This is complete reEdit of my orignal question
Let's assume I'm working on RT data gathered in a repeated measure experiment. As part of my usual routine I always transform RT to natural logarytms and then compute a Z score for each RT within each partipant adjusting for trial number. This is typically done with a simple regression in SPSS syntax:
split file by subject.
/STATISTICS COEFF OUTS R ANOVA
split file off.
#Following variable is what I would get after using SPSS code
sym<-data.frame(ob, trial, rt, cond, ZreSPSS)
group_by (ob) %>%
obM=mean(rt), obSd=sd(rt), zRev=z*obSd+obM)
magrittr, you should be able to calculate z-scores within individual with this code (it breaks things into the groups you tell it to, then calculates within that group).
experiment %<>% group_by(subject) %>% mutate(rtLN = log(rt) , ZRE1 = scale(rtLN))
You should then be able to do use that in your model. However, one thing that may help your shift to R thinking is that you can likely build your model directly, instead of having to make all of these columns ahead of time. For example, using
lme4 to treat
subject as a random variable:
withRandVar <- lmer(log(rt) ~ cond + (1|as.factor(subject)) , data = experiment)
Then, the residuals should already be on the correct scale. Further, if you use the z-scores, you probably should be plotting on that scale. I am not actually sure what running with the z-scores as the response gains you -- it seems like you would lose information about the degree of difference between the groups.
That is, if the groups are tight, but the difference between them varies by subject, a z-score may always show them as a similar number of z-scores away. Imagine, for example, that you have two subjects, one scores (1,1,1) on condition A and (3,3,3) on condition B, and a second subject that scores (1,1,1) and (5,5,5) -- both will give z-scores of (-.9,-.9,-.9) vs (.9,.9,.9) -- losing the information that the difference between A and B is larger in subject 2.
If, however, you really want to convert back, you can probably use this to store the subject means and sds, then multiply the residuals by
subjSD and add
experiment %<>% group_by(subject) %>% mutate(rtLN = log(rt) , ZRE1 = scale(rtLN) , subjMean = mean(rtLN) , subjSD = sd(rtLN))