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the significance does not only depend on the magnitude of the correlation coefficient, but also on your sample size!! The same coefficient of r=.40 could be either non-significant with a small sample size (maybe N=10 --> p=.25) or highly significant for a larger sample size (e.g. N=100 --> p=0.000037). The coefficient is the same, but the significance changes with sample size.

That is because the t-statistics for the significance test includes the sample size, t=r*sqrt((N-2)/(1-r^2)). As you can see, with growing sample size, t increases (p-value of the specific t-distribution in turn depends on df=N-2).

So, in your case, with quite a large sample size it is not surprising that approx all r> .105 are significant.

But this does not mean that some of your correlations are not nonsense correlations driven by other variables which you already partialed out, but this is with regard to content and not statistics per se. The same logic of p-values also holds for partial correlations, so if the inclusion of a third variable does not decrease the partial correlation below a specific level, it will still remain significant.

In my opinion you should think of r as an effect size and do not care so much about the significance. Is a very small, but significant correlation, e.g. r=.15 really of practical interest for you and your research (question)?? Does it explain variance of interest?


https://www.researchgate/post/All_correlations_significant_at_001_level_Is_it_okay

本文标签： significantcorrelationsLevel

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