Power for one sample proportion

Question

Can someone explain what the Power for One Sample Proportion calculator is doing?  The help documentation not particularly helpful or I didn't drink enough coffee today.

Also can anyone explain why the power curve goes up and down with sample size as shown below:

Jordan_Hiller · Accepted Answer

What do you mean by "what is it doing"? Are you asking what problem is it addressing?

Here's a reference I found on the jaggedness. It's because the exact test is discrete, and it has to do with the way that the rejection region for the test statistic is calculated. http://www.nicksun.fun/statistics/2020/11/16/sawtooth-power-curves.html

Note that the jaggedness goes away when you use the normal approximation rather than the exact test.

jiancao · Accepted Answer

Can someone explain what the Power for One Sample Proportion calculator is doing?

The first plot on the left shows the relationship between Power and Sample Size. As @Jordan_Hiller  points out, due to the binomial distribution being discrete, the power of an exact test does not always increase with a small increase in sample size.

Two other inverted bell curves show how Power increases as the Assumed Proportion moves away from the Alternative Proportion (or the Alternative Proportion moves away from the Assumed Proportion). The larger the difference between the two proportions, the higher the power, aside from any jaggedness noted above, analogous to the 'Difference to Detect" in a One-Sample Mean Test.

karencopeland · Accepted Answer

Drink more coffee and you will oscillate with the plot. I am in the process of updating the SSE documentation as many of the explorers have been moved from JSL to C++ so you will see slight differences in 19.   That said, I will try to add a note about the jagged graph, which as others have noted is due to this being an "exact" test calculation (mathematically).  In reality (at least in my experience) sample size is not an exact science, the estimates are only as good as your guesses that you feed into the calculators. They are good for showing you how increasing (decreasing) your sample size might help (hurt) you in the long run.