Decisions from tests

Many hypothesis tests are followed by some action that depends on whether we conclude that H0 or HA is true. This decision depends on the data.

Decision    Action
accept H0    some action (often the status quo)   
reject H0    a different action (often a change to a process)   

There are two ways in which an error might be made — wrongly rejecting H0 when it is true (called a Type I error), and wrongly accepting H0 when it is false (called a Type II error).

Decision
  accept H0     reject H0  
True state of nature H0 is true    correct Type I error
HA (H0 is false)     Type II error correct

A good decision rule about whether to accept or reject H0 (and perform the corresponding action) should ideally have small probabilities for both kinds of error.