求问sample size到底怎么求？

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最近在看t/z test hypothesis testing,被sample size这块完全弄混了。。。不知道
到底怎么理解。

首先，我是看到说决定sample size一般是depend on: (1)margin of error (2)
confidence level(3)standard deviation。这个我还能明白，因为me=z*std
deviation/sqrt(n)

不过后来又看到sample size取决于power (1-beta)还有effect size...那我就不明白
了。。。怎么把这两个联系起来呢？谢谢！！！

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关键词：Sample size AMPL PLE amp

They're related. First, you need to know that the type II error is a statistical term referring to the acceptance (non-rejection) of a false null hypothesis. In general, we will have that

Z_beta=[(Margin of error)-alternative difference]/SE(difference),

where Margin of error=critical value*SE(difference)=Z_{alpha/2}*SE(difference) and Z_beta=-Z_power
Then we have
-Z_power=Z_{alpha/2}-alternative difference/SE(difference),
Thus,
alternative difference/SE=Z_power+Z_{alpha/2}.
SE(difference) here can vary depending on what you are trying to test. For example, if you're testing two group mean difference, then SE=sigma/sqrt(n), where sigma=SD and n=sample size. You can also see that actually the effect size here=difference/sigma.

Hope it helps.

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bcai2019 发表于 2020-8-6 10:20
They're related. First, you need to know that the type II error is a statistical term referring to t ...

It is very helpful! Thank you so much! (I know it’s been almost a year but I totally forgot to check in here lol)

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