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I have seen various articles putting error bars on distribution density of either ordered categorical variables or categorical variables.

$Q:$ When is it appropriate to put SE error bar on estimated distribution for an ordered categorical variable? Had my study been census, there would be no error bar. If my study cannot be repeated, then what I had is a fixed population and it would not make too much sense to put error bar. I can parse the error bar in frequentist case, for variation of mean estimator. Note for multiple categories, the error bars were not constrained to sum to 1. It seems that having more than two proportions with their error bars showing up is very undesirable.

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  • $\begingroup$ Could you please explain what a "distribution density" is for any categorical variable? $\endgroup$
    – whuber ♦
    Commented Aug 25, 2023 at 21:58
  • $\begingroup$ @whuber Sorry for bad wording. I mean distribution function or estimated pmf. $\endgroup$
    – user45765
    Commented Aug 26, 2023 at 0:10
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    $\begingroup$ Can you maybe add a link to such an article where they put error bars? How do the authors describe or justify the bars? $\endgroup$
    – picky_porpoise
    Commented Aug 27, 2023 at 9:49

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