What does each F score in a two-way ANOVA primarily represent?

In a two-way ANOVA, each F score corresponds to a specific hypothesis being tested. The F score can indicate various types of variability among group means. In this context, the F score primarily represents the variance among the group means relative to the variance within the groups themselves.

When assessing the main effects of each independent variable, the F score tells us how much the means of the groups defined by one factor differ when controlling for the other factor. Similarly, when evaluating interaction effects, the F score reflects whether the impact of one independent variable on the dependent variable differs depending on the level of the other independent variable.

By indicating the ratio of explained variability (between groups) to unexplained variability (within groups), the F score provides insights into the spread and relationship of group means as affected by the independent variables. Therefore, it is accurate to say that it represents the spread of group means in the context of a two-way ANOVA.