Question

Type I and Type II errors

Statistically speaking, we are generally agnostic to which is a bigger problem, type I (false positive) errors or type II (false negative) errors. However, in certain circumstances it may be important to try and put more emphasis on avoiding one or the other. Can you think of an example of where you may want to try harder to avoid one type or another? Can you think of a policy; political, economic, social, or otherwise, that pushes people toward avoiding one type or another? What are the repercussions of such policies?

Answer 1

(1) Example where we want to try harder to avoid Type I error:
Suppose:

H0: Null Hypothesis: The defendant is innocent

HA: Alternative Hypothesis: The defendant is not innocent

Type I error: Rejection of a true null hypothesis.

Suppose in reality the defendant is innocent. But, the judge wrongly concludes that the defendant is not innocent and punishes him. Type I error is committed in this situation.

Type II error: Failure to Reject of a false null hypothesis.

Suppose in reality the defendant is not innocent. But, the judge wrongly concludes that the defendant is innocent and lets him free. Type II error is committed in this situation.

In this situation, we want to try harder to avoid Type I error, because sentencing an innocent person to a punishment is a worse consequence.

(2) Example where we want to try harder to avoid Type II error:

Suppose we are designing a medical screening for cancer.

H0: Null Hypothesis: The patient does not have cancer.

HA: Alternative Hypothesis: The defendant has cancer.

Type I error: Rejection of a true null hypothesis.

Suppose in reality The patient does not have cancer.. But, the doctor wrongly concludes that the patient has cancer.and starts further analysis.. Type I error is committed in this situation. Here because of Type I error the patient is unnecessarily put into worries that he has got cancer, whereas in reality he is normal. But, this is not very serious because in subsequent tests, the doctor will come to know that he is ok.

Type II error: Failure to Reject of a false null hypothesis.

Suppose in reality The patient   has cancer.. But, the doctor wrongly concludes that the patient does not have cancer.and stops further analysis. Type II error is committed in this situation. Here because of Type II error the doctor stops further analysis for curing cancer, whereas in reality it is very much required.. This is very serious because in subsequent days, the condition of the patient will become worse.

In this situation, we want to try harder to avoid Type II error.