Two-way ANOVA

A two-way ANOVA compares three or more sample means categorized by two factors.

Consider comparing the height of males and females from three age groups. Age is the row factor, and gender is the column factor.

State the null hypothesis that age and gender show no interaction effect on the mean height.

The interaction effect is visualized as two line segments formed by connecting the mean values of each factor.

The line segments of age and gender are roughly parallel, showing that the mean height of males and females is not affected by age and gender simultaneously.

Calculating the F statistic and P-value confirms no interaction effect, showing that age or gender independently affects mean height. We fail to reject the null hypothesis.

Next, check if age or gender affects mean height.

Separately state the null hypothesis, and compute the F statistic and P-values for age and gender.

Since age doesn't substantially affect mean height, we fail to reject the null hypothesis.

Whereas gender substantially affects the mean height. So, the null hypothesis is rejected.