Imagine for a moment that your research involves many participants, each measured on an array of predictor variables and a focal criterion variable. Imagine that, working in exploratory mode, you correlate each variable with the focal criterion variable. After you do this, you want to know whether one of the variables is more strongly associated with the criterion than the others - or a number of others. Alternatively, imagine that, working in confirmatory mode, you have a theory that predicts one variable will be more strongly associated with the criterion variable than the others.
How do you go about testing either of these things? Well, thanks to Meng, Rosenthal, and Rubin (1992), you might do it by testing contrasts among a set of correlated correlations with the following equation:
Where the upside down y is contrast weight for each X, the zr is the fisher's z transform for X on Y, rx is the median inter-correlation between Xs, and h is found by equations 2 and 3. So the full thing boils down to three equations:
We can use the code from my previous blog to find h. So that's sorted. It's just the rest we need to worry about.
The following code allows you to play along with the example in the paper. As per usual, it can be very easily modified to use with you own data. Just plug in your own coefficients, the N, and median inter-correlation. Then plug in the your contrast weights in the second step. Important: As with most of the R scripts on this blog, it wont work if the psych package is not installed and loaded.
So did you want to test whether one thing you're interested in is correlated with something to a greater or lesser extent than a bunch of other things? You can do that with this method.
No comments:
Post a Comment