This paper might be of interest: "In our study we confirmed the existence of a misconception with respect to Pearson's correlation coefficient, which has not been systematically and empirically documented until now. A large number of students appears to think that, given three quantitative random variables X, Y, and Z, a positive correlation between X and Y, and a positive correlation between Y and Z, X and Z are always positively correlated."
However, if you really do have the data (and L1 to L4 are variables in the columns of a JMP table), you can just use 'Analayze > Multivariate Methods > Multivariate' to investigate. But, then again, perhaps I misunderstand your question.
Thanks Ian for your response. I will read the paper. The correlation between groups are with the same devices. For correlation of L1 & 2, we have the data but not the same devices.
The devices in L1 and L2 together are the sames as devices in L3 and L4. The correlation between L1 and L3 is done for matched devices in between L1 and L3 and similarily for L1 and L4, and so on. The question is whether we can say that L1 and L2 are correlated or not. We don't have the same devices for L1 and L2. Please let me know if I am not clear.