T-test

T-test is a type of inferential statistics used to determine if there is a significant difference between the means of two groups. The T-test is based on the Student's t-distribution, which is a probability distribution that is used to estimate population parameters when the sample size is small and/or when the population variance is unknown.

Overview

The T-test was developed by William Sealy Gosset, a chemist working for the Guinness brewery in Dublin, Ireland. Gosset published the T-test in 1908 under the pseudonym "Student", hence the name Student's t-test.

There are three main types of T-tests: independent samples T-test, paired sample T-test, and one-sample T-test. The independent samples T-test compares the means of two independent groups. The paired sample T-test compares means from the same group at different times. The one-sample T-test tests the mean of a single group against a known mean.

Assumptions

The T-test assumes that the data is normally distributed, the samples are independent, and the variances of the two groups being compared are equal (homogeneity of variance).

Calculation

The T-test statistic is calculated as the difference between the sample means divided by the standard error of the difference. The standard error of the difference is calculated as the square root of the sum of the variances of the two groups divided by their respective sample sizes.

Interpretation

The result of a T-test is a T-value and a p-value. The T-value is a measure of the magnitude of the difference relative to the variation in the data. The p-value is the probability of observing a T-value as extreme as the one calculated if the null hypothesis is true. If the p-value is less than the chosen significance level (usually 0.05), then the null hypothesis is rejected and the difference is considered statistically significant.

See also

• Z-test
• F-test
• Analysis of variance

T-test Resources
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