Two-Way ANOVA Calculator
Two-way ANOVA answers three questions at once: does factor A matter, does factor B matter, and — often the most interesting part — do they interact, so that the effect of one factor depends on the level of the other? Choose the number of levels for each factor, paste the observations for every cell, and read the complete ANOVA table with F, p and partial η² for both main effects and the interaction. This calculator handles balanced designs (the same number of observations in every cell), where the classical sums of squares are unambiguous — the same setup you would run with aov() in R or a standard factorial ANOVA in SPSS. Results are verified against R to at least six significant digits.
AI Report
Let AI interpret your results: a downloadable Word document in APA 7 / business report format.
Frequently asked questions
How do I report two-way ANOVA results in APA 7 format?
Report each main effect and the interaction separately, e.g.: "There was a significant main effect of dose, F(2, 18) = 157.44, p < .001, ηp² = .95, and a significant dose × gender interaction, F(2, 18) = 11.15, p < .001, ηp² = .55." The AI Report writes the full results section including the ANOVA table.
What does a significant interaction mean?
It means the effect of one factor changes across the levels of the other — for example, a treatment that works for one group but not another. When the interaction is significant, interpret the main effects with caution and look at the cell means.
Why does this calculator require a balanced design?
With equal cell sizes, the Type I, II and III sums of squares coincide and the results are unambiguous. Unbalanced factorial designs require choosing among these types (typically Type III in SPSS); that choice is best made in a full statistics package.
What is partial eta squared?
Partial η² is the share of variance explained by an effect after excluding variance explained by the other effects — the effect size SPSS prints for factorial ANOVA. Rough benchmarks: .01 small, .06 medium, .14 large.