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I have collected data from all the exercise science degree programs in my nation through databases (thus representing the population under study).

  1. I would like to investigate whether certain credits awarded by degree programs are evenly distributed across the nation or is there any prevalence. I had thought of Levene's tests.

In addition, these degree programs are diversified according to 3 addresses (sports, preventive, management). 2) I would like to investigate the differences between the three addresses (sports, preventive, management) by comparing some variables they have in common to see if there is a significant difference and I had thought of ANOVA.

I just don't know if it makes sense to use inferential statistics if I have the whole population. How could I answer my research questions?

Can anyone give me a suggestion?

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    $\begingroup$ If you really, truly, conceive of this as being an entire static population, then you're stuck. The problem is that you will identify differences, but you have no basis to explain them: you can only describe and quantify them. If you wish to explain something, then you need a model for the processes that might have caused those differences. Such models often view your data as one realization of a process whose results could have turned out otherwise. In particular, they don't conceive of your data as comprising a single population. $\endgroup$
    – whuber ♦
    Commented Dec 29, 2022 at 16:19
  • $\begingroup$ related: stats.stackexchange.com/questions/32297/… $\endgroup$
    – J-J-J
    Commented Dec 29, 2022 at 17:13
  • $\begingroup$ Note that if you are in a time series domain (e.g., annual measures of European Union member nations), you do not have future states, so your inferential targets are future times in units (e.g., years in nations), even if you have complete information on member nations from all previous years. $\endgroup$
    – Alexis
    Commented Dec 29, 2022 at 17:48
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    $\begingroup$ Two little words that often help are "as if". We can think about the consequences of sampling variation even if we think we have an unrepeatable sample that is in principle the only outcome of a process. So, the Titanic sank in 1912, and there is no statistical re-creation of that accident and its data, but we can still consider the sample as if it were in principle repeatable. That is what we do with e.g. tests of sample association given the reported marginal and conditional frequencies. Similarly, the weather and climate are unrepeatable, but scientists still do statistics with the data. $\endgroup$
    – Nick Cox
    Commented Dec 29, 2022 at 18:31

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Inferential statistics allow you to use available data to infer something. When you have the entire population, you don’t have to infer anything. You have the answer. In that sense, inferential statistics do not make sense when you have the entire population.

However, I have seen many instances where people claim to have the entire population yet insist on doing inferential statistics, and it is clear to me that they do not have the entire population under study. Perhaps the population is not all people but all people who could have existed. (A related term you might hear is a “data-generating process”.) Consider if you are in such a situation.

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