I have data from an experiment where performance y on two different devices was measured over three successive sessions. The 2x3 design is completely within-subject (see simulation code at the bottom). It is assumed that participants improve with every session due to training.
Two research questions (RQ) are crucial:
- What is the improvement from sessions 1 to 2, and 2 to 3 for both devices
- How do both devices compare at the last session
My problem regards the contrasts to use. Regarding RQ1, I would choose for successive difference (aka repeated) contrasts, as is provided by the MASS library:
library(MASS) contrasts(D1$Session) <- contr.sdif(3)
That gives me the desired indicators for successive improvement. However, the intercept becomes the overall mean (for the reference level of device), which is not what I want.
How can I create custom contrasts, that combines successive differences with a reference level?
Below is a simulation of the data set. In real, I'm going use mixed-effect models to account for repeated measures, but that is not of concern here.
library(ggplot2) library(dplyr) library(plyr) set.seed(42) D1 = expand.grid(Subj = as.factor(1:20), Device = c("A", "B")) %>% join(expand.grid(Session = as.factor(1:3), Device = c("A", "B")) %>% mutate(T = c(1,.75,.5625, 1,.66,.44))) %>% join(data.frame(Device = c("A", "B"), B = c(100, 120))) %>% mutate(Y = rnorm(120, B * T, 1)) D1 %>% ggplot(aes(x = Session, y = Y, fill = Device)) + geom_boxplot() D1 %>% group_by(Device) %>% summarize(mean(Y)) M1 = lm(Y ~ Session * Device, D1) summary(M1)