# Multiplicity adjustment in correlation analysis

##### Member
Hi everyone,
I would like to know the opinion of experienced statisticians. If I perform a correlation analysis: calculation of 20 correlation coefficients: one variable with 20 other variables, should I correct for the multiplicity? If such an adjustment is needed, then which method is most appropriate?

#### Karabiner

##### TS Contributor
What is the topic of your research, and what are the reserach questions?
And what do these 21 variables represent? And how large is your sample
size?

With kind regards

Karabiner

##### Member
It is a retrospective study of the causes of pain in the spine. One variable is the measured pain (VAS), the other variables are different characteristics of a patient: age, BMI, various measurements of the back condition: facet degeneration, facet sclerosis, modic changes score, Pfirrman score and other. There was 133 patients in the study.

#### Karabiner

##### TS Contributor
Some kind of multiplicity adjustment seems reasonable here, but it also depends on what you will further do with the results of your analyses. What will happen on the basis of statstically "significant" or "nonsignificant" results, respectively? It looks like all the factors you include in your analysis may have alreaday been studied extensively in the past?

With kind regards

Karabiner

##### Member
Thank you for answer! Yes, all these factors have been studied. These correlations were provided only in descriptive manner, we didn't plan to do anything with it. I think the better way is to leave coefficients without correction. Especially because the purpose of the work is slightly different - evaluation of the treatment efficacy.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I would use a correction, in particular you should try to stay away from pvalues and just report correlation coefficients with adjusted confidence intervals. The Bonferroni correction is the easiest to conduct and explain.

I would also make note, given variable distributions, you may need to consider different types of correlation measures given variable formatting, instead of only using Pearson's, if that is what you were planning.

Thanks.

##### Member
hlsmith, thank you! Bonferroni correction is easiest, but I afraid that 99.75% CIs will be not very informative.
We used Kendalls tau because the distributions of some variables were far from the normal distribution and there were some extremal values.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Unfortunately, false discovery doesn't go on vacation if a sample size is small or there are a lot of bivariate comparisons. The opposite happens. false discovery comes knocking on your door even harder. If analyses are just for in-house use - do what you feel works. But if you plan to disseminate them - correct where necessary.