Statistical Inference: A Short Course

10.2 Errors in Testing

It should be intuitively clear that since sample information is used to test hypotheses about a population parameter, an element of uncertainty is involved in assessing the test results. Hence it is possible to reach a “false conclusion.” The two types of errors encountered are:

Type I Error (TIE): Rejecting H₀ when it is actually true.

Type II Error (TIIE): Not rejecting H₀ when it is actually false.

In fact, the complete set of possible actions given the status of the null hypothesis are presented in Table 10.1.

Table 10.1 Types of Errors.

The risks associated with wrong decisions are the (conditional) probabilities of committing Type I and Type II Errors:

P (Type I Error) = P (reject H₀/H₀ true) = α.

P (Type II Error) = P (do not reject H₀/H₀ false or H₁ true) = β.