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I have Likert-scale survey data in which the sample is 97% of the population (181 out of a possible 188 respondents). I have tried to follow the complex debate about the need and value of statistical inference tests when the sample is the population in the Cross Validated posts below (and elsewhere):

Statistical inference when the sample "is" the population

Is chi-squared necessary if comparing entire populations?

Does it make sense to compute confidence intervals and to test hypotheses when data from whole population is available?

I have now lost confidence in my thinking: a chi-square test seemed an obvious choice for me (2x5 table with ordinal data), although I am far from an expert statistician. My questions are:

  • Does it matter that my sample size virtually equals my population size when running a chi-square test?
  • Will the p-value be meaningful (ie can I consider the results in the usual way)?
  • Should I rather just do a correlation co-efficient to search out relationships since I don't need to infer from my sample to the population?

I would value any assistance, direction or being sent on to links where I can learn more.

GaryZA73
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    Are you really only interested in those 188 people? What if 189 people said they would do it? – Dave Apr 20 '21 at 15:01
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    To put it a different way, exactly what do you mean by "possible" respondents and "population"? If you can't clarify that, perhaps describe the actual population and your interest in their responses. – BruceET Apr 20 '21 at 16:12
  • Or to put it yet another way: do you only care about the results for those 188 people, or do you want to be able to generalize your results to other people similar to those 188? – EdM Apr 20 '21 at 17:19
  • Thank you for the questions, very helpful. The 188 are the total number of registered learners in a set of classes being surveyed; so I've seen this as my "population". But looking at your questions perhaps I should rethink my definition? – GaryZA73 Apr 20 '21 at 18:37

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