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A t-test (or non-parametric equivalent) can be used to determine if there is a statistically significant difference between two data sets. However, in some cases there are more than two groups of interest. For example, imagine you would like to determine if there is a difference in anxiety levels at exam time between first, second, third, and fourth year university students. One approach would be to conduct a t-test between every possible combination of years (e.g. first vs second, first vs third, etc.). However, conducting the tests separately increases the probability of a type I error.
Analysis of Variance (ANOVA) is a family of statistical tests that are useful when comparing several sets of scores. A common application of ANOVA is to test if the means of three or more groups are equal. The basic idea behind ANOVA is a comparison of the variance between the groups and the variance within the groups.
See to discussions about experiment design and parametric vs non-parametric for help selecting an appropriate test for your data.
|Independent groups||One-way ANOVA||One-way Kruskal-Wallis|
|Same subjects||Repeated measures ANOVA (rANOVA)||Friedman test|
(and Kendall's W)
The parametric tests rely on the following assumptions: