True or false? Type I (α) and type II errors (β) are linearly related.

True or false?

Type I (α) and type II errors (β) are linearly related.

Expert Solution

FALSE

Explanation- Every time, when we made any decision or conclusion using statistics there are four possible outcomes; two correct decisions, two representing errors. (as shown in the table below)

CORRECT

CONCLUSION

TYPE I ERROR

Reject a true null hypothesis

TYPE II ERROR

Accept a false null hypothesis

CORRECT

CONCLUSION

The chance of committing these two errors (type I and type II) are inversely proportional. When type I error rate decreases, type II error rate increases, and vice versa.

The Type I error or α (alpha), error rate is usually set in advance by the researcher. The Type II error rate for a given test is harder to know because it requires estimating the distribution of the alternative hypothesis, which is usually unknown.

Therefore, there is no linear relation between the two errors, and these two errors are inversely related to each other.

Rahul Sunny answered 1 year ago

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