# Pearson and non-zero correlation

I have data from a genetic experiment, where we have two lenght measurements from each subject (one for each chromosome). In normal conditions I would expect both variables to be normally distributed with similar mean and sd, and fully independent one from the other. From a technical point of view, both measures are acquired at the same time, and entried in the dataset as "minor" and "major", but could as well be exchangeable.

I want to check if in my sample diverge from the norm a.k.a. if there is a greater degree of similarity in lenght than expected by chance (i.e. because of hidden consanguineity).

I found a strong correlation on Pearson's. However, the scatterplot suggested me that this finding was at least partially the result of the way I entered the data. I thus simulated on SPSS two continuous variables with random normal distribution, same mean and sd, and 0 correlation. If I re-ordered each pair in a "minor" and "major", a r = 0.5 circa pops-up, supporting the fact that I introduced a significant artefact and my baseline is not 0.

It still seems to me that in my original data the correlation is greater than expected even taking in account this artefact, however I am stuck: how to demonstrate it? I have no rational way to enter the data in another order; should I just randomize each pair and test the randomized order? other solutions?

• How exactly do you do the reordering? What is the reason for doing this? Commented Oct 5, 2022 at 9:06
• @ChristianHennig I don't follow you, which part of my post are you referring to? Commented Oct 5, 2022 at 13:57
• " If I re-ordered each pair in a "minor" and "major"" - what exactly are you doing there? And is this the same that was done to the original data? Commented Oct 5, 2022 at 20:01

• That strikes me as being unnecessarily harsh. Another way to think of this situation is that Pearson's $\rho$ does not mean what it usually does, because these data are not independent. From this perspective there's nothing "fraudulent" about the data; there is only a misinterpretation of the correlation coefficient.