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I am wondering why/when would I be indicated to use the Fisher Exact Test as Opposed to calculating a Z-score for a test for two proportions?

I am assessing some proportions, and my understanding is that Z-score should only be used if my sample is representative of the entire population? Is that correct?

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If your sample is not representative of the population, then no statistic can be used. Fisher's exact test will (at most) give you a more precise estimate of the wrong number.

NOTE: I know there are some complex exceptions but in this context, I think the simple declarative sentence is better.

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  • $\begingroup$ I think the OP is thinking of a randomization test as a test that can be used for inference even when a sample is not a random sample from a population. $\endgroup$
    – Heteroskedastic Jim
    Commented May 10, 2018 at 12:51
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    $\begingroup$ I'm not sure what OP is thinking, but how would a randomization test work with a biased sample? You'd still get a biased estimate. $\endgroup$
    – Peter Flom
    Commented May 10, 2018 at 12:57
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    $\begingroup$ Without invoking a population, we can use randomization tests to test a zero null effect of group assignment. I guess I shouldn't have used the word, inference. $\endgroup$
    – Heteroskedastic Jim
    Commented May 10, 2018 at 13:04
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    $\begingroup$ OK, that's true. But I don't think it relates to this question. I think the OP is just starting out and having a rather basic confusion. $\endgroup$
    – Peter Flom
    Commented May 10, 2018 at 14:46

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