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I would like to analyse whether measures A, B, and C have a different influence on a measure D compared to a measure X on D. My exploratory hypothesis is that A, B, or C could influence Z negatively while X positively influences Z.

Additionally, I need to account for covariates. While the most obvious way would be to compare coefficients in a linear model, my small sample size requires me to serach for alternative analyses.

I received a recommendation to use the cocor R package for comparing partial correlation coefficients. This package mplements a z-test to compare the correlations between A~D and X~D (andother combinations) while correcting for the intercorrelation between A~X.

However, I have some doubts and questions regarding this analysis:

  1. Is this approach more powerful than using regression models, or is it similar (since I am correcting here for covariates as well)?

  2. To match the polarity between A, B, C, and X, I reversed the sign of X. My intention was to compare coefficients that have the same direction (+.3 means the same as +.4). However, the cocor z-test works with the difference between the two correlations, leading to different results (e.g., -.50 -(.30)= -.80 vs. -.50 -(-.30) = -.20!). I wonder if this kind of test is even meaningful in this context.

a.henrietty
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    In my understanding, partial correlations are not more powerful than multiple regression , they are more or less the same thing. This answer may help. What is your sample size? Comparing correlation coefficients within a small sample seems doesn't seem like a good idea to me but I may be wrong. – Sointu Aug 05 '23 at 07:44
  • How small is your sample? How many covariates? But, in general, you can't get around the small sample size by using different methods. HOWEVER, you might try a permutation test. – Peter Flom Aug 05 '23 at 12:02
  • Sample size is 24 @Sointu – a.henrietty Aug 05 '23 at 12:39
  • Number of covariates ranges between 1 and 6 (plus the 2 predictors of interest) depending on the predictors and dependent variables.. @PeterFlom – a.henrietty Aug 05 '23 at 12:39

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With 24 observations, you are going to be very limited. Even just the 2 predictors is running the risk of overfitting. Adding covariates will make it very very likely to overfit.

There is an old book by Rick Hoyle called Statistical Strategies for Small Sample Research that might help, but I read the book 20 years ago and don't remember exactly what's in it.

Peter Flom
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