). This corresponds to an effect size ofNow we will move on to a sampling exercise. If you do not have a paper copy of this exercise, you need to print this page. If you had problems with the questions preceding this section or do not feel comfortable with hypothesis testing concepts, you may want to complete the WISE hypothesis testing tutorial and return to this tutorial later. If you are unfamiliar with effect sizes, a review is provided.
If you have a paper copy of this page, go directly to the WISE power applet. The exercise will guide you through use of the applet. After completing the section below, you will go on to some additional questions.
1. Power and effect size (magnitude of differences).
For this example we will examine distributions of test scores from graduates of two training programs, Program A and Program C. For people who do not take a training course the population mean is 555 and the population standard deviation is 139. Thus, the null hypothesis for testing each program is that the population mean for graduates of the program is equal to 555.
Suppose that for graduates of training Program A, the actual mean is 667. (Assume
for this example that we know the population standard deviation, ). This corresponds to an effect size of
To continue, you must have the WISE Power Applet running on your computer (a link is also provided at the bottom of the page).
To simulate drawing samples from graduates of Program A, enter the following
information: (null mean) 
555, (alternative mean) 
667, (standard deviation) 
139,
n = 25. Press enter/return after placing the new values in the
appropriate boxes. Draw one sample (press Sample) and record
the mean and z below. Does this sample allow you to reject the null hypothesis?
Any sample mean falling to the right of the dashed line (the dark blue region
of the graph) would lead to a rejection of the null hypothesis with p<.05,
one-tailed. Sample means falling to the left of the dashed line correspond to
a failure to reject the null hypothesis (a Type II error when we are sampling
from the alternate distribution).
Now draw nine more samples and record the mean and z for each. (mean / z)
_____/_____ _____/_____ _____/_____ _____/_____ _____/_____
_____/_____ _____/_____ _____/_____ _____/_____ _____/_____
1a. What is the power for this test? ________ (Note: this is shown in the applet).
1b. How many times out of ten could you reject the null hypothesis?
(Use one-tailed alpha = .05 , z =1.645) __________
Now, examine Program C (mean = 585). This corresponds to an effect size of:
.
To simulate drawing samples from graduates of Program C. Enter the following
information:
(null mean) = 555,
(alternative mean) = 585,
(standard deviation) = 139, n = = 25. Press enter/return after placing new values in the appropriate boxes.
Before drawing samples, note how the sampling distributions differ for Program A (alternative mean = 667) vs. Program C (alternative mean = 585). What effect do you think this will have on your results -- how will this affect your ability to reject a false null hypothesis (that is, do you expect to reject the null hypotheses more or less easily for samples drawn from Program C compared to Program A)?
Draw 10 samples and record the results below.
_____/_____ _____/_____ _____/_____ _____/_____ _____/_____
_____/_____ _____/_____ _____/_____ _____/_____ _____/_____
1c. What is the power for this test? _______
1d. How many times out of ten could you reject your null hypothesis?
(Use one-tailed alpha = .05 , z =1.645) __________
Explain the difference between your findings in 1a/b and 1c/d. (Note: after completing this section, be sure to click the link titled "answer some questions" found at the bottom of the page containing the power applet.)