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Comparing two sets of data

A common scenario for psychology research is to test whether or not two data sets differ on a particular variable. For example, you may wish to determine if there is a statistically significant difference between anxiety levels before and after a proposed treatment strategy. There are a number of tests available for comparing two data sets, depending on the nature of the data and the experimental design.

Tests available online

See the discussions about experiment design and parametric vs non-parametric for help selecting an appropriate test for your data.

	Parametric	Non-parametric
Independent groups	Independent t-test	Mann-Whitney U test Wilcoxon rank-sum test
Same subjects	Paired t-test	Wilcoxon signed-rank test

Test assumptions

The parametric tests rely on the following assumptions:

Independent t-test

The sampling distribution is approximately normally distributed. Due to the central limit theorem, this assumption is usually satisfied for large data sets. The Shapiro–Wilk normality test is automatically applied by the calculator below for small data sets.
Both sets have approximately equal variance (this is sometimes known as homogeneity of variance or homoscedasticity). Levene's test for equality of variance is used by the calculator below to test this assumption.

Paired t-test

The sampling distribution is approximately normally distributed. Note that in this case, the relevant sampling distribution is derived from the difference between paired scores, rather than the raw scores themselves. Due to the central limit theorem, this assumption is usually satisfied for large data sets. The Shapiro–Wilk normality test is automatically applied by the calculator below for small data sets.