Answer to Question #187162 in Statistics and Probability for Adnan

Question

Which type of error dangerous

Answer 1

There are two kinds of errors that can be made in significance testing: (1) a true null hypothesis can be incorrectly rejected and (2) a false null hypothesis can fail to be rejected. The former error is called a Type I error and the latter error is called a Type II error. These two types of errors are defined in the table.

The probability of a Type I error is designated by the Greek letter alpha ($\alpha$ ) and is called the Type I error rate; the probability of a Type II error (the Type II error rate) is designated by the Greek letter beta (ß) .

A Type II error is only an error in the sense that an opportunity to reject the null hypothesis correctly was lost. It is not an error in the sense that an incorrect conclusion was drawn since no conclusion is drawn when the null hypothesis is not rejected. A Type I error, on the other hand, is an error in every sense of the word.

A conclusion is drawn that the null hypothesis is false when, in fact, it is true. Therefore, Type I errors are generally considered more serious(dangerous) than Type II errors.

The short answer to this question is that it really depends on the situation. In some cases, a Type I error is preferable to a Type II error, but in other applications, a Type I error is more dangerous to make than a Type II error