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I try to understand the difference of +/-1 in the result of two functions using the binomial distribution.

I need to know the critical value of a situation where I have n=9 tests, the probability of success of each one is prob = 1/10 and the type I error is 0.05.

With sensR::findcr(sample.size=9, alpha=0.05, p0=1/10, test="difference"), the result is 4.

And with qbinom(size = 9, p=0.95, prob = 1/10), the result is 3.

I tried with other sample sizes and success probabilities, out of curiosity, and this +/-1 difference is still there.

I read this conversation and saw the same difference of 1 (the line is "we see that the critical value is c=40" but it refers to qbinom(.95, 64, .5) which gives 39).

I feel stupid because there is clearly something obvious that I do not understand, could someone enlighten me, please?

Indy
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  • what kind of test are you considering? – utobi Sep 26 '22 at 12:46
  • a 2-out-of-5 test for 2 similar cosmetic products tested by 9 panelists – Indy Sep 26 '22 at 12:54
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    The only way to answer this is to consult the documentation (or code) for sensR::findcr. I suspect it's just a difference in convention, concerning whether an inequality or a strict inequality is used in defining the critical value. – whuber Sep 26 '22 at 16:20
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    thank you for pointing me in the right direction, it seems to be a inequality vs strict inequality thing – Indy Sep 27 '22 at 09:17

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