Question

A medical research group is recruiting people to complete short surveys about their medical history. For example, one survey asks about family history of cancer. So far, people who sign up complete an average of 4 surveys, with standard deviation 2.2. The research group wants to try a new interface that they think may encourage new enrollees to complete more surveys. They plan to randomize each enrollee to either the old or new interface.

a) How many new enrollees do they need for each group (old or new interface) to detect an effect size of 0.5 surveys per enrollee, if the desired power level is 80%? Let α = 0:05.

b) Explain the effect of increasing α on the power of the test. What is one disadvantage to increasing α , from a decision-making standpoint?

Answer 1

a)

is the effect size

= 1- power =0.2

( using =-NORM.S.INV(0.025)

( using excel formula = -NORM.S.INV(0.2))

b) If all factors are held constant, then as significance level increases, the power also increases.

The reason behind this is that a larger means a larger rejection region for the test, hereby increasing the probability of rejecting the null hypothesis.

The main disadvantage is with increasing , the pobability of Type I error increases.