# Mixed model ANOVA Calculator

If you want to calculate a mixed analysis of variance (2-Way ANOVA with repeated measurements), simply select one nominal variable and more than two metric variables. The results of the mixed variance analysis are displayed clearly: ## Mixed-model ANOVA

A mixed-model ANOVA (Analysis of Variance) is a statistical technique that combines features of both between-subjects (or "independent measures") and within-subjects (or "repeated measures") designs. In this context, "mixed" refers to the use of both fixed and random effects in the model.

### Factors

In the context of ANOVA, a factor is an independent variable. In a mixed-model ANOVA, you might have:

• Between-subjects factors: Different levels (or groups) of this factor are represented by different subjects. For instance, if you're testing the effects of a drug, you might have a control group and a treatment group, and each subject is in only one of these groups.
• Within-subjects factors: All subjects experience each level (or condition) of this factor. For example, if you're testing memory recall at three different times of the day (morning, afternoon, evening), then all subjects would be tested at all three times.

### Fixed vs. Random Effects

In the context of mixed models, "fixed effects" usually refer to the main effects and interactions of the factors you're specifically interested in. These are the effects that you believe generalize to a larger population. "Random effects" are random variations that can't be attributed to the fixed effects. They often represent variability due to subjects or other random factors that are not of primary interest.

One of the main benefits of a mixed-model ANOVA is that it allows you to examine the effects of a treatment or intervention across time or across different conditions while accounting for the non-independence of observations. This can give more power to detect an effect, as the variability within subjects can be separated from the variability between subjects.

### Assumptions

Like other ANOVA models, mixed-model ANOVA has several assumptions including normality, sphericity (for repeated measures), and homogeneity of variance. It's crucial to check these assumptions before interpreting the results.

### Analysis

Performing a mixed-model ANOVA can be complex and requires statistical software like SPSS, R, SAS or DATAtab. The outputs will provide information about the main effects of each factor as well as any interaction effects between factors.

In summary, a mixed-model ANOVA is a versatile tool for understanding the effects of multiple factors, especially when you have both between-subjects and within-subjects measures. As with any statistical test, it's essential to understand its assumptions and limitations.

Cite DATAtab: DATAtab Team (2023). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net