen X . State the Type I and Type II errors.

• Type I error: The researcher thinks the blood cultures do contain traces of pathogen X , when in fact, they do not.
• Type II error: The researcher thinks the blood cultures do not contain traces of pathogen X , when in fact, they do.

Suppose the null hypothesis,  H 0 , is: The victim of an automobile accident is alive when he arrives at the emergency room of a hospital.

• Type I error: The emergency crew thinks that the victim is dead when, in fact, the victim is alive.
• Type II error: The emergency crew does not know if the victim is alive when, in fact, the victim is dead.

α = probability that the emergency crew thinks the victim is dead when, in fact, he is really alive = P (Type I error). β = probability that the emergency crew does not know if the victim is alive when, in fact, the victim is dead = P (Type II error).

The error with the greater consequence is the Type I error. (If the emergency crew thinks the victim is dead, they will not treat him.)

Suppose the null hypothesis,  H0 , is: a patient is not sick. Which type of error has the greater consequence, Type I or Type II?

The error with the greater consequence is the Type II error: the patient will be thought well when, in fact, he is sick, so he will not get treatment.

It is a Boy Genetic Labs claim to be able to increase the likelihood that a pregnancy will result in a boy being born. Statisticians want to test the claim. Suppose that the null hypothesis,  H0 , is: It’s a Boy Genetic Labs has no effect on gender outcome.

• Type I error: This results when a true null hypothesis is rejected. In the context of this scenario, we would state that we believe that It’s a Boy Genetic Labs influences the gender outcome, when in fact it has no effect. The probability of this error occurring is denoted by the Greek letter alpha, α .
• Type II error: This results when we fail to reject a false null hypothesis. In context, we would state that It’s a Boy Genetic Labs does not influence the gender outcome of a pregnancy when, in fact, it does. The probability of this error occurring is denoted by the Greek letter beta, β .

The error of greater consequence would be the Type I error since couples would use the It’s a Boy Genetic Labs product in hopes of increasing the chances of having a boy.

“Red tide” is a bloom of poison-producing algae–a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts, the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 800 μg (micrograms) of toxin per kg of clam meat in any area, clam harvesting is banned there until the bloom is over and levels of toxin in clams subside. Describe both a Type I and a Type II error in this context, and state which error has the greater consequence.

In this scenario, an appropriate null hypothesis would be  H 0 : the mean level of toxins is at most 800 μ g, H 0 : μ 0 ≤ 800 μ g.

• Type I er ror: The DMF believes that toxin levels are still too high when, in fact, toxin levels are at most 800 μ g. The DMF continues the harvesting ban.
• Type II error: The DMF believes that toxin levels are within acceptable levels (are at least 800 μ g) when, in fact, toxin levels are still too high (more than 800 μ g). The DMF lifts the harvesting ban. This error could be the most serious. If the ban is lifted and clams are still toxic, consumers could possibly eat tainted food.

In summary, the more dangerous error would be to commit a Type II error, because this error involves the availability of tainted clams for consumption.

A certain experimental drug claims a cure rate of at least 75% for males with prostate cancer. Describe both the Type I and Type II errors in context. Which error is the more serious?

• Type I: A cancer patient believes the cure rate for the drug is less than 75% when it actually is at least 75%.
• Type II: A cancer patient believes the experimental drug has at least a 75% cure rate when it has a cure rate that is less than 75%.

In this scenario, the Type II error contains the more severe consequence. If a patient believes the drug works at least 75% of the time, this most likely will influence the patient’s (and doctor’s) choice about whether to use the drug as a treatment option.

Determine both Type I and Type II errors for the following scenario:

Assume a null hypothesis, H 0 , that states the percentage of adults with jobs is at least 88%.

Identify the Type I and Type II errors from these four statements.

a) Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88%

b) Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%.

c) Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%.

d) Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88%.

Type I error: c

Type I error: b

Earlier in the course, we discussed sampling distributions.  Particular distributions are associated with hypothesis testing. Perform tests of a population mean using a normal distribution or a Student’s t- distribution . (Remember, use a Student’s t -distribution when the population standard deviation is unknown and the distribution of the sample mean is approximately normal.) We perform tests of a population proportion using a normal distribution (usually n is large or the sample size is large).

If you are testing a  single population mean , the distribution for the test is for means :

[latex]\displaystyle\overline{{X}}\text{~}{N}{\left(\mu_{{X}}\text{ , }\frac{{\sigma_{{X}}}}{\sqrt{{n}}}\right)}{\quad\text{or}\quad}{t}_{{{d}{f}}}[/latex]

The population parameter is  μ . The estimated value (point estimate) for μ is [latex]\displaystyle\overline{{x}}[/latex], the sample mean.

If you are testing a  single population proportion , the distribution for the test is for proportions or percentages:

[latex]\displaystyle{P}^{\prime}\text{~}{N}{\left({p}\text{ , }\sqrt{{\frac{{{p}{q}}}{{n}}}}\right)}[/latex]

The population parameter is  p . The estimated value (point estimate) for p is p′ . [latex]\displaystyle{p}\prime=\frac{{x}}{{n}}[/latex] where x is the number of successes and n is the sample size.

Assumptions

When you perform a  hypothesis test of a single population mean μ using a Student’s t -distribution (often called a t-test), there are fundamental assumptions that need to be met in order for the test to work properly. Your data should be a simple random sample that comes from a population that is approximately normally distributed . You use the sample standard deviation to approximate the population standard deviation. (Note that if the sample size is sufficiently large, a t-test will work even if the population is not approximately normally distributed).

When you perform a  hypothesis test of a single population mean μ using a normal distribution (often called a z -test), you take a simple random sample from the population. The population you are testing is normally distributed or your sample size is sufficiently large. You know the value of the population standard deviation which, in reality, is rarely known.

When you perform a  hypothesis test of a single population proportion p , you take a simple random sample from the population. You must meet the conditions for a binomial distribution which are as follows: there are a certain number n of independent trials, the outcomes of any trial are success or failure, and each trial has the same probability of a success p . The shape of the binomial distribution needs to be similar to the shape of the normal distribution. To ensure this, the quantities np  and nq must both be greater than five ( np > 5 and nq > 5). Then the binomial distribution of a sample (estimated) proportion can be approximated by the normal distribution with μ = p and [latex]\displaystyle\sigma=\sqrt{{\frac{{{p}{q}}}{{n}}}}[/latex] . Remember that q = 1 – p .

Concept Review

In a  hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

In every hypothesis test, the outcomes are dependent on a correct interpretation of the data. Incorrect calculations or misunderstood summary statistics can yield errors that affect the results. A  Type I error occurs when a true null hypothesis is rejected. A Type II error occurs when a false null hypothesis is not rejected.

The probabilities of these errors are denoted by the Greek letters  α and β , for a Type I and a Type II error respectively. The power of the test, 1 – β , quantifies the likelihood that a test will yield the correct result of a true alternative hypothesis being accepted. A high power is desirable.

In order for a hypothesis test’s results to be generalized to a population, certain requirements must be satisfied.

When testing for a single population mean:

• A Student’s t -test should be used if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large, with an unknown standard deviation.
• The normal test will work if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large, with a known standard deviation.

When testing a single population proportion use a normal test for a single population proportion if the data comes from a simple, random sample, fill the requirements for a binomial distribution, and the mean number of success and the mean number of failures satisfy the conditions:  np > 5 and nq > n where n is the sample size, p is the probability of a success, and q is the probability of a failure.

Formula Review

H 0 and H a are contradictory.

If there is no given preconceived  α , then use α = 0.05.

Types of Hypothesis Tests

• Single population mean, known population variance (or standard deviation): Normal test .
• Single population mean, unknown population variance (or standard deviation): Student’s t -test .
• Single population proportion: Normal test .
• For a single population mean , we may use a normal distribution with the following mean and standard deviation. Means: [latex]\displaystyle\mu=\mu_{{\overline{{x}}}}{\quad\text{and}\quad}\sigma_{{\overline{{x}}}}=\frac{{\sigma_{{x}}}}{\sqrt{{n}}}[/latex]
• A single population proportion , we may use a normal distribution with the following mean and standard deviation. Proportions: [latex]\displaystyle\mu={p}{\quad\text{and}\quad}\sigma=\sqrt{{\frac{{{p}{q}}}{{n}}}}[/latex].
• OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
• Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
• Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

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10.2: Null and Alternative Hypotheses

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The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.

• The null hypothesis (\(H_{0}\)) is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
• The alternative hypothesis (\(H_{a}\)) is a claim about the population that is contradictory to \(H_{0}\) and what we conclude when we reject \(H_{0}\).

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data. After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject \(H_{0}\)" if the sample information favors the alternative hypothesis or "do not reject \(H_{0}\)" or "decline to reject \(H_{0}\)" if the sample information is insufficient to reject the null hypothesis.

\(H_{0}\) always has a symbol with an equal in it. \(H_{a}\) never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example \(\PageIndex{1}\)

• \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
• \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)

Exercise \(\PageIndex{1}\)

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

• \(H_{0}\): The drug reduces cholesterol by 25%. \(p = 0.25\)
• \(H_{a}\): The drug does not reduce cholesterol by 25%. \(p \neq 0.25\)

Example \(\PageIndex{2}\)

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

• \(H_{0}: \mu = 2.0\)
• \(H_{a}: \mu \neq 2.0\)

Exercise \(\PageIndex{2}\)

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol \((=, \neq, \geq, <, \leq, >)\) for the null and alternative hypotheses.

• \(H_{0}: \mu \  \_ \  66\)
• \(H_{a}: \mu \  \_ \  66\)
• \(H_{0}: \mu = 66\)
• \(H_{a}: \mu \neq 66\)

Example \(\PageIndex{3}\)

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

• \(H_{0}: \mu \geq 5\)
• \(H_{a}: \mu < 5\)

Exercise \(\PageIndex{3}\)

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• \(H_{0}: \mu \  \_ \  45\)
• \(H_{a}: \mu \  \_ \  45\)
• \(H_{0}: \mu \geq 45\)
• \(H_{a}: \mu < 45\)

Example \(\PageIndex{4}\)

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

• \(H_{0}: p \leq 0.066\)
• \(H_{a}: p > 0.066\)

Exercise \(\PageIndex{4}\)

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (\(=, \neq, \geq, <, \leq, >\)) for the null and alternative hypotheses.

• \(H_{0}: p \  \_ \  0.40\)
• \(H_{a}: p \  \_ \  0.40\)
• \(H_{0}: p = 0.40\)
• \(H_{a}: p > 0.40\)

COLLABORATIVE EXERCISE

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

Chapter Review

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:

• Evaluate the null hypothesis , typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or} \geq)\)
• Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
• If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
• Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

\(H_{0}\) and \(H_{a}\) are contradictory.

• If \(\alpha \leq p\)-value, then do not reject \(H_{0}\).
• If\(\alpha > p\)-value, then reject \(H_{0}\).

\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .

Contributors

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

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Hypothesis: An Introduction

You must have heard about hypotheses that led to several achievements in scientific inventions. A hypothesis is a milestone in any research; it is the point of the research where we propose an analysis. The hypothesis of any research corresponds to the assumptions we conclude from the evidence gathered. The hypothesis consists of the points or the concepts that are proven successful. Now, let us learn about what exactly a hypothesis means and the type of hypothesis along with examples.

What is Hypothesis?

An assumption that is made based on some limited evidence collected is known as a hypothesis. It is the beginning point of study that translates research questions into predictions that might or might not be true. It depends on the variables and population used, also the relation between the variables. The hypothesis used to test the relationship between two or multiple variables is known as the research hypothesis.

Hypothesis Properties

The properties of the hypothesis are as follows:

It should be empirically tested irrespective of being right or wrong.

It should establish the relationship between the variables that are considered.

It must be specific, clear, and precise.

It should possess the scope for future studies and be capable of conducting more tests.

It should be capable of testing it in a reasonable time and it must be reliable.

Types of Hypothesis

Hypothesis can be classified as follows:

Null Hypothesis

Simple hypothesis

Directional hypothesis

Complex hypothesis

Non-directional hypothesis

Causal and associative hypothesis

It states that one variable doesn't affect the other variables being studied. A null hypothesis asserts that two factors or groups are independent of each other and that some traits of a population or process are identical. To contradict or invalidate the null hypothesis, we must assess the likelihood of the alternative hypothesis in addition to the null hypothesis.

Simple Hypothesis

There are two types of variables i.e, dependent and independent variables. A simple hypothesis shows the relationship between the dependent and independent variables. For example, if you pump petrol into your bike, you can go for long rides. Here bike is the dependent variable and petrol is the independent one.

Directional Hypothesis

A directional hypothesis is a researcher's prediction of a positive or negative change, relationship, or difference between two variables in a population. This statement is often supported by prior research, a widely established theory, considerable experience, or relevant literature.

For example, students who do proper revision and assignments could score more marks than the students who skipped. Here, we already know the process and its impact on the outcome. This is what we call a directional hypothesis.

Complex Hypothesis

The complex hypothesis shows the relationship that comes between two or more dependent and independent variables. For example, if you pump petrol in your bike, you can go for long rides, also you become an expert in riding a bike, you explore more places and come across new things.

Non-directional Hypothesis

There is no theory for this kind. Unlike the directional hypothesis, there are no predictions. We can say there is a relation between the variables but prediction and nature are unknown.

Causal and Associative Hypothesis

If there is a change in one variable and as a result, it affects the other variable, then we say it is associative. Meanwhile, the causal hypothesis comes into play when the cause and effect interaction occurs between two or more variables.

Sources of Hypothesis

The major sources of hypothesis are:

Scientific theories

Personal experience and conclusion arrived

Studies that underwent in the past

The resemblances between the phenomena, that is the pattern observed in common

Common thoughts and thinking

Functions of Hypothesis

The functions of hypothesis are as follows:

It tells us the specific aspects of studies we investigate. It provides study with focus.

The cnstruction of the hypothesis led to objectivity in the investigation

It helps to formulate the theory for the research work and sort out what is wrong and right.

It filters out the data that have to be collected for the work.

Hypothesis Examples

Some examples of hypotheses are as follows

Consumption of tobacco led to cancer, which is an example of a simple hypothesis.

If a person does work out daily, his/her skin, body, and mind remain healthy and fresh, which is an example of a directional hypothesis.

If you consume tobacco it not only causes cancer, but also affects your brain, turns your lips black, etc.

Role of Hypothesis in the Scientific Method

Experimental designing

Predicting results

Background research

Question formation

Data collection

Verification of results

Concluding the experiment

Being a future reference for the further studies

Role of hypothesis in the scientific method

In conclusion, it can be understood that a hypothesis is an assumption that researchers make on the basis of the limited evidence collected. It is the starting point of study that translates research questions into predictions. The various types of hypotheses include Null Hypothesis, Simple hypothesis, Directional hypothesis, Complex hypothesis, Non-directional hypothesis, and Causal and associative hypothesis. We proceed with our research or experiments according to the hypothesis we design.

FAQs on Hypothesis

1. Why is a hypothesis important?

Hypothesis plays an important role in any research project; it's a stepping stone to proving a theory. Hypothesis serves in establishing a connection to the underlying theory and particular research subject. It helps in data processing and evaluates the reliability and validity of the study. It offers a foundation or supporting evidence to demonstrate the accuracy of the study. A hypothesis allows researchers not only to get a relationship between variables, but also to predict a relationship based on theoretical guidelines and/or empirical proof.

2. How do I write a hypothesis?

Writing a good hypothesis starts before you even begin to type. Like several tasks, preparation is vital, thus you begin first by conducting analysis yourself, and reading all you can regarding the subject that you decide to do research on. From there, you’ll gain the information you need to know , where your focus within the subject will lie. Keep in mind that a hypothesis may be a prediction of the relationship that exists between 2 or more variables. The hypothesis should be straightforward and concise , the result should be predictable , clear and with no assumptions about the reader's knowledge.

3. What are a few examples of hypotheses?

Consumption of drugs leads to depression is an example of a simple hypothesis. If a person has a proper diet plan, his/her skin, body, and mind remain healthy and fresh. This is an example of a directional hypothesis. If you consume drugs it not only causes depression, but also affects your brain, leads to addiction, etc. If you pump petrol in your bike, you can go for long rides, also you become an expert in riding a bike, you explore more places and come across new things.

Your Article Library

Hypotheses: meaning, types and sources | social research.

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After reading this article you will learn about:- 1. Meaning of Hypotheses 2. Types of Hypotheses 3. Sources.

Meaning of Hypotheses:

Once the problem to be answered in the course of research is finally instituted, the researcher may, if feasible proceed to formulate tentative solutions or answers to it. These proposed solutions or explanations are called hypotheses which the researcher is obliged to test on the basis of fact already known or which can be made known.

If such answers are not formulated, even implicitly, the researcher cannot effectively go ahead with the investigation of his problem because, in the absence of direction which hypotheses typically provide, the researcher would not know what facts to look for and what relation or order to search for amongst them.

The hypotheses guide the researcher through a bewildering Jungle of facts to see and select only those that are relevant to the problem or difficulty he proposes to solve. Collection of facts merely for the sake of collecting them will yield no fruits.

To be fruitful, one should collect such facts as are for or against some point of view or proposition. Such a point of view or proposition is the hypothesis. The task of the inquiry or research is to test its accord with facts.

Lundberg aptly observes, “The only difference between gathering data without a hypothesis and gathering them with one, is that in the latter case, we deliberately recognize the limitations of our senses and attempt to reduce their fallibility by limiting our field of investigation so as to prevent greater concentration for attention on particular aspects which past experience leads us to believe are irrelevant as insignificant for our purpose.”

Simply stated, an hypothesis helps us see and appreciate:

(1) The kind of data that need be collected in order to answer the research question and

(2) The way in which they should be organized most efficiently and meaningfully.

Webster’s New International Dictionary of English Language, 1956, defines the term “hypothesis” as “proposition, condition or principle which is assumed, perhaps without belief, in order to draw out its logical consequences and by this method to test its accord with facts which are known or may be determined.”

Cohen and Nagel bring out the value of hypothesis thus:

“We cannot take a single step forward in any inquiry unless we begin with a suggested explanation or solution of the difficulty which originated it. Such tentative explanations are suggested to us by something in the subject-matter and by our previous knowledge. When they are formulated as propositions, they are called hypotheses.”

Once the scientist knows what his question (problem) is, he can make a guess, or a number of guesses as to its possible answers. According to Werkmeister, “The guesses he makes are the hypotheses which either solve the problems or guide him in further investigation.”

It is clear now that a hypothesis is a provisional formulation; a tentative solution of the problem posed by the scientist. ‘The scientist starts by assuming that the solution is true without, of course, personally believing in its truthfulness.

Based on this assumption, the scientist anticipates that certain logical consequences will be observed on the plane of observable events or objects. Whether these anticipations or expectations really materialize is the test of the hypothesis, its proof or disproof.

If the hypothesis is proved, the problem of which it was a tentative solution is answered. If it is not proved, i.e., falsified owing to non-support of proof, alternative hypotheses may be formulated by the researcher. An hypothesis thus stands somewhere at the midpoint of research; from here, one can look back to the problem as also look forward to data.

The hypothesis may be stated in the form of a principle, that is, the tentative explanation or solution to the questions how? Or why? May be presented in the form of a principle that X varies with Y. The inquiry established that an empirical referent of X varies with the empirical referent of Y in a concrete observable situation (i.e., the hypothesis is proved) then the question is answered.

Hypotheses, however, may take other forms, such as intelligent guesses, conditions, propositions deduced from theories, observations and findings of other scholars etc.

Proceeding on the basis of hypotheses has been the slow and hard way of science. While some scientific conclusions and premises seem to have arisen in the mind of the investigator as if by flashes of insight, in a majority of cases the process of discovery has been a slower one.

“The scientific imagination devises a possible solution, a hypothesis and the investigator proceeds to test it. He makes intellectual keys and then tries to see whether they fit the lock. If the hypothesis does not fit, it is rejected and another is made. The scientific workshop is full of discarded keys.”

Cohen and Nagel’s statement that one cannot take a single step forward in any inquiry without a hypothesis may well be a correct statement of the value of hypothesis in scientific investigation generally, but it hardly does justice to an important function of scientific research, i.e., the “formulation hypotheses.”

Hypotheses are not given to us readymade. Of course in fields with a highly developed theoretic structure it is reasonable to expect that most empirical studies will have at least some sharp hypotheses to be tested.

This is so especially in social sciences where there has not yet evolved a highly developed theoretic system in many areas of its subject-matter which can afford fruitful bases for hypothesis-formulation.

As such, attempts to force research into this mould are either deceitful or stultifying and hypotheses are likely to be no more than hunches as to where to look for sharper hypotheses in which case the study may be described as an intelligent fishing trip.

As a result, in the social sciences at least, a considerable quantum of research endeavour is directed understandably toward ‘making’ hypotheses rather than at testing them.

A very important type of research has as its goal, the formulation of significant hypotheses relating to a particular problem. Hence, we will do well to bear in mind that research can begin with well formulated hypotheses or it may come out with hypotheses as its end product.

Let us recapitulate the role of hypotheses for research in the words of Chaddock who summarizes it thus:

“(A hypothesis) in the scientific sense is … an explanation held after careful canvass of known facts, in full knowledge of other explanations that have been offered and with a mind open to change of view, if the facts disclosed by the inquiry warrant a different explanation. Another hypothesis as an explanation is proposed including investigation all available and pertinent data either to prove or disprove the hypothesis…. (A hypothesis) gives point to the inquiry and if founded on sufficient previous knowledge, guides the line of investigation. Without it much useless data maybe collected in the hope that nothing essential will be omitted or important data may be omitted which could have been easily included if the purpose of inquiry had been more clearly defined” and thus hypotheses are likely to be no more than hunches as to where to look for pertinent data.

An hypothesis is therefore held with the definite purpose of including in the investigating all available and pertinent data either to prove or disprove the hypothesis.

Types of Hypotheses :

There are many kinds of hypotheses the social researcher has to be working with. One type of hypotheses asserts that something is the case in a given instance; that a particular object, person or situation has a particular characteristic.

Another type of hypotheses deals with the frequency of occurrences or of association among variables; this type of hypotheses may state that X is associated with y a certain (Y) proportion of times, e.g., that urbanism tends to be accompanied by mental disease or that something is greater or lesser than some thing else in a specific setting.

Yet another type of hypotheses assert that a particular characteristic is one of the factors which determine another characteristic, i.e., S is the producer of Y (product). Hypotheses of this type are known as causal hypotheses.

Hypotheses can be classified in a variety of ways. But classification of hypotheses on the basis of their levels of abstraction is regarded as especially fruitful. Goode arid Hatt have identified three differential levels of abstraction reached by hypotheses. We shall here be starting from the lowest level of abstraction and go over to the higher ones.

(a) At the lowest level of abstraction are the hypotheses which state existence of certain empirical uniformities. Many types of such empirical uniformities are common in social research, for instance, it may be hypothesized with reference to India that in the cities men will get married between the age of 22 and 24 years.

Or, the hypotheses of this type may state that certain behaviour pattern may be expected in a specified community. Thus, hypotheses of this type frequently seem to invite scientific verification of what are called “common sense propositions,” indeed without much justification.

It has often been said by way of a criticism of such hypotheses that these are not useful in as much as they merely state what everyone seems to know already. Such an objection may however be overruled by pointing out that what everyone knows is not often put in precise terms nor is it adequately integrated into the framework of science.

Secondly, what everyone knows may well be mistaken. To put common sense ideas into precisely defined concepts and subject the proposition to test is an important task of science.

This is particularly applicable to social sciences which are at present in their earlier stage of development. Not only social science but all sciences have found such commonsense knowledge a fruitful item of study. It was commonsense knowledge in the olden days that sun revolved round the earth. But this and many other beliefs based on commonsense have been exploded by patient, plodding, empirical checking of facts.

The monumental work, The American Soldier by Stouffer and associates was criticized in certain quarters, for it was according to them mere elaboration of the obvious. But to this study goes the credit of exploding some of the commonsense propositions and shocking many people who had never thought that what was so obvious a commonsense could be totally wrong or unfounded in fact.

(b) At a relatively higher level of abstraction are hypotheses concerned with complex ‘ideal types.’ These hypotheses aim at testing whether logically derived relationship between empirical uniformities obtain. This level of hypothesizing moves beyond the level of anticipating a simple empirical uniformity by visualizing a complex referent in society.

Such hypotheses are indeed purposeful distortions of empirical exactness and owing to their remoteness from empirical reality, these constructs are termed ‘ideal types.’ The function of such hypotheses is to create tools and formulate problems for further research in complex areas of investigation.

An example of one such hypothesis may be cited. Analyses of minority groups brought to light empirical uniformities in the behaviour of members of a wide variety of minorities. It was subsequently hypothesized that these uniformities pointed to an ‘ideal type’.

First called by H. A. Miller the ‘oppression psychosis,’ this ideal-typical construction was subsequently modified as the ‘Marginal man’ by E. Stone Quist and associates. Empirical evidence marshaled later substantiated the hypothesis, and so the concept of marginality (marginal man) has very much come to stay as a theoretic construct in social sciences, and as part of sociological theory.

(c) We now come to the class of hypotheses at the highest level of abstraction. This category of hypotheses is concerned with the relation obtaining amongst analytic variables. Such hypotheses are statements about, how one property affects other, e.g., a statement of relationship between education and social mobility or between wealth and fertility.

It is easy to see that this level of hypothesizing is not only more abstract compared to others; it is also the most sophisticated and vastly flexible mode of formulation.

This does not mean, however, that this type of hypotheses is ‘superior’ or ‘better’ than the other types. Each type of hypotheses has its own importance depending in turn upon the nature of investigation and the level of development the subject has achieved.

The sophisticated hypotheses of analytical variables owe much of their existence to the building-blocks contributed by the hypotheses existed at the lower orders of abstraction.

Sources of Hypotheses :

Hypotheses may be developed from a variety of sources. We examine here, some of the major ones.

(1) The history of sciences provides an eloquent testimony to the fact that personal and idiosyncratic experiences of the scientist contribute a great deal to type and form of questions he may ask, as also to the kinds of tentative answers to these questions (hypotheses) that he might provide. Some scientists may perceive an interesting pattern in what may merely, seem a jumble of facts to the common man.

The history of science is full of instances of discoveries made just because the ‘right’ person happened to make the ‘right’ observation owing to his characteristic life-history and exposure to a unique mosaic of events. Personal life-histories are a factor in determining the kinds of a person’s perception and conception and this factor may in turn direct him to certain hypotheses quite readily.

An illustration of such individual perspectives in social sciences may be seen in the work of Thorstein Veblen whom Merton describes as a sociologist with a keen eye for the unusual and paradoxical.

A product of an isolated Norwegian community, Veblen lived at a time when the capitalistic system was barely subjected to any criticism. His own community background was replete with derivational experiences attributable to the capitalist system.

Veblen being an outsider, was able to look at the capitalist economic system more objectively and with dispassionate detachment. Veblen was thus strategically positioned to attack the fundamental concepts and postulates of classical economics.

He was an alien who could bring a different experience to bear upon the economic world. Consequently, he made penetrating analyses of society and economy which have ever since profoundly influenced social science.

(2) Analogies are often a fountainhead of valuable hypotheses. Students of sociology and political science in the course of their studies would have come across analogies wherein society and state are compared to a biological organism, the natural law to the social law, thermodynamics to social dynamics, etc. such analogies, notwithstanding the fact that analogies as a class suffer from serious limitations, do provide certain fruitful insight which formulated as hypotheses stimulate and guide inquiries.

One of the recent orientations to hypotheses formulation is provided by cybernetics, the communication models now so well entrenched in the social science testify to the importance of analogies as a source of fruitful hypotheses. The hypothesis that similar human types or activities may be found occupying the same territory was derived from plant ecology.

When the hypothesis was borne out by observations in society, the concept of segregation as it is called in plant ecology was admitted into sociology. It has now become an important idea in sociological theory. Such examples may be multiplied.

In sum, analogy may be very suggestive but care needs to be taken not to accept models from other disciplines without a careful scrutiny of the concepts in terms of their applicability to the new frame of reference in which they are proposed to be deployed.

(3) Hypotheses may rest also on the findings of other studies. The researcher on the basis of the findings of other studies may hypothesize that similar relationship between specified variables will hold good in the present study too. This is a common way of researchers who design their study with a view of replicating another study conducted in a different concrete context or setting.

It was said that many a study in social science is exploratory in character, i.e., they start without explicit hypotheses, the findings of such studies may be formulated as hypotheses for more structured investigations directed at testing certain hypotheses.

(4) An hypothesis may stem from a body of theory which may afford by way of logical deduction, the prediction that if certain conditions are present, certain results will follow. Theory represents what is known; logical deductions from this constitute the hypotheses which must be true if the theory was true.

Dubin aptly remarks, “Hypothesis is the feature of the theoretical model closest to the ‘things observable’ that the theory is trying to model.” Merton illustrates this function of theory with his customary felicity. Basing his deductions on Durham’s theoretic orientation, Merton shows how hypotheses may be derived as deductions from theoretic system.

(1) Social cohesion provides psychic support to group members subjected to acute stresses and anxieties.

(2) Suicide rates are functions of unrelieved anxieties to which persons are subjected.

(3) Catholics have greater social cohesion than protestants.

(4) Therefore, lower suicide rates should be expected among Catholics than among protestants.

If theories purport to model the empirical world, then there must be a linkage between the two. This linkage is to be found in the hypotheses that mirror the propositions of the theoretical model.

It may thus appear that the points of departure vis-a-vis hypotheses-construction are in two opposite directions:

(a) Conclusions based on concrete or empirical observations lead through the process of induction to more abstract hypotheses and

(b) The theoretical model through the process of logical deduction affords more concrete hypotheses.

It may be well to bear in mind, however, that although these two approaches to hypotheses formulation seem diametrically opposed to each other, the two points of departure, i.e., empirical, observations and the theoretical structure, represent the poles of a continuum and hypotheses lie somewhere in the middle of this continuum.

Both these approaches to hypotheses-construction have proved their worth. The Chicago School in American sociology represents a strong empirical orientation whereas the Mertonian and Parsonian approach is typified by a stress on theoretic models as initial bases for hypotheses-construction. Hence hypotheses can be deductively derived from theoretic models.

(5) It is worthy of note that value-orientation of the culture in which a science develops may furnish many of its basic hypotheses.

That certain hypotheses and not others capture the attention of scientists or occur to them in particular societies or culture may well be attributed to the cultural emphases. Goode and Hatt contend that the American emphasis upon personal happiness had had considerable effect upon social science in that country.

The phenomenon of personal happiness has been studied in great detail. In every branch of social science, the problem of personal happiness came to occupy a position meriting central focus. Happiness has been correlated with income, education, occupation, social class, and so on. It is evident that the culture emphasis on happiness has been productive of a very wide range of hypotheses for the American social science.

Folk-wisdom prevalent in a culture may also serve as source of hypotheses. The sum and substance of the discussion is aptly reflected in Larrabee’s remark that the ideal source of fruitful and relevant hypotheses is a fusion of two elements: past experience and imagination in the disciplined mind of the scientist.

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• Role of Hypothesis in Social Research
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Research , Social Research , Hypotheses

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• Scientific Methods

What is Hypothesis?

We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.

A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

• The hypothesis should be clear and precise to consider it to be reliable.
• If the hypothesis is a relational hypothesis, then it should be stating the relationship between variables.
• The hypothesis must be specific and should have scope for conducting more tests.
• The way of explanation of the hypothesis must be very simple and it should also be understood that the simplicity of the hypothesis is not related to its significance.

Sources of Hypothesis

Following are the sources of hypothesis:

• The resemblance between the phenomenon.
• Observations from past studies, present-day experiences and from the competitors.
• Scientific theories.
• General patterns that influence the thinking process of people.

Types of Hypothesis

There are six forms of hypothesis and they are:

• Simple hypothesis
• Complex hypothesis
• Directional hypothesis
• Non-directional hypothesis
• Null hypothesis
• Associative and casual hypothesis

Simple Hypothesis

It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.

Complex Hypothesis

It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.

Directional Hypothesis

It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.

Non-directional Hypothesis

It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.

Null Hypothesis

It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.

Associative and Causal Hypothesis

Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.

Examples of Hypothesis

Following are the examples of hypotheses based on their types:

• Consumption of sugary drinks every day leads to obesity is an example of a simple hypothesis.
• All lilies have the same number of petals is an example of a null hypothesis.
• If a person gets 7 hours of sleep, then he will feel less fatigue than if he sleeps less. It is an example of a directional hypothesis.

Functions of Hypothesis

Following are the functions performed by the hypothesis:

• Hypothesis helps in making an observation and experiments possible.
• It becomes the start point for the investigation.
• Hypothesis helps in verifying the observations.
• It helps in directing the inquiries in the right direction.

How will Hypothesis help in the Scientific Method?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

• Formation of question
• Doing background research
• Creation of hypothesis
• Designing an experiment
• Collection of data
• Result analysis
• Summarizing the experiment
• Communicating the results

Frequently Asked Questions – FAQs

What is hypothesis.

A hypothesis is an assumption made based on some evidence.

Give an example of simple hypothesis?

What are the types of hypothesis.

Types of hypothesis are:

• Associative and Casual hypothesis

State true or false: Hypothesis is the initial point of any investigation that translates the research questions into a prediction.

Define complex hypothesis..

A complex hypothesis shows the relationship between two or more dependent variables and two or more independent variables.

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| Bioinformatics |

• Basics Definitions

Bioinformatics

Sunday, April 16, 2017

Mcqs 2 on "hypothesis testing" statistics.

• All of the above
• Level of confidence
• Level of significance
• Power of the test
• Difficult to tell
• Critical region
• Critical value
• Acceptance region
• Significant region
• Right tailed
• Left tailed
• Null hypothesis
• Alternative hypothesis
• None of these
• Composite hypotheses
• Left-tailed test
• Right-tailed test
• Two-tailed test
• Right one-sided test
• Left one-sided test
• Two-sided test
• Neither (a), (b) and (c)
• Test-statistic
• Population statistic
• Both of these
• None of the above
• 0 to ∞
• -∞ to +∞

1.. 2.. 3..

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