ANOVA
Analysis of variance, a test that compares means across three or more groups by partitioning variability between and within groups.
ANOVA, or analysis of variance, tests whether the means of three or more groups differ more than chance would predict. It compares variability between group means to variability within groups, producing an F statistic and a p-value. A significant result says at least one group differs, but not which; post hoc comparisons identify the specific pairs. Factorial ANOVA adds multiple factors and their interactions, and repeated-measures ANOVA handles the same participants measured several times.
ANOVA assumes independent observations, roughly normal residuals, and similar variances across groups; a rank-based non-parametric alternative exists when these fail.
In a thesis, ANOVA is the standard tool when a design has more than two conditions, and it avoids the inflated error rates of running many separate t-tests. Report the F statistic with both degrees of freedom, the p-value, an effect size, and the post hoc results.
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