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Suppose that, from a finite population, we estimated the minimum sample size as 1000 to reach our desired confidence level and error.

Data was collected using an online survey and the survey remained open after reaching 1000 to increase sample size and get more precise estimates.

3000 questionnaires were collected but, due to the way the information about the questionnaire was spread, we observed some selection bias and the distribution of some variables is quite different from the population. E.g.: 1800 female and 1200 male while in the population the share is around 50%.

  • Can I RANDOMLY discard 600 female questionnaires to get a representative sample and do my analysis?

  • Considering the problem arises also to other variables, if I do the same, applying DIFFERENT cuts for each analysis (always focusing on the "exact strata" for the dependent variable, for instance), what are the statistical implications?

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  • $\begingroup$ Sounds like you might be interested in doing a weighted analysis. $\endgroup$
    – David B
    Commented Feb 9, 2023 at 1:54
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    $\begingroup$ You definitely don't want to do this. You want to post-stratify. $\endgroup$
    – num_39
    Commented Feb 9, 2023 at 8:59

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I'd not advise throwing out data, but instead doing post-stratification weighting. When you have multiple known demographic targets (e.g. sex, age group, location etc.), the "rake" of Deming & Stephan can adjust the weights on such that all targets are hit simultaneously. A copy of their paper can be found here.

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