Big picture

If there are only two rows and two columns, Prism (starting with version 8) reports the interaction confidence interval. The interaction is defined as (A1 - B1) - (A2 -B2), where each of those values is the mean of replicates in one of the four cells.

Calculation details ANOVA

•The standard error of the difference is computed using the equation below, where MSresiduals is the mean square of the residuals reported in the ANOVA table, and the four n values are the four sample sizes.

•The margin of error equals SEdifference multiplied by the  critical value of the t distribution, using the residual degrees of freedom reported in the ANOVA table.

•The confidence interval equals the difference between means plus or minus the margin of error.

Calculation details mixed model

In this case the computation of SE(differences) is more complicated. General idea is using of respective contrast that defines this kind of comparison ((A1-B1) - (A2-B2)) and estimated covariance matrix.