The Analysis of Covariance

4/25/2002

This lab is intended to raise some important questions with respect to the Analysis of Covariance and standard t tests. It is based on an actual study: Rodriguez, N., Ryan, S. W., Vande Kemp, H., and Foy, D. W. (1997) Posttraumatic stress disorder in adult female survivors of childhood sexual abuse: A comparison study. Journal of Consulting and Clinical Psychology, 65, 53-59. The first part of the study is a fairly close replication of their results, but the "treatment" part is pure fabrication.

The data can be found at sexabuse.sav.

Rodriguez et al. collected data on childhood sexual abuse from 45 adult women who reported abuse, and 31 women who did not report abuse. We will treat these as our two groups. The dependent variable was a measure of lifetime PTSD, based on the Structured Clinical Interview for DSM-III-R (SCID). This measure is labeled as PTSD. They also collected data on childhood physical abuse, using a measure known as AEIII, and this variable in denoted PhysAbus.

Be careful about one problem. When I speak of Sexual Abuse I am talking about a dichotomous variable, where 1 = Yes, 2 = No. When I speak about Physical Abuse, I am speaking about a continuous variable where higher scores mean more abuse. That is the nature of the data that they collected.

The first part of this lab asks you to investigate these variables. Cast your answers in some form of analysis of variance or regression analysis..

Do women who have a history of childhood sexual abuse show elevated levels of Lifetime-PTSD when compared to women who do not have such a history.
Does Lifetime-PTSD relate to a prior history of childhood physical abuse?
How do the sexual abuse groups differ in terms of prior physical abuse?
Do differences between groups in Lifetime-PTSD remain after we control for childhood physical abuse?

Now comes the fictitious part. Assume that we intervened with these women and provided some form of therapy. Therapy might not actually be appropriate for the non-abused women, but we intervened anyway. I have given you another dependent variable called PostPTSD that represents a hypothetical set of scores that might reasonably be obtained after a very effective form of therapy.

It is important to understand how I generated the PostPTSD data. I assumed that there would be no mean change in the non-abused group, so I just added a random number to every value. These numbers were N(0,3), so some people went up and some went down. For the abused group, I assumed that the effect of therapy was to reduce their pre-therapy score to 60% of what it was initially (plus or minus the same kind of error applied to the non-abused group.) How would you have created PostPTSD for this group?

What effect would adding the random error component have in the non-abused group?
Is the above description the way that you would have generated PostPTSD scores for the Abused group? You might just have subtracted some value from the PTSD score for the abused group, rather than multiplying by .60. Why is my approach better or worse than yours? What does it assume about the effect of therapy? What would your approach assume about the effect of therapy?

I have deliberately led you into a confusing situation--but one that is perfectly conceivable. If these were my data I could see several ways to deal with them, and they may not all be equally good.

First I could ignore the non-abused group, on the grounds that they probably don't need therapy. I could then run a matched sample t test comparing PTSD and PostPTSD for the abused subjects.
Second, I could again ignore the non-abused group and run a repeated-measures Anova with PTSD and PostPTSD as my repeated measures.
Third, I could subtract PostPTSD from PTSD to get a "change" score, and then compare the two groups on change.
Fourth, I could use both groups of subjects, and run a repeated measures Anova with groups as a between-subject measure and PTSD, PostPTSD as my repeated measures. If I did, what effect would be of most interest?
Fifth, I could run a between-subjects Anova on groups, with PostPTSD as my dependent variable, and PTSD as a covariate.

Run each of these analyses and draw conclusions.

Which analysis was most appropriate, and why?

Last revised: 04/20/02