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.