# Rho Spearman correlation test interpretation for sample equal to population

I have done a pair of cuestionaries to measure a pair of variables in a small population, 87 people, so I have taken the whole population as a sample, the cuestionaries have likert scales as answers (5 levels). I decided to use rho spearman test to analize the correlation between both variables. I am not sure if i can interpret the p values, I mean, if I have taken the whole population it means there is no error from sample variation right? and if I can$$`$$t use the p-value, should i just interpret the correlation coefficient instead? or there is another way to analize correlation when im taking the whole population?

I decided to use rho spearman test to analize the correlation between both variables.

What do you mean by "analyze"? What substantive question are you trying to answer (the actual research question, not an attempt to translate it into a statistical question).

I am not sure if i can interpret the p values,

Not the ones you obtained, no.

The p-value you have was computed assuming you're sampling an infinitely large population (or that you're sampling with replacement); ether way it's not the case, since you're sampling without replacement until you obtain a complete census.

If you calculate the "sampling without replacement" distribution of your correlation correctly it will have variance zero once you collect the entire population (and so any non-zero observed correlation would have p-value 0 -- it's certainly different from 0); these points are perfectly consistent with the understanding that "we have the whole population so we know the value of the population correlation exactly; there's nothing to test, we can just look to see what the population value is".

should i just interpret the correlation coefficient instead?

You haven't identified what the point of your analysis is, so this is not possible to answer. Likely yes, but we can't tell until you make the question you're trying to answer from the data more clear.

• The question that I'm trying to answer is if there is or not a relation between the two variables. It is a descriptive study, I aim to describe the level of each variable and the possible relation between them. – WalquerX Feb 15 '19 at 3:15
• +1. Walquer, It's certainly the case there is a "relation" between the two variables: it consists of precisely what your data indicate. It's likely not a linear relation, though. This line of reasoning quickly becomes unproductive: it is extremely rare that the extent of conclusions one wishes to draw are limited to a set of subjects whose responses were measured perfectly (with no error), which is what you assume. – whuber Feb 18 '19 at 0:09