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Consider a set of $100$ people, for each person we have 4 values which are: weight, height, age and the value of a medical exam, which will be called "A" for simplicity. I want to compute the correlation between weight and A, height and A and age and A.

Should I use one or two sided Pearson coefficient?

I computed the Pearson coefficient with the excel function (which I imagine is 1-sided) and the highest coefficient (all coefficients are >0) was the one of weight-A, about 0,077. But then I computed the 2-sided Pearson value with the help of this site http://www.wessa.net/rwasp_kendall.wasp#output and the coefficient of weight-A is the lowest (all coefficients are positive), the highest was the one of age-A, about 0,578.

What does it mean? Which coefficient should I consider?

Thank you

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Pearson correlation coefficient it's just one coefficient - the "one sided" or "two sided" are different ways of testing hyphotesis. This correlation estimator is suitable for continuous variables. In this case, if the value of a medical exam is measured in a continuous scale, then it is correct to use Pearson.

But if the results of the exam are coded in an ordinal scale, like "low", "medium" and "high"; then you should use Kendall coefficient.

In any case, when interpreting a correlation you should mention first its direction - positive or negative, and then its intensity, based on the p-value provided in your link (if it's larger than 0.05 then it is not significant) or based on your previuos knowledge on the subject.

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