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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?

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    $\begingroup$ How exactly do you do the reordering? What is the reason for doing this? $\endgroup$
    – Christian Hennig
    Oct 5, 2022 at 9:06
  • $\begingroup$ @ChristianHennig I don't follow you, which part of my post are you referring to? $\endgroup$
    – goingnuts
    Oct 5, 2022 at 13:57
  • $\begingroup$ " 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? $\endgroup$
    – Christian Hennig
    Oct 5, 2022 at 20:01

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The pairing between the two variables is paramount when it comes to any kind of investigation of dependence or independence. If your data entry introduced or destroyed patterns, and you cannot go back to see what the true pairing was, the results from your false bivariate data are worthless, arguably fraudulent.

I think that’s the right way to think about it: while your lab equipment measured every univariate value you report, your bivariate data are made up.

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  • $\begingroup$ I would argue that there is no "true pairing". While all of us have two pair of each chromosomes, the decision to call each item of the pair chromosome A or B is arbitrary. The measures are obtained by observing two physical lines in the same run (see the wiki page for western blot for an image similar to the one obtained). How would you address the data entry then? $\endgroup$
    – goingnuts
    Oct 5, 2022 at 13:51
  • $\begingroup$ If there is no true pairing, then I do not see any meaning to the multivariate probability distribution you are trying to infer. You just have unrelated observations of multiple variables. If, however, you have observations that correspond to the same subject (in some sense of a subject), that would represent a true pairing. If your data entry lost this information, then I see your options being: 1) Do the experiment again and collect meaningful data 2) Falsify data and commit fraud. I oppose the latter option. $\endgroup$
    – Dave
    Oct 5, 2022 at 13:56
  • $\begingroup$ 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. $\endgroup$
    – whuber ♦
    Oct 5, 2022 at 14:52

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