What is a good rule of thumb for how to choose the question for the null hypothesis.
For instance, if I want to check if the hypothesis B is true, should I use B as the null, B as the alternative hypothesis, or NOT B as the null?
I hope the question is clear. I know that it has something to do with the error I want to minimize (Type I?), but I keep forgetting how it goes, because I don’t have a clear intuition built for it.
A rule of the thumb from a good advisor of mine was to set the Null-Hypothesis to the outcome you do not want to be true i.e. the outcome whose direct opposite you want to show.
Basic example: Suppose you have developed a new medical treatment and you want to show that it is indeed better than placebo. So you set Null-Hypothesis H0:=new treament is equal or worse than placebo and Alternative Hypothesis H1:=new treatment is better than placebo.
This because in the course of a statistical test you either reject the Null-Hypothesis (and favor the Alternative Hypothesis) or you cannot reject it. Since your “goal” is to reject the Null-Hypothesis you set it to the outcome you do not want to be true.
Side Note: I am aware that one should not set up a statistical test to twist it and break it until the Null-Hypothesis is rejected, the casual language was only used to make this rule easier to remember.