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)