Mixed ANOVA
Mixed Between-Within Subjects Analysis of Variance · Also known as: split-plot ANOVA, mixed-design ANOVA, between-within ANOVA, Karma ANOVA (Mixed ANOVA — Gruplar Arası × Tekrarlı)
Mixed ANOVA is a parametric factorial analysis of variance that simultaneously examines at least one between-subjects factor and at least one within-subjects (repeated-measures) factor. Rooted in R. A. Fisher's ANOVA framework formalised in 1925, it is the standard method for experimental and longitudinal designs in which different groups are each measured across multiple time points or conditions.
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When to use it
Use Mixed ANOVA when you have at least one categorical between-subjects grouping variable, at least one within-subjects (repeated-measures) factor, and a single continuous dependent variable. The design suits longitudinal studies tracking groups over time, pre-post experiments with a control and a treatment group, and any factorial design that mixes independent groups with repeated conditions. Core assumptions: approximate normality within each cell (check with Shapiro-Wilk per cell or group), sphericity of the within-subjects factor (check with Mauchly's test — correct with Greenhouse-Geisser if violated), homogeneity of variance across between-subjects groups (check with Levene's test), and independence of observations within each between-subjects group.
Strengths & limitations
- Simultaneously tests between-subjects effects, within-subjects effects, and their interaction — capturing differential trajectories across groups.
- More statistically powerful than separate analyses because within-subjects comparisons use individual participants as their own controls, reducing error variance.
- Partial eta-squared provides a meaningful, widely reported effect-size index for each tested effect.
- Handles both experimental (randomly assigned groups) and quasi-experimental (pre-existing groups) longitudinal designs.
- Sensitive to sphericity violations; Mauchly's test must be checked and the appropriate epsilon correction applied.
- Assumes approximate normality in each cell; with small cell sizes, non-normality can distort Type I error rates.
- Cannot accommodate missing data on the repeated-measures factor without listwise deletion, which reduces power and can introduce bias — mixed-effects models (e.g. LMM) are preferred when data are missing at random.
- The interaction effect requires careful interpretation; significant main effects may be misleading when the interaction is present.
Frequently asked
What is the difference between Mixed ANOVA and Repeated Measures ANOVA?
Repeated Measures ANOVA has only within-subjects factors — all participants are in the same group. Mixed ANOVA adds at least one between-subjects grouping factor, which allows you to test whether the pattern of change over time (or across conditions) differs between distinct groups. If you have only one group measured repeatedly, use repeated measures ANOVA; if you have two or more groups each measured repeatedly, use Mixed ANOVA.
My Mauchly's test is significant — what should I do?
Apply a sphericity correction to the within-subjects and interaction F tests. The Greenhouse-Geisser correction is more conservative and preferred when epsilon is below 0.75; the Huynh-Feldt correction is slightly less conservative and preferred when epsilon exceeds 0.75. Most software reports both automatically. Do not simply ignore the violation, as uncorrected F ratios will have inflated Type I error rates.
The interaction is significant — how should I follow it up?
A significant interaction means the effect of one factor depends on the level of the other. Follow it up with simple effects analyses: examine the within-subjects factor separately at each level of the between-subjects factor (or vice versa). Apply appropriate post-hoc corrections (e.g. Bonferroni) to control the familywise error rate across multiple comparisons.
Can I use Mixed ANOVA with more than two groups or more than two time points?
Yes. Mixed ANOVA extends naturally to any number of groups (between-subjects levels) and any number of repeated measurement occasions (within-subjects levels). With more than two levels of the within-subjects factor, sphericity becomes an increasingly important concern and corrections are more likely to be needed. More levels also increase the complexity of interaction interpretation.
Sources
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE. ISBN: 978-1526419521
How to cite this page
ScholarGate. (2026, June 1). Mixed Between-Within Subjects Analysis of Variance. ScholarGate. https://scholargate.app/en/statistics/mixed-anova
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ANCOVAStatistics↔ compare
- MANOVAStatistics↔ compare
- One-way ANOVAStatistics↔ compare
- Paired t-testStatistics↔ compare
- Repeated-measures ANOVAStatistics↔ compare
- Two-Way ANOVAStatistics↔ compare