Section author: Danielle J. Navarro and David R. Foxcroft

Assumption checking

As with one-way ANOVA, the key assumptions of factorial ANOVA are homogeneity of variance (all groups have the same standard deviation), normality of the residuals, and independence of the observations. The first two are things we can check for. The third is something that you need to assess yourself by asking if there are any special relationships between different observations, for example repeated measures where the independent variable is time so there is a relationship between the observations at time one and time two: observations at different time points are from the same people. Additionally, if you aren’t using a saturated model (e.g., if you’ve omitted the interaction terms) then you’re also assuming that the omitted terms aren’t important. Of course, you can check this last one by running an ANOVA with the omitted terms included and see if they’re significant, so that’s pretty easy. What about homogeneity of variance and normality of the residuals? As it turns out, these are pretty easy to check. It’s no different to the checks we did for a one-way ANOVA.

Homogeneity of variance

As mentioned in subsection Checking the homogeneity of variance assumption, it’s a good idea to visually inspect a plot of the standard deviations compared across different groups / categories, and also see if the Levene test is consistent with the visual inspection. The theory behind the Levene test was discussed in that section, so I won’t discuss it again. This test expects that you have a saturated model (i.e., including all of the relevant terms), because the test is primarily concerned with the within-group variance, and it doesn’t really make a lot of sense to calculate this any way other than with respect to the full model. The Levene test can be specified under the ANOVA Assumption Checks → Homogeneity Tests option in jamovi, with the result shown as in Fig. 153. The fact that the Levene test is non-significant means that, providing it is consistent with a visual inspection of the plot of standard deviations, we can safely assume that the homogeneity of variance assumption is not violated.

Fig. 153 Checking assumptions in an ANOVA model

Normality of residuals

As with one-way ANOVA we can test for the normality of residuals in a straightforward fashion (see Checking the normality assumption). Primarily though, it’s generally a good idea to examine the residuals graphically using a QQ-plot. See Fig. 153.