Mixed Model ANOVA Calculator

A mixed model ANOVA combines both between-subjects and within-subjects factors in a single analysis. 'Between-subjects' means different participants are in different groups (e.g., control vs. treatment), while 'within-subjects' means the same participants are measured across multiple conditions or time points. This design is powerful because it controls for individual differences while also detecting group effects.

A between-subjects factor assigns each participant to only one group — for example, one group receives a drug and another receives a placebo. A within-subjects factor measures the same participant under all conditions — for example, measuring performance at Week 1, Week 2, and Week 3. Mixed ANOVA includes at least one of each type.

The interaction effect (Group × Condition) tests whether the pattern of change across conditions differs between groups. For example, if the treatment group improves over time but the control group does not, that is a significant interaction. A significant interaction is often the most theoretically interesting finding in a mixed ANOVA.

A p-value below your chosen significance level (α) indicates that the observed effect is statistically significant — i.e., unlikely to be due to chance. For example, with α = 0.05, a p-value of 0.03 means the effect is significant. A p-value above α (e.g., 0.12) means the effect is not statistically significant at that threshold.

Eta-squared (η²) is a measure of effect size — it tells you what proportion of the total variance is explained by each factor. Common benchmarks are: small effect = 0.01, medium effect = 0.06, large effect = 0.14. It ranges from 0 to 1, and higher values indicate a stronger effect.

Each group should have at least 3 subjects for the calculation to be meaningful, though larger sample sizes (10 or more per group) produce more reliable and powerful results. Both groups must have the same number of subjects since the same individuals are measured repeatedly within each group.

Key assumptions include: (1) normality — scores within each group-condition cell are approximately normally distributed; (2) sphericity — the variances of differences between all pairs of within-subjects conditions are equal (tested with Mauchly's test); (3) homogeneity of variance — variance is similar across groups; and (4) independence of observations between subjects.

This calculator is designed for a two-group mixed ANOVA (one between-subjects factor with two levels). For designs with three or more groups, or more complex factorial designs, you would need specialised statistical software such as SPSS, R, or Python's statsmodels library.