## What is a T Test?

A **T Test**, also known as Student’s T Test, is a statistical hypothesis test that is used to determine whether there is a significant difference between the means of two groups. It is a type of inferential statistic which allows researchers to make inferences about the population based on a sample.

## Types of T Tests

There are three main types of T Tests: Independent Samples T Test, Paired Sample T Test, and One Sample T Test. Each of these tests has a specific use case and is applied based on the nature of the data and the research question.

### Independent Samples T Test

The **Independent Samples T Test** is used when comparing the means of two independent groups. For example, comparing the average scores of two different groups of students.

### Paired Sample T Test

The **Paired Sample T Test** is used when comparing the means of the same group at two different times. For example, measuring the performance of a group of students before and after a specific training.

### One Sample T Test

The **One Sample T Test** is used when comparing the mean of a single group against a known mean. For example, comparing the average score of a class to the known average score of the entire school.

## How Does a T Test Work?

The T Test works by comparing the means of two groups and determining whether the difference between these means is statistically significant. The test calculates a T-value, which is the ratio of the difference between the group means to the difference within the groups. The larger the absolute value of the T-value, the greater the evidence against the null hypothesis, which is the assumption that there is no significant difference between the group means.

## Interpreting T Test Results

The results of a T Test are usually reported as a T-value and a p-value. The T-value is a measure of the size of the difference relative to the variation in your sample data. The p-value is the probability that you would observe the effect seen in your sample data if the null hypothesis were true.

If the p-value is less than the chosen significance level (usually 0.05), then the null hypothesis is rejected and the difference between the groups is considered statistically significant.

## Applications of T Tests

T Tests are widely used in both research and business. In research, they are used to test hypotheses and draw conclusions about populations based on sample data. In business, they can be used to compare performance metrics, customer satisfaction levels, product quality, and many other applications.

## Limitations of T Tests

While T Tests are a powerful tool, they do have limitations. They assume that the data is normally distributed, that the samples are independent, and that the variances of the two groups being compared are equal. If these assumptions are not met, the results of the T Test may not be valid.