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Let's say I have a classic dataset containing some data about participants. The data includes gender, weight, length, area code, income. Let's also assume that gender is binary encoded, whereas weight, length, income are numeric/continuous variables and the area codes are categorical.

I am trying to find some correlations between these variables with a simple Pearson test for each possible combination. You'll get the following pairs for which Pearson's is calculated:

gender - weight
gender - length
gender - income
gender - area
weight - length
weight - income
weight - area
length - income
length - area
income - area

When I showed these pairs (and their respective r-correlations and p-values), my promoter told me it seemed more logical to them to split up the dataset based on the binary variable, i.e., build two sets one where gender == 0 and one where gender == 1, and then calculate correlations for the remaining variables. So for each set, that would mean the following remaining pairs:

weight - length
weight - income
weight - area
length - income
length - area
income - area

When we have done this, we could then compare the results of both tests, they said. But I am confused, why would you do it like this? What is the benefit?

How I see it, in my approach you calculate the correlation between the gender variable and the other variables. You get a detailed analysis (r and p) so you know how big a role the gender variable plays for each variable. The proposed approach simply calculates something different: it will show whether the variables are correlated when gender is 0, and when it is 1 - but there is no information on how large the role is that the gender variable plays.

My question, then, is: what is the best approach if you are simply trying to find correlations between a set of independent variables? When should I split up my dataset in smaller datasets? And if I have split up my datasets, is there a way to find the impact of splitting up (i.e., the impact of the binary variable)?

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Fundamentally, correlations are bivariate. With a single correlation matrix, you have an assessment of the strength of relation of each possible pairwise combination of variables, but not accounting for any other variables.

Splitting the data by gender allows the correlations between two other variables to vary by group. This is essentially allowing an interaction--a coefficient relating two variables that depends on the level of the third.

That said, just splitting the group and eyeballing differences doesn't tell you anything about the precision or significance with which you have observed a difference. If you are interested in this interaction, but want to keep the bivariate relations non-directional, I'd recommend a multiple-group model in path analysis software. That would let you directly estimate and test differences in the covariances between any other two variables as a function of gender.

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