P values
When interpreting the results of fitting a mixed model, interpreting the P values is the same as two-way ANOVA. So read the general page on interpreting two-way ANOVA results first. Also read the general page on the assumption of sphericity, and assessing violations of that assumption with epsilon.
Random effects SD and variance
The mixed effects model treats the different subjects (participants, litters, etc) as a random variable. The residual random variation is also random. The effect of all random variables is quantified with its variation. Prism presents the variation as both a SD and a variance (which is the SD squared). You, or more likely your statistical consultant, may be interested in these values to understand the relative variation among subjects responses (the subject variance) and within the repeated responses from the same subject (the residual variance). compare with other programs.
Was the matching effective?
A repeated-measures experimental design can be very powerful, as it controls for random factors that cause or unmeasured variability between subjects. If the matching is effective, the repeated-measures test will yield a smaller P value than an ordinary ANOVA. The repeated-measures test is more powerful because it separates between-subject variability from within-subject variability. If the pairing is ineffective, however, the repeated-measures test can be less powerful because it has fewer degrees of freedom.
Prism tests whether the matching was effective and reports a P value. This P value comes from a chi-square statistic that is computed by comparing the fit of the full mixed effects model to a simpler model without accounting for repeated measures. If this P value is low, you can conclude that the matching was effective. If the P value is high, you can conclude that the matching was not effective and should reconsider your experimental design for your next study.
Goodness of fit
Prism expresses the goodness-of-fit in a few ways. These will only be meaningful to someone who understand mixed effects models deeply. Most scientists will ignore these results or not check the option so they never get reported. But some journals may ask you to report at least one measure of goodness of fit.
Degrees of freedom
The denominator degrees of freedom reported for each main effect and for the interaction depend on which method you chose in the parameters dialog. Kenward-Roger, which is the default, and Satterthwaite both estimate them from your data and usually report values that are not whole numbers. The Legacy method reports whole numbers taken from the design.
Fractional degrees of freedom are expected with Kenward-Roger and Satterthwaite, and are not a sign that anything went wrong. Nor is seeing different degrees of freedom on different rows of a multiple comparisons table. Each comparison gets its own.
If a random effect with an estimated SD of zero was removed from the model, neither of those two methods can be computed, so Prism falls back to the Legacy method and tells you so in a floating note. For what the three methods do and how to choose among them, see denominator degrees of freedom in the mixed model.
Sphericity and the mixed effects model
When Prism fits a mixed effects model, it does not apply the Geisser-Greenhouse correction. The sphericity section of the Repeated Measures tab is unavailable and set to Yes. No correction. The Satterthwaite and Kenward-Roger methods estimate the denominator degrees of freedom from the fitted variance structure, so they take the place of that correction rather than being combined with it.
To use the Geisser-Greenhouse correction and see epsilon, choose repeated measures ANOVA (based on GLM) instead. That requires data with no missing values.
Multiple comparisons tests and analysis checklist
Learn about multiple comparisons tests after repeated measures ANOVA.
Before interpreting the results, review the analysis checklist.
