Interpret the power of a significance test and describe what factors affect the power of a test.
Activity: Will Mrs. Gallas Prove Herself?
Of course TheStatsMedics think that the average SAT math score at East Kentwood High School is better than the national average. So we are going to take a random sample of 8 students to collect some evidence for our claim. We will then use this sample to perform a significance test. Students use this context and this applet to understand the interpretation of power and the factors that can increase power.
Hopefully students will discover the three factors that can increase the power of a significance test.
Increasing the sample size
Increase the alpha level
Increasing the difference between the null and alternative hypothesis values
Try to get students to master these concepts rather than memorize the list. They need a good fundamental understanding of why each of these changes would increase the power. Here are the short reasons why:
A larger sample size gives more information about the true parameter.
Using a larger significance level makes it easier to reject H0 when Ha is true.
It is easier to detect a bigger difference between the null and alternative parameter value.