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I have been struggling with this statistical issue for quite some time. I have four continuous variables. Thus far, I have found that correlations AC and BC are significantly different from one another. However, I would now like to find out if a fourth variable, D, explains that difference. The sample size is ~450 individuals. A, B, C and D are all summed scores of psychological questionnaires.

My goal is really to create a model such that a single P-value will tell me whether or not D significantly explains the difference between AC and BC. Is there anyone out there who knows how to do this? I would be beyond appreciative!!!

M BG
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  • Can you give some more details? Sample size? Nature of the variables (what do they represent in real life?) That would help understand what you mean by D explaining the difference. Maybe first regress out D and compute so correlations on the residuals? Or start out with some visualizations, examples in https://stats.stackexchange.com/questions/203494/can-i-analyze-or-model-a-conditional-correlation/368228#368228 – kjetil b halvorsen May 14 '20 at 12:50
  • Sure. The sample size is ~450 individuals. A, B, C and D are all summed scores of psychological questionnaires. My goal is really to create a model such that a single P-value will tell me whether or not D significantly explains the difference between AC and BC. Thank you for your help! – M BG May 15 '20 at 16:50
  • Can you please add that info (as an edit) to the ain post! Not everybody reads comments ... – kjetil b halvorsen May 15 '20 at 16:52
  • Okay, I edited the original! – M BG May 15 '20 at 17:08

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Interesting question. Sounds at first like a case calling for mediation, but on closer inspection, it's not. Nor is it a typical moderation (interaction) situation.

You could assess to what extent AC and BC are different at different levels of D. You'd have to divide D into categories -- with an overall N of 450, perhaps 3-6 categories would work well.

Moreover, you'd have to rely on descriptive results, whether tabular-numerical or graphical. There's no inferential test I can imagine that would produce a p-value for your correlation differences, because there's no null-hypothesis process known to produce a certain distribution for the difference between one variable's correlations with each of two others. Without such a known distribution, you'd have nothing against which to compare your results and thus no basis for a p-value.

rolando2
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