Your two-way ANOVA has a significant interaction. Now what?

A significant interaction changes the meaning of everything above it in the table. This is the most common misreading in applied statistics.

What it means

The effect of one factor depends on the level of the other. Your drug works in males and not females. Your treatment helps at week 2 and not week 12.

Why your main effects may now mislead

A main effect averages over the other factor. If a drug raises the outcome by 10 in males and lowers it by 10 in females, the main effect is roughly zero. Reporting "no significant effect of drug" would be true and completely wrong.

When the interaction is significant, do not interpret main effects in isolation, and say so explicitly.

What to do instead: simple effects

Test factor A separately at each level of factor B. "There was a significant effect of treatment in males, F(1, 36) = 12.4, p = .001, but not in females, F(1, 36) = 0.31, p = .58." Correct for the number of simple-effects tests you run.

What to report

The interaction with F, df, p and effect size; an explicit statement that it qualifies the main effects; the simple effects with their correction; and a plot. An interaction plot communicates this faster than any table.

In Plotara

Two-way, N-way, repeated-measures and mixed ANOVA with Type II sums of squares, and a summary stating the model-level verdict and each individual effect separately.