The bigger the sample size, the more power we have.
We also lower our chances of making either error.
More Sample Size!
We need to be careful with REALLY big sample sizes.
The standard deviation gets really small and you'll always get a small p-value.
This can cloud practical significance: use a confidence interval instead!
Ho is false!
If the Ho is really false, we have lots of power and very little Type
II error (dumb criminal).
If the true value differs only slightly from the Ho, we have little
power and may make a Type II error. (smart criminal)
This is called effect size.
Changing alpha
Making alpha smaller (0.01) makes it harder to reject.
We do this if want less Type I, but are willing to tolerate more Type
II and less power.
i.e., death penalty
Alpha and medicine
If the established treatment is highly effective, you demand a very
small p-value before rejecting (low alpha).
If the standard treatment is not very effective and you have reason to
believe it can be easily improved, you would be more willing to accept
a new treatment even though the p-value is larger (higher alpha).
