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## What Is a T-Test?

Understanding the t-test, using a t-test, which t-test to use.

- T-Test FAQs
- Fundamental Analysis

## T-Test: What It Is With Multiple Formulas and When To Use Them

Read how this calculation can be used for hypothesis testing in statistics

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

A t-test is an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related. T-tests are used when the data sets follow a normal distribution and have unknown variances, like the data set recorded from flipping a coin 100 times.

The t-test is a test used for hypothesis testing in statistics and uses the t-statistic, the t-distribution values, and the degrees of freedom to determine statistical significance.

## Key Takeaways

- A t-test is an inferential statistic used to determine if there is a statistically significant difference between the means of two variables.
- The t-test is a test used for hypothesis testing in statistics.
- Calculating a t-test requires three fundamental data values including the difference between the mean values from each data set, the standard deviation of each group, and the number of data values.
- T-tests can be dependent or independent.

Investopedia / Sabrina Jiang

A t-test compares the average values of two data sets and determines if they came from the same population. In the above examples, a sample of students from class A and a sample of students from class B would not likely have the same mean and standard deviation. Similarly, samples taken from the placebo-fed control group and those taken from the drug prescribed group should have a slightly different mean and standard deviation.

Mathematically, the t-test takes a sample from each of the two sets and establishes the problem statement. It assumes a null hypothesis that the two means are equal.

Using the formulas, values are calculated and compared against the standard values. The assumed null hypothesis is accepted or rejected accordingly. If the null hypothesis qualifies to be rejected, it indicates that data readings are strong and are probably not due to chance.

The t-test is just one of many tests used for this purpose. Statisticians use additional tests other than the t-test to examine more variables and larger sample sizes. For a large sample size, statisticians use a z-test . Other testing options include the chi-square test and the f-test.

Consider that a drug manufacturer tests a new medicine. Following standard procedure, the drug is given to one group of patients and a placebo to another group called the control group. The placebo is a substance with no therapeutic value and serves as a benchmark to measure how the other group, administered the actual drug, responds.

After the drug trial, the members of the placebo-fed control group reported an increase in average life expectancy of three years, while the members of the group who are prescribed the new drug reported an increase in average life expectancy of four years.

Initial observation indicates that the drug is working. However, it is also possible that the observation may be due to chance. A t-test can be used to determine if the results are correct and applicable to the entire population.

Four assumptions are made while using a t-test. The data collected must follow a continuous or ordinal scale, such as the scores for an IQ test, the data is collected from a randomly selected portion of the total population, the data will result in a normal distribution of a bell-shaped curve, and equal or homogenous variance exists when the standard variations are equal.

## T-Test Formula

Calculating a t-test requires three fundamental data values. They include the difference between the mean values from each data set, or the mean difference, the standard deviation of each group, and the number of data values of each group.

This comparison helps to determine the effect of chance on the difference, and whether the difference is outside that chance range. The t-test questions whether the difference between the groups represents a true difference in the study or merely a random difference.

The t-test produces two values as its output: t-value and degrees of freedom . The t-value, or t-score, is a ratio of the difference between the mean of the two sample sets and the variation that exists within the sample sets.

The numerator value is the difference between the mean of the two sample sets. The denominator is the variation that exists within the sample sets and is a measurement of the dispersion or variability.

This calculated t-value is then compared against a value obtained from a critical value table called the T-distribution table. Higher values of the t-score indicate that a large difference exists between the two sample sets. The smaller the t-value, the more similarity exists between the two sample sets.

A large t-score, or t-value, indicates that the groups are different while a small t-score indicates that the groups are similar.

Degrees of freedom refer to the values in a study that has the freedom to vary and are essential for assessing the importance and the validity of the null hypothesis. Computation of these values usually depends upon the number of data records available in the sample set.

## Paired Sample T-Test

The correlated t-test, or paired t-test, is a dependent type of test and is performed when the samples consist of matched pairs of similar units, or when there are cases of repeated measures. For example, there may be instances where the same patients are repeatedly tested before and after receiving a particular treatment. Each patient is being used as a control sample against themselves.

This method also applies to cases where the samples are related or have matching characteristics, like a comparative analysis involving children, parents, or siblings.

The formula for computing the t-value and degrees of freedom for a paired t-test is:

T = mean 1 − mean 2 s ( diff ) ( n ) where: mean 1 and mean 2 = The average values of each of the sample sets s ( diff ) = The standard deviation of the differences of the paired data values n = The sample size (the number of paired differences) n − 1 = The degrees of freedom \begin{aligned}&T=\frac{\textit{mean}1 - \textit{mean}2}{\frac{s(\text{diff})}{\sqrt{(n)}}}\\&\textbf{where:}\\&\textit{mean}1\text{ and }\textit{mean}2=\text{The average values of each of the sample sets}\\&s(\text{diff})=\text{The standard deviation of the differences of the paired data values}\\&n=\text{The sample size (the number of paired differences)}\\&n-1=\text{The degrees of freedom}\end{aligned} T = ( n ) s ( diff ) mean 1 − mean 2 where: mean 1 and mean 2 = The average values of each of the sample sets s ( diff ) = The standard deviation of the differences of the paired data values n = The sample size (the number of paired differences) n − 1 = The degrees of freedom

## Equal Variance or Pooled T-Test

The equal variance t-test is an independent t-test and is used when the number of samples in each group is the same, or the variance of the two data sets is similar.

The formula used for calculating t-value and degrees of freedom for equal variance t-test is:

T-value = m e a n 1 − m e a n 2 ( n 1 − 1 ) × v a r 1 2 + ( n 2 − 1 ) × v a r 2 2 n 1 + n 2 − 2 × 1 n 1 + 1 n 2 where: m e a n 1 and m e a n 2 = Average values of each of the sample sets v a r 1 and v a r 2 = Variance of each of the sample sets n 1 and n 2 = Number of records in each sample set \begin{aligned}&\text{T-value} = \frac{ mean1 - mean2 }{\frac {(n1 - 1) \times var1^2 + (n2 - 1) \times var2^2 }{ n1 +n2 - 2}\times \sqrt{ \frac{1}{n1} + \frac{1}{n2}} } \\&\textbf{where:}\\&mean1 \text{ and } mean2 = \text{Average values of each} \\&\text{of the sample sets}\\&var1 \text{ and } var2 = \text{Variance of each of the sample sets}\\&n1 \text{ and } n2 = \text{Number of records in each sample set} \end{aligned} T-value = n 1 + n 2 − 2 ( n 1 − 1 ) × v a r 1 2 + ( n 2 − 1 ) × v a r 2 2 × n 1 1 + n 2 1 m e an 1 − m e an 2 where: m e an 1 and m e an 2 = Average values of each of the sample sets v a r 1 and v a r 2 = Variance of each of the sample sets n 1 and n 2 = Number of records in each sample set

Degrees of Freedom = n 1 + n 2 − 2 where: n 1 and n 2 = Number of records in each sample set \begin{aligned} &\text{Degrees of Freedom} = n1 + n2 - 2 \\ &\textbf{where:}\\ &n1 \text{ and } n2 = \text{Number of records in each sample set} \\ \end{aligned} Degrees of Freedom = n 1 + n 2 − 2 where: n 1 and n 2 = Number of records in each sample set

## Unequal Variance T-Test

The unequal variance t-test is an independent t-test and is used when the number of samples in each group is different, and the variance of the two data sets is also different. This test is also called Welch's t-test.

The formula used for calculating t-value and degrees of freedom for an unequal variance t-test is:

T-value = m e a n 1 − m e a n 2 ( v a r 1 n 1 + v a r 2 n 2 ) where: m e a n 1 and m e a n 2 = Average values of each of the sample sets v a r 1 and v a r 2 = Variance of each of the sample sets n 1 and n 2 = Number of records in each sample set \begin{aligned}&\text{T-value}=\frac{mean1-mean2}{\sqrt{\bigg(\frac{var1}{n1}{+\frac{var2}{n2}\bigg)}}}\\&\textbf{where:}\\&mean1 \text{ and } mean2 = \text{Average values of each} \\&\text{of the sample sets} \\&var1 \text{ and } var2 = \text{Variance of each of the sample sets} \\&n1 \text{ and } n2 = \text{Number of records in each sample set} \end{aligned} T-value = ( n 1 v a r 1 + n 2 v a r 2 ) m e an 1 − m e an 2 where: m e an 1 and m e an 2 = Average values of each of the sample sets v a r 1 and v a r 2 = Variance of each of the sample sets n 1 and n 2 = Number of records in each sample set

Degrees of Freedom = ( v a r 1 2 n 1 + v a r 2 2 n 2 ) 2 ( v a r 1 2 n 1 ) 2 n 1 − 1 + ( v a r 2 2 n 2 ) 2 n 2 − 1 where: v a r 1 and v a r 2 = Variance of each of the sample sets n 1 and n 2 = Number of records in each sample set \begin{aligned} &\text{Degrees of Freedom} = \frac{ \left ( \frac{ var1^2 }{ n1 } + \frac{ var2^2 }{ n2 } \right )^2 }{ \frac{ \left ( \frac{ var1^2 }{ n1 } \right )^2 }{ n1 - 1 } + \frac{ \left ( \frac{ var2^2 }{ n2 } \right )^2 }{ n2 - 1}} \\ &\textbf{where:}\\ &var1 \text{ and } var2 = \text{Variance of each of the sample sets} \\ &n1 \text{ and } n2 = \text{Number of records in each sample set} \\ \end{aligned} Degrees of Freedom = n 1 − 1 ( n 1 v a r 1 2 ) 2 + n 2 − 1 ( n 2 v a r 2 2 ) 2 ( n 1 v a r 1 2 + n 2 v a r 2 2 ) 2 where: v a r 1 and v a r 2 = Variance of each of the sample sets n 1 and n 2 = Number of records in each sample set

The following flowchart can be used to determine which t-test to use based on the characteristics of the sample sets. The key items to consider include the similarity of the sample records, the number of data records in each sample set, and the variance of each sample set.

Image by Julie Bang Â© Investopedia 2019

## Example of an Unequal Variance T-Test

Assume that the diagonal measurement of paintings received in an art gallery is taken. One group of samples includes 10 paintings, while the other includes 20 paintings. The data sets, with the corresponding mean and variance values, are as follows:

Though the mean of Set 2 is higher than that of Set 1, we cannot conclude that the population corresponding to Set 2 has a higher mean than the population corresponding to Set 1.

Is the difference from 19.4 to 21.6 due to chance alone, or do differences exist in the overall populations of all the paintings received in the art gallery? We establish the problem by assuming the null hypothesis that the mean is the same between the two sample sets and conduct a t-test to test if the hypothesis is plausible.

Since the number of data records is different (n1 = 10 and n2 = 20) and the variance is also different, the t-value and degrees of freedom are computed for the above data set using the formula mentioned in the Unequal Variance T-Test section.

The t-value is -2.24787. Since the minus sign can be ignored when comparing the two t-values, the computed value is 2.24787.

The degrees of freedom value is 24.38 and is reduced to 24, owing to the formula definition requiring rounding down of the value to the least possible integer value.

One can specify a level of probability (alpha level, level of significance, p ) as a criterion for acceptance. In most cases, a 5% value can be assumed.

Using the degree of freedom value as 24 and a 5% level of significance, a look at the t-value distribution table gives a value of 2.064. Comparing this value against the computed value of 2.247 indicates that the calculated t-value is greater than the table value at a significance level of 5%. Therefore, it is safe to reject the null hypothesis that there is no difference between means. The population set has intrinsic differences, and they are not by chance.

## How Is the T-Distribution Table Used?

The T-Distribution Table is available in one-tail and two-tails formats. The former is used for assessing cases that have a fixed value or range with a clear direction, either positive or negative. For instance, what is the probability of the output value remaining below -3, or getting more than seven when rolling a pair of dice? The latter is used for range-bound analysis, such as asking if the coordinates fall between -2 and +2.

## What Is an Independent T-Test?

The samples of independent t-tests are selected independent of each other where the data sets in the two groups don’t refer to the same values. They may include a group of 100 randomly unrelated patients split into two groups of 50 patients each. One of the groups becomes the control group and is administered a placebo, while the other group receives a prescribed treatment. This constitutes two independent sample groups that are unpaired and unrelated to each other.

## What Does a T-Test Explain and How Are They Used?

A t-test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment has an effect on the population of interest, or whether two groups are different from one another.

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## Try Qualtrics for free

An introduction to t-test theory for surveys.

8 min read What are t-tests, when should you use them, and what are their strengths and weaknesses for analyzing survey data?

## What is a t-test?

The t-test, also known as t-statistic or sometimes t-distribution, is a popular statistical tool used to test differences between the means (averages) of two groups, or the difference between one group’s mean and a standard value. Running a t-test helps you to understand whether the differences are statistically significant (i.e. they didn’t just happen by a fluke).

For example, let’s say you surveyed two sample groups of 500 customers in two different cities about their experiences at your stores. Group A in Los Angeles gave you on average 8 out of 10 for customer service, while Group B in Boston gave you an average score of 5 out of 10. Was your customer service really better in LA, or was it just chance that your LA sample group happened to contain a lot of customers who had positive experiences?

T-tests give you an answer to that question. They tell you what the probability is that the differences you found were down to chance. If that probability is very small, then you can be confident that the difference is meaningful (or statistically significant).

In a t-test, you start with a null hypothesis – an assumption that the two populations are the same and there is no meaningful difference between them. The t-test will prove or disprove your null hypothesis.

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## Different kinds of t-tests

So far we’ve talked about testing whether there’s a difference between two independent populations, aka a 2-sample t-test. But there are some other common variations of the t-test worth knowing about too.

## 1-sample t-test

Instead of a second population, you run a test to see if the average of your population is significantly different from a certain number or value.

Example: Is the average monthly spend among my customers significantly more or less than $50?

## 2-sample t-test

The classic example we’ve described above, where the means of two independent populations are compared to see if there is a significant difference.

Example: Do Iowan shoppers spend more per store visit than Alaskan ones?

## Paired t-test

With a paired t-test, you’re testing two dependent (paired) groups to see if they are significantly different. This can be useful for “before and after” scenarios.

Example: Did the average monthly spend per customer significantly increase after I ran my last marketing campaign?

You can also choose between one-tailed or two-tailed t-tests.

- Two-tailed t-tests tell you only whether or not the difference between the means is significant.
- One-tailed t-tests tell you which mean is the greater of the two.

## When should I use a t-test?

A t-test is used when there are two or fewer groups. If you have more than two groups, another option, such as ANOVA , may be a better fit.

There are a couple more conditions for using a 2 sample t-test, which are:

- Your data is expressed on an interval or ordinal scale (such as ranking or numerical scores)
- The two groups you’re comparing are independent of each other (one doesn’t affect the other). This one doesn’t apply if you’re doing a paired t-test.
- Your sample is random
- The distribution is normal (the results form a bell curve with the average in the middle)
- There is a similar amount of variance in each group (i.e. how far the data points are scattered from the average is similar for each group)

You also need to have a big enough sample size to make sure the results are sound. However, one of the benefits of the t-test is that it allows you to work with relatively small quantities of data, since it relies on the mean and variance of the sample, not the population as a whole.

The table shows alternative statistical techniques that can be used to analyze this type of data when different levels of measurement are available.

## Why is it called the Student’s t-test?

You may sometimes hear the t-test referred to as the “Student’s t-test”. Although it is regularly used by students, that’s not where the name comes from.

The t-distribution was developed by W. S. Gosset (1908), an employee of the Guinness brewery in Dublin. Gosset was not allowed to publish research findings in his own name, so he adopted the pseudonym “Student”. The t-distribution, as it was first designated, has been known under a variety of names, including the Student’s distribution and Student’s t-distribution.

## How to run a t-test

In order to run a t-test, you need 5 things:

- The difference between the mean values of your data sets (known as the mean difference)
- The standard deviation for each one (that’s the amount of variance)
- The number of data values in each group
- An 𝝰 (alpha) value. This is a parameter for how much risk of getting it wrong you’re prepared to accept. An 𝝰 of 0.05 means a 5% risk.
- For manual calculations, you’ll need a critical value table, which will help you interpret your results. These are widely available online, for example from university websites .

From there, you can either use formulae to run your t-test manually (we’ve provided formulae at the end of this article), or use a stats software package such as SPSS or Minitab to compute your results.

The outputs of a t-test are:

This is made up of two elements: the difference between the means in your two groups, and the variance between them. These two elements are expressed as a ratio. If it’s small, there isn’t much difference between the groups. If it’s larger, there is more difference.

## b) Degrees of freedom

This relates to the size of the sample and how much the values within it could vary while still maintaining the same average. Numerically, it’s the sample size minus one. You can also think of it as the number of values you’d need to find out in order to know all of the values. (The final one could be deduced by knowing the others and the total.)

Going the manual route, with these two numbers in hand, you can use your critical value table to find:

## c) the p-value

This is the heart of the matter – it tells you the probability of your t-value happening by chance. The smaller the p-value, the surer you can be of the statistical significance of your results.

## Stats iQ – statistically backed results in plain English

We know not everyone running survey software is a statistician, or wants to spend time learning statistical concepts and methods. That’s why we developed Stats iQ. It’s a powerful computational tool that gives you results equivalent to methods like the t-test, expressed in a few simple sentences.

## Formulae for manual t-test calculation

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## OpenAI teases an amazing new generative video model called Sora

The firm is sharing Sora with a small group of safety testers but the rest of us will have to wait to learn more.

- Will Douglas Heaven archive page

OpenAI has built a striking new generative video model called Sora that can take a short text description and turn it into a detailed, high-definition film clip up to a minute long.

Based on four sample videos that OpenAI shared with MIT Technology Review ahead of today’s announcement, the San Francisco–based firm has pushed the envelope of what’s possible with text-to-video generation (a hot new research direction that we flagged as a trend to watch in 2024 ).

“We think building models that can understand video, and understand all these very complex interactions of our world, is an important step for all future AI systems,” says Tim Brooks, a scientist at OpenAI.

But there’s a disclaimer. OpenAI gave us a preview of Sora (which means sky in Japanese) under conditions of strict secrecy. In an unusual move, the firm would only share information about Sora if we agreed to wait until after news of the model was made public to seek the opinions of outside experts. [Editor’s note: We’ve updated this story with outside comment below.] OpenAI has not yet released a technical report or demonstrated the model actually working. And it says it won’t be releasing Sora anytime soon. [ Update: OpenAI has now shared more technical details on its website.]

The first generative models that could produce video from snippets of text appeared in late 2022. But early examples from Meta , Google, and a startup called Runway were glitchy and grainy. Since then, the tech has been getting better fast. Runway’s gen-2 model, released last year, can produce short clips that come close to matching big-studio animation in their quality. But most of these examples are still only a few seconds long.

The sample videos from OpenAI’s Sora are high-definition and full of detail. OpenAI also says it can generate videos up to a minute long. One video of a Tokyo street scene shows that Sora has learned how objects fit together in 3D: the camera swoops into the scene to follow a couple as they walk past a row of shops.

OpenAI also claims that Sora handles occlusion well. One problem with existing models is that they can fail to keep track of objects when they drop out of view. For example, if a truck passes in front of a street sign, the sign might not reappear afterward.

In a video of a papercraft underwater scene, Sora has added what look like cuts between different pieces of footage, and the model has maintained a consistent style between them.

It’s not perfect. In the Tokyo video, cars to the left look smaller than the people walking beside them. They also pop in and out between the tree branches. “There’s definitely some work to be done in terms of long-term coherence,” says Brooks. “For example, if someone goes out of view for a long time, they won’t come back. The model kind of forgets that they were supposed to be there.”

Impressive as they are, the sample videos shown here were no doubt cherry-picked to show Sora at its best. Without more information, it is hard to know how representative they are of the model’s typical output.

It may be some time before we find out. OpenAI’s announcement of Sora today is a tech tease, and the company says it has no current plans to release it to the public. Instead, OpenAI will today begin sharing the model with third-party safety testers for the first time.

In particular, the firm is worried about the potential misuses of fake but photorealistic video . “We’re being careful about deployment here and making sure we have all our bases covered before we put this in the hands of the general public,” says Aditya Ramesh, a scientist at OpenAI, who created the firm’s text-to-image model DALL-E .

But OpenAI is eyeing a product launch sometime in the future. As well as safety testers, the company is also sharing the model with a select group of video makers and artists to get feedback on how to make Sora as useful as possible to creative professionals. “The other goal is to show everyone what is on the horizon, to give a preview of what these models will be capable of,” says Ramesh.

To build Sora, the team adapted the tech behind DALL-E 3, the latest version of OpenAI’s flagship text-to-image model. Like most text-to-image models, DALL-E 3 uses what’s known as a diffusion model. These are trained to turn a fuzz of random pixels into a picture.

Sora takes this approach and applies it to videos rather than still images. But the researchers also added another technique to the mix. Unlike DALL-E or most other generative video models, Sora combines its diffusion model with a type of neural network called a transformer.

Transformers are great at processing long sequences of data, like words. That has made them the special sauce inside large language models like OpenAI’s GPT-4 and Google DeepMind’s Gemini . But videos are not made of words. Instead, the researchers had to find a way to cut videos into chunks that could be treated as if they were. The approach they came up with was to dice videos up across both space and time. “It’s like if you were to have a stack of all the video frames and you cut little cubes from it,” says Brooks.

The transformer inside Sora can then process these chunks of video data in much the same way that the transformer inside a large language model processes words in a block of text. The researchers say that this let them train Sora on many more types of video than other text-to-video models, varied in terms of resolution, duration, aspect ratio, and orientation. “It really helps the model,” says Brooks. “That is something that we’re not aware of any existing work on.”

“From a technical perspective it seems like a very significant leap forward,” says Sam Gregory, executive director at Witness, a human rights organization that specializes in the use and misuse of video technology. “But there are two sides to the coin,” he says. “The expressive capabilities offer the potential for many more people to be storytellers using video. And there are also real potential avenues for misuse.”

OpenAI is well aware of the risks that come with a generative video model. We are already seeing the large-scale misuse of deepfake images . Photorealistic video takes this to another level.

Gregory notes that you could use technology like this to misinform people about conflict zones or protests. The range of styles is also interesting, he says. If you could generate shaky footage that looked like something shot with a phone, it would come across as more authentic.

The tech is not there yet, but generative video has gone from zero to Sora in just 18 months. “We’re going to be entering a universe where there will be fully synthetic content, human-generated content and a mix of the two,” says Gregory.

The OpenAI team plans to draw on the safety testing it did last year for DALL-E 3. Sora already includes a filter that runs on all prompts sent to the model that will block requests for violent, sexual, or hateful images, as well as images of known people. Another filter will look at frames of generated videos and block material that violates OpenAI’s safety policies.

OpenAI says it is also adapting a fake-image detector developed for DALL-E 3 to use with Sora. And the company will embed industry-standard C2PA tags , metadata that states how an image was generated, into all of Sora’s output. But these steps are far from foolproof. Fake-image detectors are hit-or-miss. Metadata is easy to remove, and most social media sites strip it from uploaded images by default.

“We’ll definitely need to get more feedback and learn more about the types of risks that need to be addressed with video before it would make sense for us to release this,” says Ramesh.

Brooks agrees. “Part of the reason that we’re talking about this research now is so that we can start getting the input that we need to do the work necessary to figure out how it could be safely deployed,” he says.

Update 2/15: Comments from Sam Gregory were added .

## Artificial intelligence

Ai for everything: 10 breakthrough technologies 2024.

Generative AI tools like ChatGPT reached mass adoption in record time, and reset the course of an entire industry.

## What’s next for AI in 2024

Our writers look at the four hot trends to watch out for this year

- Melissa Heikkilä archive page

## Google’s Gemini is now in everything. Here’s how you can try it out.

Gmail, Docs, and more will now come with Gemini baked in. But Europeans will have to wait before they can download the app.

## Deploying high-performance, energy-efficient AI

Investments into downsized infrastructure can help enterprises reap the benefits of AI while mitigating energy consumption, says corporate VP and GM of data center platform engineering and architecture at Intel, Zane Ball.

- MIT Technology Review Insights archive page

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A t test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population of interest, or whether two groups are different from one another. t test example

In simple terms, a Student's t-test is a ratio that quantifies how significant the difference is between the 'means' of two groups while taking their variance or distribution into account. Go to: Issues of Concern Selecting appropriate statistical tests is a critical step in conducting research. [2]

A t test is a statistical hypothesis test that assesses sample means to draw conclusions about population means. Frequently, analysts use a t test to determine whether the population means for two groups are different. For example, it can determine whether the difference between the treatment and control group means is statistically significant.

A p-value from a t test is the probability that the results from your sample data occurred by chance. P-values are from 0% to 100% and are usually written as a decimal (for example, a p value of 5% is 0.05). Low p-values indicate your data did not occur by chance.

The t-test is a test used for hypothesis testing in statistics. Calculating a t-test requires three fundamental data values including the difference between the mean values from each data...

A t test is a type of statistical test that is used to compare the means of two groups. It is one of the most widely used statistical hypothesis tests in pain studies [ 1 ]. There are two types of statistical inference: parametric and nonparametric methods.

A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero. Frequently asked questions: Statistics

T-tests are statistical hypothesis tests that you use to analyze one or two sample means. Depending on the t-test that you use, you can compare a sample mean to a hypothesized value, the means of two independent samples, or the difference between paired samples.

Student's t-test, in statistics, a method of testing hypotheses about the mean of a small sample drawn from a normally distributed population when the population standard deviation is unknown.. In 1908 William Sealy Gosset, an Englishman publishing under the pseudonym Student, developed the t-test and t distribution. (Gosset worked at the Guinness brewery in Dublin and found that existing ...

The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the analysis for the posttest-only two-group randomized experimental design. Figure 1.

The t-test is a widely used statistical method for comparing means of two groups. This article reviews the history, principles, assumptions, and applications of the t-test, with a focus on the independent samples t-test. It also provides examples and guidance on how to perform and interpret the t-test using different software packages.

The t test is one type of inferential statistics. It is used to determine whether there is a significant difference between the means of two groups. With all inferential statistics, we assume the dependent variable fits a normal distribution. When we assume a normal distribution exists, we can identify the probability of a particular outcome.

Aug 5, 2022. 5. Photo by Andrew George on Unsplash. Student's t-tests are commonly used in inferential statistics for testing a hypothesis on the basis of a difference between sample means. However, people often misinterpret the results of t-tests, which leads to false research findings and a lack of reproducibility of studies.

The t-test is used as an example of the basic principles of statistical inference. One of the simplest situations for which we might design an experiment is the case of a nominal two-level explanatory variable and a quantitative outcome variable. Table 6.1 shows several examples.

This procedure is an inferential statistical hypothesis test, meaning it uses samples to draw conclusions about populations. The independent samples t test is also known as the two sample t test. This test assesses two groups.

The t-test is a test in statistics that is used for testing hypotheses regarding the mean of a small sample taken population when the standard deviation of the population is not known. The t-test is used to determine if there is a significant difference between the means of two groups.

A T-test is the final statistical measure for determining differences between two means that may or may not be related. The testing uses randomly selected samples from the two categories or groups. It is a statistical method in which samples are chosen randomly, and there is no perfect normal distribution.

A t Test is a parametric test that is used to compare the means of two groups (Kim, 2015). The reason is to verify whether there is a significant difference between the means of independent...

Definition: T-test. T-statistics compare the means of two samples using statistical analysis. It is used in hypothesis testing with the null hypothesis (where the difference between the group means is zero) and the alternate hypothesis (the difference is not equal to zero). When data sets have a normal distribution, but you are unsure about the ...

XM for Strategy & Research Research. Get faster, richer insights with qual and quant tools that make powerful market research available to everyone. ... The t-test, also known as t-statistic or sometimes t-distribution, is a popular statistical tool used to test differences between the means (averages) of two groups, or the difference between ...

A t-test is a statistical calculation that measures the difference in means between two sample groups. T-tests can help you measure the validity of results in fields like marketing, sales and accounting. Conducting a t-test involves inputting the mean and standard deviation values into a defined formula.

T-Test is a method used in statistics to derive some conclusions for a population which is based upon some sample data using values of means and variances. Here, a population refers to the entities or a group of entities that are in our study of interest.

A paired samples t-test is used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample. This tutorial explains the following: The motivation for performing a paired samples t-test. The formula to perform a paired samples t-test.

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