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I'm currently analyzing the data of an experiment and faced a couple of questions. I want to test the hypothesis that: Variable A predicts Variable B.

The two variables are the results of 2 tests. Variable A is the average of items 1-22. Variable B is the average of 3 test components. Variable A is not normally distributed. B is normally distributed There is no linearity between the 2 variables. There is a very weak correlation after testing with Spearman's rho (0.18) and Kendall's tau (0.13).

Initially, the experiment had 4 conditions. Could the bad correlation and the no normal distribution be explained because of the 4 conditions and should I look for the correlation within the groups then - like testing for correlation between A and B in the first condition, then in the second, and so on...

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  • $\begingroup$ I think more information is needed. If I understand correctly, you ran a test with 4 conditions and measured A and B (both continuous?) in each condition. But you say you "initially" had 4 conditions - what does that mean? Was the design within or between-subjects? $\endgroup$
    – Sointu
    Commented Aug 23, 2022 at 7:39
  • $\begingroup$ Hello Sointu, yes, they are both continuous and it's a between-subject design. I decided to not look for differences between the groups, because it's not what my hypothesis aims to answer. The thing is, the data that I have is collected through those 4 conditions. I found out that A variable is normally distributed in 3 out of 4 conditions and I thought that's a point for further analysis and that I did the correlation analysis wrongly. This is what i did in SPSS: - Analyze - Correlate - Bivariate - Kendal/Spearman -OK. $\endgroup$
    – eagersquirrel
    Commented Aug 23, 2022 at 14:53

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OK, thanks for the clarification!

I don't think I have a great answer, however: if you want to include the experimental conditions in the analysis, and B is roughly normally distributed in each of the 4 conditions (or maybe drop the one condition where it's non-normally distributed, though that may be problematic), you can use ANOVA with condition as a fixed factor, B as the dependent, and A as a covariate, and include an interaction effect between condition and A (In SPSS Analyze...General Linear Model...Univariate... and then use the "Build terms" option). Then, if the interaction is significant, you can check the relationship between A and B separately for each condition.

If we ignore the experimental conditions (and ignoring them may present problems, but that's something you need to consider based on your design, research questions, and measures), you could first make a scatterplot of A and B (in SPSS Graph...Chart builder...Scatter/Dot...) and check if there are any curvilinearity (a U or inverse U -shaped relationship) between them. If there is, you could perhaps use a regression model with A and A-squared predicting B. A does not have to be normally distributed for this. However, establishing a curvilinear relationship typically requires quite large sample size.

If the relationship is even more complex (based on your visual inspection of the scatterplot), then I'm not sure what to do - maybe some type of non-parameteric regression.

In my opinion, just computing correlations separately for each condition is not the right way here.

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