Power Demo 1

Questions to be answered before the simulation are not yet implemented in this test version.


Begin by answering the questions, even if you have to guess. The first time you answer the questions you will not be told whether you are correct or not.


Once you have answered all the questions, answer them again using the simulation to help you. This time you will get feedback about each individual answer.


General Instructions


This simulation illustrates the effect of (a) sample size, (b) the difference between population mean and hypothesized mean, (c) the standard deviation, (d) the type of test (one-tailed or two), and (e) significance level on the power of a two-sample t test.


You specify the difference between the population mean and hypothesized mean by either enterng text in the box or by moving the slider. The populaton standard deviation can be entered in the box or specified by the pop-up menu. Finally, you specify the number of tails of the test. A power graph for the significance level 0.10, 0.05, and 0.01 significance levels as a funtion of sample size is displayed.


Step By Step Instructions


1. Examine the power curves. There are three curves, one for the 0.01, one for the 0.05, and one for the 0.10 significance level. The X axis shows sample size, the Y axis shows power. Note the effect of sample size and significance level on power.


2. The default difference between the population mean and hypothesized mean is 1.55. Use the slider to change this value and note the effect on the power curves.


3. Change the population standard deviation (sd) and notice its effect on power.


4. Compare the power of one-tailed and two-tailed tests when the difference between the population mean and hypothesized mean is 2. Determine which is higher.


5. Set the difference between the population mean and hypothesized mean to zero. Since the null hypothetsis is true, the Y axis no shows the Type I error rate, not power. Note the effect of sample size on the Type I error rate.


6. Determine the effect of changing the standard deviation on the Type I error rate.


Summary


Power is increased by increasing the sample size, increasing the difference between the population mean and hypothesized mean, and decreasing the standard deviation. When the null hypothesis is true, neither the sample size nor the standard deviation affect the Type I error rate. Power is higher with one-tailed than two-tailed tests as long as the difference between population mean and hypothesized mean is in the hypothesized direction.