True or False: The F ratio is calculated differently for main effects and interaction effects.

The statement is false because the F ratio is calculated in the same way for both main effects and interaction effects in an analysis of variance (ANOVA). The F ratio is a measure of variance, specifically the ratio of the variance explained by the model to the variance that is not explained by the model (the error variance).

In both cases—whether for main effects or interaction effects—the formula for the F ratio is fundamentally the same. It involves the mean squares (MS) derived from the sum of squares (SS) for the respective effects divided by the degrees of freedom (df). For main effects, the mean square associated with that effect is divided by the mean square of the error. For interaction effects, the same principle applies, where the interaction mean square is divided by the error mean square.

Therefore, the calculation of the F ratio does not change based on whether you are examining main effects or interaction effects; it remains consistent across different types of effects in the ANOVA framework.