T-Test Essentials: Definition, Formula and Calculation

One-Sample t-test

The one-sample t-test, also known as the single-parameter t test or single-sample t-test, is used to compare the mean of one sample to a known standard (or theoretical / hypothetical) mean.

Generally, the theoretical mean comes from:

• a previous experiment. For example, comparing whether the mean weight of mice differs from 200 mg, a value determined in a previous study.
• or from an experiment where you have control and treatment conditions. If you express your data as “percent of control”, you can test whether the average value of treatment condition differs significantly from 100.

Unpaired t-test

The unpaired t-test is used to compare the mean of two independent groups.

For example, you might want to compare the average weights of individuals grouped by gender: male and female groups, which are two unrelated/independent groups.

The independent samples t-test comes in two different forms:

• the standard Student’s t-test, which assumes that the variance of the two groups are equal.
• the Welch’s t-test, which is less restrictive compared to the original Student’s test. This is the test where you do not assume that the variance is the same in the two groups, which results in the fractional degrees of freedom.

The two methods give very similar results unless both the group sizes and the standard deviations are very different.

Paired t-test

The paired t-test is used to compare the means of two related groups of samples. Put into another words, it’s used in a situation where you have two values (i.e., pair of values) for the same samples.

For example, you might want to compare the average weight of 20 mice before and after treatment. The data contain 20 sets of values before treatment and 20 sets of values after treatment from measuring twice the weight of the same mice. In such situations, paired t-test can be used to compare the mean weights before and after treatment.

Related articles

• Comparing Means of Two Groups in R