I am trying to compare a group's performance on a test over the course of three measurements*. Because of the nature of the testing on the 3rd measurement, I cannot directly compare data across all measurements. Therefore, I just standardized my data in SPSS and will now work with the "z-scores"

* [The grading scale for the test is from 1 to 100 points in the first two measurements, and for the third one is from 1 to 125 (this is an example)]

I want to see how their performance varies with age, i.e. if there is a correlation between age and performance. However, I have no clue what kind of correlation analysis I can perform since as far as I know Pearson's $r$ makes comparisons by making use of z-scores and I have deleted the effect of those.

  • $\begingroup$ You are right, I took it off $\endgroup$ – CoffeeSurfer Jul 29 '16 at 13:20

Since Pearson correlation may be defined as

$$ r = \frac{\sum_{i=1}^n Z^{(X)}_i Z^{(Y)}_i}{n-1} $$

where $Z^{(X)}_i$ and $Z^{(Y)}_i$ are $z$-scores of $X_i$ and $Y_i$, then by converting your variables to $z$-scores you are one step closer to calculating it! See also this answer, as it relates to your question: Can Spearman's correlation be run on z scores?

  • $\begingroup$ Perfect! One extra question actually - How does one perform a correlation analysis over repeated measures? (or do I post this elsewhere?) $\endgroup$ – CoffeeSurfer Jul 29 '16 at 13:27
  • $\begingroup$ This sounds like a different question. Check e.g. stats.stackexchange.com/questions/44134/… $\endgroup$ – Tim Jul 29 '16 at 13:30

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