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In the study I am conducting, (Group A) the correlation coefficient between black & white imagery and retention is given by R1 and is significant. And (Group B) the correlation coefficient between colorful imagery and retention is given by R2 and is significant.

When I compare R1 and R2 (correlation coefficient), I get R2>R1. Using the Fisher Z-Transform, I found that Zobs did not fall within the range -1.96 < Zobs < 1.96, and therefore they are statistically significant.

Can we deduce retention was NOT equivalent for both groups A and B. I am not sure how to best interpret this analysis. Kindly advise.

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Short answer: no

The fact that the correlations are different in both groups is different does not mean the retentions are significantly different. The black & white imagery could be different in both groups for example, while the retentions are similar. Also remember that correlation is a scale-free measure.

If you want to know about differences in retention between both groups, you should try comparing them directly with a statistical test, such as t-test or Wilcoxon rank sum test.

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  • $\begingroup$ That helps. I understand that it is not a good practice to compare R1 and R2 between the two groups. May I know in which type of situation do we use such kind of comparisons. Thanks $\endgroup$
    – Vyas
    Commented Sep 1, 2017 at 13:57
  • $\begingroup$ @Vyas I'm not very familiar with these types of analysis, but it could be that the relation between the two quantities is noisier in one setting than in another. This will lead to a lower correlation in the noisier setting, which can be detected by the Fisher z-transform you proposed. $\endgroup$
    – Knarpie
    Commented Sep 1, 2017 at 14:19

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