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I am struggling to understand what "number of samples" for correlation tests refers to.

Let's say you run a correlation test between weight and age.

You take 12 measurements of weight, and 12 of age, and find a positive correlation.

You decide to report the results as "Weight and age showed a positive correlation (r coefficient, number of samples, significance level)...".

Is the number of samples 12 (the number of measurements taken for each variable), 2(the number of variables) or 24 (the total number of variables used in the correlation test)?

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If you are looking at the correlation between two variables, it means they have been measured together. If I took 24 people and asked 12 their weight and 12 their age, could I say anything about the association between the two? Of course not. You ask the same 12 people for both and look at how the two quantities are associated. So you've sampled 12 'things' but taken two measurements for each.

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Sample size is N. In your case it equals 12. If one variable had one missing value, it would be 11.

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