This lab is designed to help you to become more familiar with Repeated Measures Anova on SPSS. The following experiment is somewhat hypothetical, but it is based on a recent study by Evans, Bullinger, and Hygge (1998). .
Evans et al were interested in the effects of noise exposure on the physiological responses of children. It comes down to the old question of whether the loud noise from airports is a serious stressor to those who live nearby. Recently the city of Munich built a new airport, and the authors were able to test children before the airport was built, 6 months after it was opened, 18 months after it was opened, and, for my purposes, 36 months after it was opened. They used the same subjects at each of the four times, and they had control groups of children in the same city but living outside the noise impact zone. (For Group, 1 = Near Airport; 2 = Away from Airport.) The dependent variable I have chosen is epinephrine level in these children, which is a variable that would be expected to increase with increased stress.
Because we have each child measured repeatedly, we have a repeated measures design. In other words, we will have the same groups of children measured at times –6, +6, +18, and +36 months from the completion of the airport. The interesting thing is that each of you will have a different set of data.
I spent a lot of time getting a program to work that will draw samples for you. I have fixed the population correlation coefficients at .60 for each pair of intervals. Your sample data will not have exactly those correlations.
Work through the following problems, at each step thinking about what I am trying to demonstrate. The syntax file is at airport.sps. (Clicking on that link in Netscape will open a web page with the syntax. Copy that syntax to the clip board, and then paste it into a blank sps file. Clicking on that link in I.E. 6 will allow you to save to a file. Do that and then open that file from within SPSS as a syntax file.) You MUST each set your random number seed so that you don’t have the same data.
Run the syntax program to get your data. I would suggest that you immediately save that data file.
I want you to see what the correlation matrix of your Time levels looks like. First use the correlation command to get the 4´ 4 matrix of correlations. (Request covariances as well.) Does this matrix look like you would expect it to?
The pattern of covariances isn't quite what I would like to see, but don't worry. Before you get panicked about them, split your file by Location and run the correlations again. Does this look better? Why is there such a big difference when you split the file?
The next question gets at one of the root concerns with repeated measures designs. What is the basic assumption about the covariance matrices, and does it look as if you have come reasonably close to meeting that assumption? (You may want to check with the book.)
Go ahead and run the repeated measures analysis of variance, regardless of how well the assumptions are met. You have a 2 ´ 4 Anova, with repeated measures on the second variable and between-subjects measures on the first. I would suggest that you print out this result. In the process, request a plot of the dependent variable with Time on the X-axis and separate lines for Location.
Now make up a summary table similar in design to the ones that I have in the book, and fill it in with the results that you found in SPSS. Leave out the stuff that doesn’t fit in the table you drew up.
Here is a case where one or more of the simple effects are worth looking at. Calculate the simple effect of time at both locations. What do I suggest in the book about how you would deal with the error terms—should you use a pooled term or separate terms for the two analyses?
Going back to the overall analysis and double click on the output for the within subjects effects. Now select "pivot trays" if they are not already selected, and play with moving the little icons to see different ways to display the G-G or H-F corrections to the degrees of freedom. (Be sure that you first issue incantations to the pivot-table god.)
Because we have an ordered variable (though not with equal intervals) for the abscissa, it makes sense to ask about trend. (From looking at the plot that you printed earlier, what would you expect? Here we will use the contrast button in the dialogue box to ask for a polynomial trend analysis on Time. Be sure that after you select it, you click on change. Do you think that it makes more sense to apply these trend analyses to the main effects or the simple effects?
Whatever your answer to the previous question, also apply trend to the main effects and interpret the printout with respect to the interaction. A significant linear component for the interaction really means the whatever linear relationship there is over time for one group is different from the linear relationship for the other group. Similarly with the quadratic relationships.
The data that I have here give very realistic results, although I did have to guess on the correlation matrix. What can you conclude from this experiment? (If anyone tells me that "location makes a difference," I will hand the paper back to be redone.)
How might you go about designing this study to make it better, assuming that strictly ethical behavior is something that you leave to Bill Clinton. (Don’t be draconian, but don’t be overly fastidious either.)
What have you learned from this exercise? What could be done to make it better?
If you want to see the original study, it is in the January, 1998 edition of Psychological Science.
Last revised: 02/10/02