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I have randomized strings undergoing two different tests. There's a pretty clear difference in their proportions, but it reminded me of apstats where you would often do 2prop Z-tests to compare to proportions given that they're normal and come up with a mathematical 'confidence level' as to how clear one proportion was greater than the other.

What is a randomized string? I certainly can't describe it as normal (there's no feature that tapers off in rarity in both directions). I can only think of the data as some uniform blob of stuff that happens to fail some tests slightly more than another uniform blob of stuff. Thinking about this made me wonder if there's some statistical method to compare the proportions I'm getting. In reality this isn't helping me at all given that I can just raise my samplesize as high as I want to be 'certain', but I'd imagine something like this would be useful to save computational power/time in some huge project.

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The two-proportion Z-test does not require normally distributed data. It is an "asymptotic" tests, in that it relies on the Central Limit Theorem for its justification: the sampling distribution of the "sample proportion" estimator appraoches a normal distribution as the sample size approaches infinity.

The actual underlying data are for both your "random strings" and the Z-test would be binomially distributed (i.e., each "bit" is a bernoulli(p) random variate, with P(1)=p & P(0)=1-p being constant for each bit)

The Z-test should be fine if your strings are long enough (say approx 50 for proportions near 0.5).

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