Statistical Methods

Unit 4 - Testing of hypotheses

4.3.Type I and Type II errors
In testing a hypothesis two kinds of errors are likely to be committed. They are Type I and Type II errors. If null hypothesis is rejected when it is actually true, then such error is called Type I error. On the other hand, if null hypothesis is accepted when it is false, then Type II error is committed.
This is summarized in the following table:

Table: Statistical decision table

In order that any test of hypothesis to be good, it must be so designed as to minimize both the errors i.e. minimize both α and β.

For a fixed sample, size it is difficult to minimize both α and β, as an attempt to decrease one may lead to an increase in the other. It is customary to fix α at a predetermined level and choose a test procedure that minimizes β i.e., α is prefixed in a test and β is minimized. Thus, we run the risk of rejecting a true H0 but reduce β, the acceptance of false H0 to minimum. Test criterion is developed on these principles.