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I am running a bivariate correlation analysis in SPSS, and I am performing multiple comparisons (there are 8 variables in total). I want to correct for multiple comparisons because I am aware that any 'significant' results could simply be flukes.

However, the Bonferroni correction is not appropriate in this case (it is too strict).

Does anyone know how to correct for multiple comparisons in SPSS?

Consider some sample data as follows. There are 4 'independent variables' and 4 'dependent variables'.

Independent variables:

  1. Blood flow through middle cerebral artery
  2. Blood flow through anterior cerebral artery
  3. Blood flow through posterior cerebral artery
  4. Blood flow through anterior communicating artery.

Dependent variables

  1. Performance on cognitive test #1
  2. Performance on cognitive test #2
  3. Performance on cognitive test #3
  4. Performance on cognitive test #4

The 4 'independent' variables are not uncorrelated to each other. The 4 'dependent' variables are also not going to be uncorrelated to each other (i.e., if a person does well on one test, chances are they will also do well on another test).

(I realize that it is wrong to call these variables 'independent' and 'dependent', since correlation does not prove causality, but this is the way that I have framed them in my mind)

I suppose that there are 2 problems here:

  1. how to correct for multiple comparisons (from a statistics point of view) and
  2. how to actually implement this in SPSS (a practical problem).

Any help would be much appreciated (especially for problem #2).

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1 Answer 1

This first part of my response won't address your two questions directly since what I am suggesting departs from your correlational approach. If I understand you correctly, you have two blocks of variables, and they play an asymmetrical role in the sense that one of them is composed of response variables (performance on four cognitive tests) whereas the other includes explanatory variables (measures of blood flow at several locations). So, a nice way to answer your question of interest would be to look at PLS regression. As detailed in an earlier response of mine, Regression with multiple dependent variables?, the correlation between factor scores on the first dimension will reflect the overall link between these two blocks, and a closer look at the weighted combination of variables in each block (i.e., loadings) would help interpreting the contribution of each variable of the $X$ block in predicting the $Y$ block. The SPSS implementation is detailed on Dave Garson's website. This prevents from using any correction for multiple comparisons.

Back to your specific questions, yes the Bonferroni correction is known to be conservative and step-down methods are to be preferred (instead of correcting the p-values or the test statistic in one shot for all the tests, we adapt the threshold depending on the previous HT outcomes, in a sequential manner). Look into SPSS documentation (or Pairwise Comparisons in SAS and SPSS) to find a suitable one, e.g. Bonferroni-Holm.

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