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If there's a given population X, and I chose to send out surveys to Y amount of people, but only Z amount of people respond - Would the sample size be Y, or Z? Survey Monkey states that the sample size is only the amount of responses received from the survey (respondents), while other websites state that it's the amount sent out and the amount returned does not change the sample size.

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Both numbers can be described as a sample size, because both the group of people you sent the survey to, and the subset of that group who responded to the survey, can be regarded as samples. It's common for research projects to have a hierarchy of samples, and hence a hierarchy of sample sizes, in this fashion. If you're wondering which number to report in the write-up of your study, the answer is that in general, you should report all of them.

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