(Reply sent to DCH and to the list. -- DFB.) Dunno as I have an answer for you, but maybe thinking aloud (so to speak!) will stimulate an idea or two. Thinking of this in a slightly more general sense, and assuming that the persons or objects being correlated are the same at both times (because if they aren't you'd treat the coefficients as unrelated and wouldn't have a question), we have a correlation matrix of at least four rows & columns. To avoid messy subscripts, I'll use t = x at time 1, u = y at time 1, v = x at time 2, w = y at time 2. The question your querent wants to address involves comparing r(tu) with r(vw). (Side comment: formally equivalent, so far as I can see, to asking whether the pre-post correlation in x, r(tv), differs from the pre-post correlation in y, r(uw). In any case there are 6 different off-diagonal values, one pair of which is of particular interest here.)
My first question to your querent would be, "Why do you want to know?" What difference does it make if the correlations are indistinguishable, or if the correlation at time 1 exceeds that at time 2, or vice versa? And if you want to know only so's you can predict r(xy) at time 3, why not just wait and see (let the universe unfold as it will)? One interesting possibility occurs to mind: you could orthogonalize v and w with respect to t and u, yielding variables v* and w*; then r(tv*) = 0 and r(uw*) = 0, and with a certain amount of hand-waving one might be able to convince oneself that comparing r(tu) with r(v*w*) using the independent-samples method may be both (1) legitimate and (2) useful. If, as may be the case, the underlying concern is whether r(xy) remains approximately constant over time, I think of generating r(xy) at a number of different times. Then I might think of plotting r(xy) as a function of time, maybe surrounding each value with a suitable confidence interval, and looking for a trend that might be in danger of moving r(xy) at a sufficiently later time out of the CI for r(xy) at time 1. This too is hand-waving, since the CI presumably would incorporate the assumption that the several times did not entail troublesome effects from previous times. And I cannot resist pointing out that if the variables x and y are positively correlated across time (as one would tend to expect), a test that assumes independence across times will be less sensitive to real differences than a test (if one could be found or invented) that took those temporal correlations into account: that is, it would be "conservative". Anyway -- maybe that's worth 2 cents, but I wouldn't gamble on it. Good luck! -- Don. On Thu, 25 Mar 2004, David C. Howell wrote: > I was asked a question this morning that I can't answer (hardly a new > experience). It may be that the answer is obvious and that I just can't see > it, or that it is a question that does not have an easy answer. > > It is well known how to test the difference between correlations in two > independent samples. It is also well known how to test the difference > between r(xy) and r(xz) by taking into account the correlation between y > and z. But what about the correlation between xy and time 1 and xy at time > 2? Presumably we need to take into account the lack of independence between > Time 1 and Time 2, which means the correlation between x1 and x2 and the > correlation between y1 and y2. > > Can anyone tell me how to go about this? Am I just being blind? ------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
