correlation and Bonferroni correction

[Silke Matura]

Hello,

Correlating neuropsychological test scores with brain imaging data, I have done two correlations with the same data set. Since one variable is not normally distributed, I have used Kendall’s tau correlation for that variable (Recognition scores) and for the normally distributed variable (cued recall) I have used Pearson Moment correlation. The reviewer has asked for Bonferroni correction, since I have done multiple (two) correlations with the same data set. I am unsure if Bonferroni correction is necessary since I have used two different statistical tests for correlation (Kendall’s tau and Pearson Moment correlation). I would be very grateful for your comments on this issue.

Best,

Silke

[Dave Collingridge]

Generally speaking, running multiple tests on the same data requires adjustment to control for Type I errors, I think this would apply to different correlations on the same data. If the results of the same tests are significant after correction (i.e., p< .05/2 or 0.025), then give the reviewer what he/she wants. If the results were not previously significant then a bonferroni will not change anything either. If one of your tests becomes non-significant and this bothers you then consider changing to a one-tail test if you have not already done so, assuming that a one-tailed test is justified in that you expected the difference to occur in a certain direction. If that does not work then ask yourself whether your study is exploratory or causal in nature. If a study is exploratory then I think that one is justified in not running a correction for fear of missing potentially meaningful findings that should be explored in a follow up study with more controls. If that does not work run a power calculation. If your power is low due to low sample size that can be a reason to not use a correction like bonferroni. If that does not help then consider reporting both corrected and uncorrected results. If you must report non-significant results due to a correction, you are always free to inject your own views which may be that the results are significant, but you were unable to show it statistically in your study.

[Dave Collingridge]

Silke, mir sagen wenn einer meiner Vorschläge für Sie geeignet ist.

Dave

[Silke Matura]

Lieber Dave,

sorry that I haven’t replied to your suggestions yet. Your suggestions were very helpful. I think I will go for the power analysis – the sample size was not very big (n = 63) and that might have resulted in low power. I read some comments by Andy Field  and he stated that the correlation coefficient (Kendall’s Tau) can be interpreted as the effect size and that p-values for correlations are usually not as meaningful as the correlation coefficient. Since the analysis produced a pretty decent tau auf 0.39, I am quite confident that there really is a meaningful correlation, although the p-value is slightly larger (0.035) than it should be (0.025). Anyhow, I am very grateful for your help and impressed by your German.

Best,

Silke

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