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One of the three conditions that should be checked before conducting two-sampled z-test for proportions is "check for normality"(link for the source: https://vitalflux.com/two-sample-z-test-for-proportions-formula-examples/). But how can we check whether binary data is normal?enter image description here

user378299
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    Most of this is garbage. (That's no criticism of you!) The final paragraph is especially egregious, because the principal distinction between a Z-test and a Student t-test is that the latter is indicated when the SD must be estimated: that's it's original claim to fame. – whuber Jan 24 '23 at 17:26
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    ok, can you help me to understand what requirements should I check to use z-test for proportions? For example I wanna use that python package https://www.statsmodels.org/dev/generated/statsmodels.stats.proportion.proportions_ztest.html – user378299 Jan 24 '23 at 18:00
  • This is extensively discussed in many of our threads about two-sample binomial tests. You can learn about alternatives to a Z test (that is, a Normal approximation) as well as read evaluations of standard rules of thumb for applying a Z test. – whuber Jan 24 '23 at 19:02

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Any assumption about normality is totally violated for a binary variable: normal distributions take values on the entire real line, while binary variables take two values, and $2\ne\infty$. Consequently, that reference is wrong about this topic and likely makes mistakes on other topics, too, and I would not trust it.

Dave
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