The null hypothesis is that there is no interaction between columns (data sets) and rows.

Therefore it computes P values that test three null hypotheses (repeated measures two-way ANOVA adds yet another P value). Two-way ANOVA partitions the overall variance of the outcome variable into three components, plus a residual (or error) term. The F ratios are not very informative by themselves, but are used to determine P values. If the null hypothesis is not true, the F ratio is likely to be greater than 1.0. If the null hypothesis is true, the F ratio is likely to be close to 1.0. Each F ratio is the ratio of the mean-square value for that source of variation to the residual mean square (with repeated-measures ANOVA, the denominator of one F ratio is the mean square for matching rather than residual mean square). For each component, the table shows sum-of-squares, degrees of freedom, mean square, and the F ratio. Most scientists will skip these results, which are not especially informative unless you have studied statistics in depth. The ANOVA table shows how the sum of squares is partitioned into the four components. Variation among replicates not related to systematic differences between rows and columns. These are differences between rows that are not the same at each column, equivalent to variation between columns that is not the same at each row. The ANOVA table breaks down the overall variability between measurements (expressed as the sum of squares) into four components:

Others call these values eta squared or the correlation ratio. These values (% of total variation) are called standard omega squared by Sheskin (equations 27.51 - 27.53, and R 2 by Maxwell and Delaney (page 295).

The remainder of the variation is among replicates (also called residual variation). Prism tabulates the percentage of the variability due to interaction between the row and column factor, the percentage due to the row factor, and the percentage due to the column factor. Two-way ANOVA divides the total variability among values into four components.

For example, you might measure a response to three different drugs in both men and women. Two-way ANOVA determines how a response is affected by two factors.

Graphpad prism 8 two way anova