[EMAIL PROTECTED] (nothanks) wrote: > I have a client who wants to compare the relationship/association > of two variables (Y1 and Y2) between 2 groups (say Gender). > They (statistically challenged) have left it to me to decide > on method (and how to measure association). > > Y1 and Y2 are ordinal, but are actually continuous variables > binned into 0, .5, 1, 2 and 3. So, I'm o.k. with treating them > as continuous.
Step 1: go back to your client and get the unbinned values, if it's at all possible. It seems unlikely that you will get better results by throwing away some information. At the very least you will have the opportunity to rebin the variables in the way most appropriate for the analysis you do. > 1) Fit a linear model Y1 = Y2 + Gender + Y2*Gender, > and see if the interaction term is signficant. > > I figured the differences in slope would give me a decent comparison of the > differences in association between Y1 and Y2, between the two groups. > Keep in mind, I'm not wedded to actually comparing the Pearson correlation. > Hence, > > 2) Use a Fisher's Z' Statistic to compare the Pearson Correlation. Keep in mind that a significance test of the usual kind will indicate a significant result no matter how small the effect, if the sample is large enough. By construction, statistical significance does not account for the practical consequences of the effect, so a significant result has no bearing on what your client should do. What your client should do will depend on the magnitude of the association between gender and the other variables, so you'll want to establish a way to quantify the difference in the distribution of Y1 and Y2 as a function of gender. BTW examining the interaction term Y2*gender, as suggested above, seems unnecessarily limited; you would not notice a change in intercept alone. Comparing Pearson correlations has the same problem. Stating something like "the difference of slopes is 0.053 and the difference of intercepts in 1.82" will immediately lead your client to ask, "So what?" The best way to measure the association would be in terms of the loss or gain the client receives as a result of ignoring gender or taking it into account -- that is to say, an economic criterion. It may or may not be difficult to formulate such a criterion for your client; but remember that any other kind of criterion is just a stand-in for net gain. A generally useful measure of association is the mutual information, which is measured in bits, and so MI has an absolute magnitude. On the technical side, the integral which defines MI can be difficult to evaluate, but it's nothing that creative and dedicated numerical analysis can't overcome. More seriously, MI is the appropriate economic criterion if you are compressing data in some fashion, and outside that domain its applicability is more tenuous. But recall the words of Mach -- ``The goal which it [physical science] has set itself is the simplest and most economical abstract expression of facts,'' so perhaps compression is what it's all about. For what it's worth, Robert Dodier . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
