13.1 How to deal with more than one hypothesis test

In this chapter we focus on hypothesis testing to make inference.

When making a hypothesis testing, the steps are:

In general, we have two hypotheses \(H_{0}\) and \(H_{a}\):

\[H_{0}:\text{the mean in the control group equals the mean in the treatment group}\] \[H_{0}:\mu_{t}=\mu_{c}\] and

\[H_{a}:\text{mean values are not equal}\]

Now we want to test some particular set of null hypotheses:

\[\text{m are the number of hypotheses we make}\]

\[H_{01},...,H_{0m}\]

\(H_{0j}\) is the mean value of the \(j^{th}\) value

Multiple testing lead to the False discovery rate (1990)