ANOVA compares three or more group means. The arithmetic is the easy part; the friction is choosing the right variant, checking the assumptions, and turning the result into a table and a post-hoc comparison you can defend. Magic Stat keeps all of that in one window.
One-way ANOVA tests whether the means of three or more independent groups are equal, by comparing the variation between groups with the variation inside them. That ratio is the F statistic. Welch's ANOVA relaxes the equal-variance assumption and is the safer choice when the groups differ in spread or in size — the same logic as Welch's t for two groups.
When the response is not roughly normal, the rank-based routes are Kruskal-Wallis and Mood's median test, and a permutation F test is available as a check that does not rely on a distributional formula. For two factors at once, the factorial ANOVA adds the interaction term — the question of whether the effect of one factor depends on the level of the other — and Magic Stat computes it with Type III sums of squares. The non-parametric counterpart of the two-way design, Scheirer-Ray-Hare, tests the interaction too.
Designs beyond the simple one-way are where general-purpose tools usually stop: a nested (hierarchical) design, where each level of one factor belongs to exactly one level of another, and block designs such as the Latin square, the 2×2 crossover and the balanced incomplete block. Those are in the same dialog, with the sums-of-squares decomposition each design requires.
One-way family: One-way ANOVA (equal variances) · Welch's ANOVA (unequal variances) · Kruskal-Wallis · Mood's median test · permutation test.
Post-hoc: Tukey HSD · Bonferroni · Dunn-Sidak · Games-Howell · Dunn's test · Conover-Iman · Dunnett (vs control), with a compact letter display.
Factorial: Type III sums of squares with the interaction, or the non-parametric Scheirer-Ray-Hare; partial eta-squared for A, B and A×B.
Other designs: nested (hierarchical) two levels · Latin square · 2×2 crossover · balanced incomplete block.
Welch's does not assume equal variances and is the safer default when the groups differ in spread or size. The classical one-way F is exact when the variances are equal and the design is balanced. Both are offered, so you can see whether the conclusion depends on the assumption.
Tukey HSD for equal variances and a balanced design; Games-Howell when variances or sizes differ; Bonferroni or Dunn-Sidak when you want a conservative correction for any design; Dunn or Conover-Iman after Kruskal-Wallis; Dunnett when every group is compared against a control. The dialog lists them with their assumptions.
For one factor, Kruskal-Wallis or Mood's median test; for two factors with an interaction, Scheirer-Ray-Hare tests the interaction as well. A permutation F test is also available. The app reports the choice rather than making it silently.
Use the factorial tab of the ANOVA dialog. It computes a two-way ANOVA with Type III sums of squares and the interaction term, and partial eta-squared for each effect.
Not the same one-way dialog — the same subjects measured several times need the repeated-measures route, where the within-subject structure is handled explicitly. That lives in the Repeated Measures tab of the same ANOVA window.
Post-hoc tests → Planned contrasts → ANCOVA → Non-parametric tests →