andrewgelman
commented
3 years ago Good catch! It's kind of confusing (including to me, apparently!). If you plug in p = 0.6, then you get an sd of sqrt(0.6*0.4/n) = 0.49/sqrt(n), so I wrote the text like that. But when you're doing the power calculation, you have to allow for the possibility that p_hat is near 0.5 in this example, so that the sd could be as high as 0.5/sqrt(n), hence when I did the calculations, I assumed 0.5. I think in this example we're safer using 0.5 and 196, so I'll just have to fix and add some text to explain.
avehtari
On page 295, we see the equation $n = (2.8 ∗ 0.49/0.1)^2 = 196$. It's incorrect. I suspect y'all meant either $n = (2.8 ∗ 0.5/0.1)^2 = 196$ or $n = (2.8 ∗ 0.49/0.1)^2 = 188.2$. To see, execute the following:
Which yields:
If it's indeed $n = (2.8 ∗ 0.49/0.1)^2 = 188.2$, this will have implications for the lower row of Figure 16.2.