Question

The two components that are MOST important to the POWER to find a significant result are:

a) the size of the result only

b) sample size and mean

c) mean and median for a group

d) sample size and the size of the result

Answer 1

Sample size and the size of the result are more important to the power to find a significant result.

Increasing sample size makes the hypothesis test more sensitive - more likely to reject the null hypothesis when it is, in fact, false. Thus, it increases the power of the test. The greater the difference between the "true" value of a parameter and the value specified in the null hypothesis, the greater the power of the test. That is, the greater the effect size, the greater the power of the test.

Further if the level of significance is increased, the power of the test increases. If you reduce the significance level (e.g., from 0.05 to 0.01), the region of acceptance gets bigger. As a result, you are less likely to reject the null hypothesis. This means you are less likely to reject the null hypothesis when it is false, so you are more likely to make a Type II error, that is the power of the test decreases.