Cross Validated Asked on January 3, 2022

Consider this answer on how to design an NHST. I don’t quite understand what **exact process** one is supposed to follow to determine the **minimum sample size** once we have:

- A
**null hypothesis**that is**falsifiable**. The choice of this null hypothesis will inform the assumed distribution of the data*under the null*. - A
**minimum***effect*size that we want to be able to observe. - A
**maximum***false positive rate*, i.e. the significant level $alpha$ against which we’ll compare a computed $p$ value. - The
**maximum***false negative rate*= 1-$beta$, i.e. where $beta$ is called the power or sensitivity of the experiment.

If simpler, let’s assume a 1D Normal distribution for the Null.

My recollection is that one is supposed to use the **CDF** of the Null somehow for the test, but how? E.g. how does the chosen value for the minimum effect size inform the sample size?

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