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Please note: the variables named in this example do not correspond with actual variable type values, but are simplified for clarity purposes.

I have 13 groups, each containing values X of, say, the weights of individuals of a country. So each of the groups contains data of a different country. Now, for each country we have a known value Y, e.g. how many neighbours the country has (which is fixed, not an average).

X for each group can contain a high number of samples from 1000 to up to 150000, such that all individuals within the population are measured, the sample is thus not a subsample.

Now, I want to correlate the mean value of each group, |x|, with Y. In this example, to see if the mean weight correlates with how many neighbours the country has.

My question is: can I correlate mean values? Or do I need to do the correlation on all values X with Y?

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No, you can not.

Using mean/median values will discard the original standard deviation each group sample, in this case the weights of individuals of countries, which is very valuable information.

E.g.: say that the mean of the first group was 1.1 with a standard deviation of 0.6 (e.g. due to a small sample size), and the second group was 1.9 +- 0.1. These standard deviations will influence the probability of the correlation coefficient, i.e. to determine whether the found correlation is statistically different from a correlation randomly encountered.

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