## TYPE I AND TYPE II ERRORS

The question of how to determine the critical region ideally should depend on the cost of making a wrong decision. In this regard it is useful to define the following two types of error.

DEFINITION 9.2.1 A Type I error is the error of rejecting H0 when it is true. A Type II error is the error of accepting H0 when it is false (that is, when Hi is true).

figure 9.1 Relationship between a and p |

The probabilities of the two types of error are crucial in the choice of a critical region. We denote the probability of Type I error by a and that of Type II error by p. Therefore we can write mathematically

(9.2.1) a = P(X Є R І Нй) and

(9.2.2) p = Р(ХЄД|#і).

The probability of Type I error is also called the size of a test.

Sometimes it is useful to consider a test which chooses ...

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