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Let's say my survey population size is 1000 and I send a survey to all 1000. And only 200 responded. Is the 200 considered my sample size? If yes, can I calculate a margin of error on the questions in the responses?

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  • $\begingroup$ You conducted a census with a 80% non-response rate. In your place, I'd be worried about participation bias and volunteer bias.(See en.wikipedia.org/wiki/Participation_bias methods.sagepub.com/reference/encyc-of-research-design/n492.xml ). If your question is if it's reasonable to simply ignore this non-response problem and treat it like a random sample without giving a thought about it, then unfortunately it's probably not. There may be ways to deal with this issue, but it's difficult to suggest something without more info about the survey and the population. (cont'd) .../... $\endgroup$
    – J-J-J
    Apr 5, 2023 at 19:52
  • $\begingroup$ .../... For example, do you have some other relevant information about the whole population (gender, age...), that would allow for a comparison with the respondents? What are some of the questions you asked and the answers the respondents could give? etc. $\endgroup$
    – J-J-J
    Apr 5, 2023 at 19:54

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Good question. I think it depends on what you are planning to do with that data. For a regression model or hypothesis tests, you'd probably consider 200 as the sample size as you are not including these non-responses in the model. On the other hand, if you are using something like a decision tree (or any machine learning extension like random forests), you might include missing responses as an explicit outcome (probably not for 800 out of 1000, but in principle you might). I believe in your use-case it would be 200.

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