What is T-Test?

The t-test is named after William Sealy Gosset’s Student’s t-distribution, created while he was writing under the pen name “Student.”

A t-test is a type of inferential statistic test used to determine if there is a significant difference between the means of two groups. It is often used when data is normally distributed and population variance is unknown.

The t-test is used in hypothesis testing to assess whether the observed difference between the means of the two groups is statistically significant or just due to random variation.

T-test

In statistics, various tests are used to compare different samples or groups and draw conclusions about populations. These tests, known as statistical tests, focus on analyzing the likelihood or probability of obtaining the observed data under specific assumptions or hypotheses. They provide a framework for assessing evidence in support of or against a particular hypothesis.

A statistical test begins by formulating a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis represents the default assumption, typically stating no effect or no difference, while the alternative hypothesis suggests a specific relationship or effect.

There are different statistical tests like Z-test, T-test, Chi-squared tests, ANOVA, Z-test, and F-test, etc. which are used to compute the p-value. In this article, we will learn about the T-test.

Table of Content

  • What is T-Test?
  • Assumptions in T-test
  • Prerequisites for T-Test
  • Types of T-tests
  • One sample T-test
  • Independent sample T-test
  • Paired Two-sample T-test
  • Frequently Asked Questions on T-Test

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What is T-Test?

The t-test is named after William Sealy Gosset’s Student’s t-distribution, created while he was writing under the pen name “Student.”...

Assumptions in T-test

Independence: The observations within each group must be independent of each other. This means that the value of one observation should not influence the value of another observation. Violations of independence can occur with repeated measures, paired data, or clustered data.Normality: The data within each group should be approximately normally distributed i.e the distribution of the data within each group being compared should resemble a normal (bell-shaped) distribution. This assumption is crucial for small sample sizes (n < 30).Homogeneity of Variances (for independent samples t-test): The variances of the two groups being compared should be equal. This assumption ensures that the groups have a similar spread of values. Unequal variances can affect the standard error of the difference between means and, consequently, the t-statistic.Absence of Outliers: There should be no extreme outliers in the data as outliers can disproportionately influence the results, especially when sample sizes are small....

Prerequisites for T-Test

Let’s quickly review some related terms before digging deeper into the specifics of the t-test....

Types of T-tests

There are three types of t-tests, and they are categorized as dependent and independent t-tests....

One sample T-test

One sample t-test is one of the widely used t-tests for comparison of the sample mean of the data to a particularly given value. Used for comparing the sample mean to the true/population mean....

Independent sample T-test

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Paired Two-sample T-test

An Independent sample t-test, commonly known as an unpaired sample t-test is used to find out if the differences found between two groups is actually significant or just a random occurrence....

Conclusion

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Frequently Asked Questions on T-Test

Paired sample t-test, commonly known as dependent sample t-test is used to find out if the difference in the mean of two samples is 0. The test is done on dependent samples, usually focusing on a particular group of people or things. In this, each entity is measured twice, resulting in a pair of observations....