How to Determine Whether to Use a One-Sample, Paired, or Unpaired T-Test

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So you're taking statistics and you know you need to use a t-test, but are stumped on what kind of t-test to use? This simple article shows you how to determine whether a paired, unpaired, or one-sample t-test is appropriate in your particular situation.

    Ask yourself: Do I want to compare the means of two groups, or do I only care how the mean of a single group compares to some number? If you want to compare the means of two groups, continue to Step 2.

    However, if you only care how the mean of a single group compares to a single number, use a one-sample t-test. An examples of a case where a one-sample t-test is appropriate would be if one is testing whether the average student consumes significantly more than 2000 calories a day (e.g., you are comparing the mean number of calories consumed to see whether it is significantly greater than the number 2000).

    If you are comparing the means of two groups, next ask yourself: Did the two groups of numbers that we are comparing come from the same people? If so, we need to use a paired-samples t-test (also known as a repeated-samples t-test).

    For example, let's say we are comparing the weight of every person in a group of people before they went on a diet with their weight after they completed the diet program. We want to know whether each person's weight after the program is significantly greater than their weight beforehand. The two sets of numbers we are comparing come from the same set of people: one set represents their weights before treatment, and the other set represents their weights after treatment. This is called a within-subjects variable. In a case like this, use a paired-samples t-test (also known as a repeated-samples t-test).

    There is one more case in which a paired-samples t-test is appropriate: if the researcher is doing a "matched" design in which they purposefully chose pairs of subjects that are similar in various characteristics (e.g., age, gender, medical history, etc.) Anytime that numbers in the first and second group are paired, there is a meaningful relationship between a value in the first group of scores and the corresponding value in the second group of scores, a paired-samples t-test is appropriate.

    In any other case where a t-test is appropriate, it's best to use an independent-samples t-test. This is appropriate for "between-subjects" designs where two groups of subjects are intended to differ on a critical manipulation. For example, if testing the effect of caffeine on the growth of plants, you might have two groups: one control group that was given water, and one experimental group of plants that was given a caffeine solution. Since you're using totally different plants in each group, there's no meaningful pairing between the scores in the two groups, and you should use an independent-samples t-test.

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