I have numerous non-normal distributions that, for the most part, have the same shape (n = 190). The variables are test scores and have a floor value of 5 and maximum of 50. They appear to be highly correlated, however this is not consistent with theory. Our sample was biased because we explicitly tried to recruit individuals on the lower end of V1. We did not target lower score individuals on the other variables (V2 in this case).
Graphically examining where low scorers on V1 fall on V2+ suggests that they stay in the low end of the distribution whereas those who score in the middle of the V1 distribution fall more widely on the distribution of V2+. Is there anyway to test for this difference? Specifically that when you score low on V1 it predicts your scores on V2+ more than if you score average on V1.
I provided two images of the distributions with one showing a section of the middle of V1 and the other showing the low scores of V1 and where these two groups fall on V2.
if you have a sound theory, you can categorize V1 into two groups: low vs. high
Then you can test the mean difference between the two groups for V2 (as DV) using ANOVA.
Hello Zachary,
With independent batches, the Fisher-z method offers a simple way to compare correlations across groups (see this link: http://vassarstats.net/rdiff.html).
If one of your samples was chosen purposively for having extreme scores on a fallible variable (e.g., V1), then the "regression effect" alone will account for some apparent absolute/relative score location differences or "movement" on a second fallible variable. Do bear this in mind when interpreting the results of your comparison(s).
Good luck with your work.
Try to perform a Spearman Theil modeling and check linearity and correlation, you can rely on a T statistic for this.
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