I have computed multiple Pearson’s correlations for different neuropsychological and sociodemographic variables in the same sample (e.g. correlation age and memory performance, correlation education and attention performance etc.). Now I wonder wheter I have to correct the p value for multiple comparisons. When is correction for multiple comparisons necessary in correlational analyses and when not? I would be very happy for an answer.
You could say it depends. If your study is largely exploratory then I would not recommend correcting for multiple comparisons. It is possible to be too strict when controlling for alpha inflation and miss potential associations. If your study is more cause and effect then it may be a good idea to correct for multiple comparisons if you repeatedly analyse the same data.