ANOVA is used in Hypothesis testing to compares the means of three or more groups, differently from t-test where this is true for only two groups.
- The Null Hypothesis is: “All groups have the same mean”.
- The Alternate Hypothesis is: “At least one group mean is different from the others”.
Note
ANOVA doesn’t tell us which specific groups differ from each other; it only indicates whether at least one group differs.
ANOVA uses an F-statistic, which compares the variance between gropup means to the variance within each group. If the F-statistic is large, it indicates that the variation between group means is large, relative to the variation within grups, suggesting there is a significant difference among means.
Why Not Use Multiple t-tests Instead of ANOVA?
- For three or more groups, running multiple t-tests increases the risk of a Type I error (false positive), since each test has its own probability of incorrectly rejecting the null hypothesis.
- ANOVA controls for this error by testing all group means simultaneously, ensuring that the overall probability of a Type I error remains at the chosen significance level.