Question

If Monica decides that a 5% chance of a Type I error is too high, and therefore changes the acceptable risk of a Type I error in her experiment to 1%, what happens to the power of her experiment?

Answer 1

When Monica changes the acceptable risk of a Type I error in her experiment to 1%, the power of her experiment may decrease.

Step-by-step explanation:

When Monica changes the acceptable risk of a Type I error in her experiment to 1%, the power of her experiment may decrease. The power of a test is equal to 1 minus the probability of a Type II error (β). As Monica decreases the acceptable risk of a Type I error, she is making it more difficult to reject the null hypothesis and thus reducing the probability of detecting a true alternative hypothesis. This decrease in the probability of detecting the alternative hypothesis can result in a decrease in the power of the experiment.

For example, if Monica originally had a Type I error rate of 5% (α = 0.05) and a power of 0.9 (β = 0.1), changing the acceptable risk of a Type I error to 1% (α = 0.01) may reduce the power to a lower value, such as 0.8 (β = 0.2).

Therefore, reducing the acceptable risk of a Type I error can lead to a decrease in the power of an experiment.