I've performed a two-way ANOVA with two categorical variables that each have two levels (treatment vs. control and genotype 1 vs. genotype 2). I'm interested in whether or not genotype has a significant effect on response to treatment, so I want to test for an interaction. My initial test for interaction is significant:
model <- lm(y ~ genotype + treatment + genotype:treatment, data = df) summary(aov(model) Df Sum Sq Mean Sq F value Pr(>F) genotype 1 3.53 3.53 6.068 0.0299 * treatment 1 50.58 50.58 86.850 7.63e-07 *** genotype:treatment 1 2.86 2.86 4.903 0.0469 * Residuals 12 6.99 0.58
In terms of reporting, I would like to estimate the difference in treatment response due to genotype, but I am not sure how to frame this in terms of post-hoc testing. I.e., I want to estimate the difference of differences between (treatment - control)[genotype 1] vs. (treatment - control)[genotype 2] with confidence intervals and controlling for error rate. If I perform a Tukey HSD test, I get the pairwise differences:
TukeyHSD(aov(model)) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = lm) $genotype diff lwr upr p adj wt-ko -0.9398734 -1.771217 -0.1085296 0.0298603 $treatment diff lwr upr p adj ctrl-treat 3.555875 2.724531 4.387218 8e-07 $`genotype:treatment` diff lwr upr p adj wt:treat-ko:treat -1.78476896 -3.386802 -0.1827359 0.0277338 ko:ctrl-ko:treat 2.71097908 1.108946 4.3130121 0.0014610 wt:ctrl-ko:treat 2.61600122 1.013968 4.2180343 0.0019526 ko:ctrl-wt:treat 4.49574804 2.893715 6.0977811 0.0000129 wt:ctrl-wt:treat 4.40077019 2.798737 6.0028032 0.0000160 wt:ctrl-ko:ctrl -0.09497786 -1.697011 1.5070552 0.9979518
But I believe I now want to estimate the value of
ko:ctrl-ko:treat with an appropriate confidence interval (wanting to test if the difference is non-zero). Is there a way to supply a contrast to look at such a difference, or is this a separate analysis/test? And/or is this an appropriate analysis to pursue, or is the fact that the interaction term is significant the answer to my question (treatment effect depends on genotype), and does my attempt to associate this with an effect size (difference of differences) misunderstand the framework?