There are two different approaches to the study of power. You can compute the power for a study that you are about to run, which is certainly a good idea, or you can compute post-hoc power after an experiment is done. We are going to do both of those in this lab, though we will restrict most of our interest to Student's t test for simplicity. (The application to other statistical tests is reasonably straightforward.)
Bushman (1998) investigated the effects of violent videos on the production of aggressive free associates in children. The reference is Bushman, B. J. (1998). Priming effects of media violence on accessibility of aggressive constructs in memory. Personality and Social Psychology Bulletin, 24, 537-545. To quote his introductory theme:
Actors in the mass media, for example, may serve as aggressive models. More than half of major actors, and about one third of all actors shown on network television are involved in violent interactions (Gerbner, 1994). Viewers are most likely to imitate aggressive models in the mass media when violence is rewarded or goes unpunished. In a detailed content analysis of more than 5,000 hours of programming on cable and broadcast television, it was found that violence was explicitly rewarded 15% of the time and went unpunished 73% of the time (National Television Violence Study, 1996, 1997).
Bushman selected 200 undergraduates (100 men and 100 women) and divided them into two equal groups. (We'll ignore sex here.) One group watched Karate Kid III which was a very violent video. The other group watched Gorillas in the Mist, which was a documentary with no violence, but was still exciting..
Subjects were then presented with a word association task, in which half of the words were homonyms which had both an aggressive and a nonaggressive meaning (e.g. box, strike), and the other half were nonaggressive words. The dependent variable was the number of aggressive associations each subject made to the two kinds of words.
The first t test will compare number of aggressive associations made to homonyms by the violent and nonviolent video groups. (We are ignoring the responses to non-homonyms for the moment.) We have no way of knowing what kinds of means or standard deviations to expect, so we can't calculate d and d. Instead, we will have to ask what level of power we might expect if we had what Cohen defined as a medium effect size, which is a d = .50.
We have the advantage of knowing what Bushman actually found. If we ignore sex, the mean number of aggressive associates was 7.1 for the violent video group, and 5.65 for the nonviolent video group. The corresponding standard deviations were 4.6 and 3.15, respectively. Assume that these are the true population values of the parameters. (Notice that we are comparing two independent groups.)
Now we are going to see if that's right. We will generate populations with these characteristics, draw multiple pairs of samples, and calculate t for each. Then we'll see how often we reject the null.
new file.
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Run this syntax program and record all 10 values of t. I will collect them and compile them into one file. (Give them to me with exactly 2 decimal places.) I will display the file on the screen, and we can determine how often we actually would reject the null.
Finally, let's look at one example of a repeated-measures t. We will use the same example, except that we will look only at those who saw violent videos, and compare the number of aggressive words in their responses to homonyms and nonaggressive words (the non-homonyms).
In a way this is a perfectly legitimate calculation for a pretty stupid question. Of course people are likely to give more aggressive words to stimuli that have at least one aggressive meaning than to stimuli without aggressive meanings. But I wanted a repeated measures example from this same data set, and this is the best I could do. The calculation is legitimate, even if you don't care for the question.
I'll define
where
Assume that we want to compare the aggressive responses in the violent group between homonyms and nonagressive stimulus words (e. g. to Box and Carton). The homonyms had a mean of 7.1 and a st. dev. of 4.4. The Nonaggressive words had a mean of 0.15 and a st. dev. of 0.7.
Assume further that the correlation between the number of aggressive responses to the two types of words was 0.20. (Why might it be that low?). What is the power for this experiment, assuming that the values above reasonably reflect the population?
The results of the first half of this lab can be found in bushmantvalues.sav. If it would load when you double click on the link, hold down the shift key while you click, and it will ask where you want to save the file. I have had a lot of trouble getting this file, so I have created an ASCII file named bushmantvalues.dat. I would recommend that you use that.
Last revised: 10/25/01
