I am measuring two continuous variables (X,Y) for 21 subjects. X and Y have 216 data points each (per subject). I would like to see if X and Y are correlated at the group level. I can think of 3 options:
a) Concatenate all the subjects together and compute the correlation. I believe this method will inflate my Type I error rate quite a bit and seems like a bad idea.
b) Run a separate correlation for each subject, and then run a 2nd level analysis to see if the t-values from each correlation are significantly different from 0 (single sample t-test). This seems to be quite prominent in analyzing fMRI data at the group level.
c) Construct a mixed-effect linear model, treating subject as a random variable. I've done this in R using
lmer(y ~ x + (1|sub)) and got the same result as b, albeit a different p-value. However, I use R infrequently and am somewhat suspect when
pvals.fnc reports a p value of "0" (which I interpret as less than .0001).
What is the proper way to run this analysis, and more specifically what are the differences between (b) and (c)?