Give an example of a situation in which you believe a Type I

Give an example of a situation in which you believe a Type I Error is more serious. Give an example of a situation in which you believe a Type II Error is more serious. In each case, why do you think so?

Solution

If you were a potential consumer of a new drug, which of these types of errors would you consider more serious? Your initial response might be that it is more serious to make the Type II error, to declare an unsafe drug as being safe. Having decided that the Type II error is more serious, one should consider techniques to decrease the probability of making such an error, beta. One way to decrease beta is to increase alpha. That is, one might be willing to trade an increased risk of a Type I error for a decreased risk of a Type II error. It is, however, possible to decrease beta without increasing alpha. Additional power (ability to detect the falsity of the null hypothesis, (1 - beta) may be obtained by using larger sample sizes, more efficient statistics, and/or by reducing \"error variance\" (any variance in the dependent variable not caused by the independent variable).