I have developed a special hearing test and carried out a study on the
effect of musical training on the test scores. Briefly, the results
are as follows: When subjects are categorized as "professionals",
"amateurs", and "non-musicians" (nominal variable), there is a large
difference between groups (unpaired t-tests). When a correlation is
calculated between the continuous variables "hours of previous musical
training" (which is linked to the nominal variable of ?subject group?)
and "test scores", as expected, the result is also highly significant.
However, this does not provide any information, whether the effect is
due to a priori differences between the groups (e.g. musical talents;
form of training) or to the time spent with training. I therefore
calculated correlations within each single group. In this case, in
none of the groups a correlation "hours of training"-"test score" was
observed. This suggests that only between-group differences are of
importance (either because of differences in musical talents or the
form of musical training), but that the time of training, per se, does
not have an effect. However, before I accept this result I want to
make sure that the loss of correlation is not simply due to a
reduction in sample size. The total number of subjects was 62 (21
professionals, 22 amateurs, 19 non-musicians). So it would be a great
advantage to retain the sample size of 62, while treating the factor
of "musical experience" (the 3 nominal groups) as something like a
covariate, in order to isolate the effect of "hours of training". My
question is whether it would be legitimate to perform a
z-transformation within each of the groups (means of 0 and standard
deviation of +-1) and then to calculate a gross correlation across all
62 subjects. Or do you see any other possibilities?

Thank you very much for your support.