Multiple Comparisons and Trend Analysis
1/23/98
The major purpose of this lab is to illustrate the use of trend analysis as a form of
multiple comparison procedures. We will also spend some time just looking at plain
multiple comparisons, but you have seen a lot of these.
The following is a fictitious study, which is very loosely based
on a study by Nolen-Hoeksema and Morrow (1991) on post-traumatic
stress syndrome (PTSD). I am modifying the study substantially, but I hope that I'm not
altering the underlying results. The most important thing that I am doing is to record
data from distinct groups of subjects at the different time intervals.
Nolen-Hoeksema and Morrow just happened to collect data on PTSD from a large group of
college subjects just before a very substantial earthquake (the Loma Prieta earthquake) in
California in 1989. Having been provided with a natural disaster, they went back to those
students after the earthquake and collected data again. We are going to simplify this
study by assuming that each week after the quake (for 5 weeks) they collected data from a
different group of subjects. This gives them a total of 6 observation times, at weeks 0,
1, 2, 3, 4, and 5. The data are found in a text file named earthquake.dat.
You can read in this file and use it for the first analysis. The first variable is Group,
and the second is the dependent variable.
I repeatedly generated datasets until I found one with a nice quadratic set of data. I
want you to first run an analysis of variance on these data, asking whether the level of
symptoms varies as a function of time since the stressful event. Then I want you to create
a scatterplot with Time on the X axis and Stress on the Y axis. After the
scatterplot appears, click on Edit and select Chart/options from the menu.
Check the box next to total under Fit line, and then click OK a
couple of times. This will draw the best-fitting straight line through your data. (You
will be under-whelmed.). Now go back and do the same thing, but this time select Fit
Options and tell it to fit a quadratic. Notice how this fit is much better than the
linear fit. If you want to print this out, double-click on the axis labels and make them
neater and more informative. (You can also add a title.)
Now start again, and this time when you ask for the Anova, also click on Contrasts
and tell it to do polynomial contrasts of degree = quadratic. Relate the printout this
gives you to what you found when you plotted the data.
Finally, we will practice with our contrasts option. The coefficients for the
linear and quadratic components are
Linear -5 -3 -1 1 3 5
Quadratic 5 -1 -4 -4 -1 5
You enter these by choosing the Contrast option and entering a -5 in the box,
clicking ADD, entering -3 in the box, clicking ADD, etc. Then click on Next
and start all over with the second set. For purposes of comparison, make sure that the polynomial/quadratic
boxes are also checked, which means that you are looking at these components twice. I want
you to compare the two sets of results. They are the same, except that one uses F
and the other uses t.
The above data were generated by a fairly simple set of syntax commands in SPSS, and
each of you analyzed the same set of data. After you have run the data above, I want you
to load that syntax file, set your random seed at some value, and run the syntax. The file
is named earthquake.syntax. This will generate a whole new
set of data and do the polynomial fit. How do the results of this run differ from the
results you got before?
The next step involves forgetting all about that trend stuff, and running a Tukey test
on the canned data that I gave you.
Finally, I want you to write up this study as if you had run it. I don't want a lot of
text, but I want something to make it clear that you understand the results and what they
mean. Include important parts of the results in your write-up.
dch
3/6/2009