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I sent a postal questionnaire to 1618 schools. In total, 220 responded (13.6% response rate). For one question, which had Yes, No and Don't know response options, 217 schools responded (Yes=85, No=127, Don't know=5). I'd like to find the margin of error for Yes, No and Don't know (with 95% confidence) so I can work out what the responses for each would have been if all 1618 schools had responded.

Do I work out the overall margin of error based on the response rate for the whole questionnaire (i.e., 220 of 1618 schools) and apply the upper and lower % to this particular question, or do I use the response rate for each answer in this particular question to find out the margin of error? For example, for Yes, should I use 85/1618, 85/220 or 85/217 to work out the margin of error? There is a big difference in results depending on which one I use.

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If you assume that the schools that responded are a random sample of the total, then statistical calculations would be useful. But it seems likely to me that the 14% of the schools that responded are likely to be different in important ways than the 86% that didn't bother to answer. If so, statistical calculations would be misleading/unhelpful/pointless.

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  • $\begingroup$ Many thanks for your reply. I appreciate you getting back to me about this. Based on the responses to other questions in the questionnaire, I would assume that the 220 schools that responded to the questionnaire are a random sample of the total 1618 schools. Should I use 85/1618, 85/220 or 85/217 to work out the margin of error for this specific question? Thanks again. N $\endgroup$
    – user53557
    Aug 6, 2014 at 14:55
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    $\begingroup$ Not 85/1618! That would be very misleading, implying that everyone who didn't send back the questionairre would have answered no. 85/217 is the fraction of those answering yes or no who answered yes. 85/220 is the fraction of those answering yes, no or don't-know who answered yes. $\endgroup$ Aug 7, 2014 at 15:42

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