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This example is based on a study by Foa, Rothbaum, Riggs, and Murdock (1991) in the Journal of Counseling and Clinical Psychology. The subjects were 45 rape victims who were randomly assigned to one of four groups.

The four groups were:

**1) Stress Inoculation Therapy** **(SIT)** in which subjects were taught a variety of coping skills (similar to cognitive therapy);

**2) Prolonged Exposure (PE)** in which subjects went over the rape in their mind repeatedly for seven sessions (the idea being the more we are exposed to something the less we have anxiety about it);

**3) Supportive Counseling (SC)** which was a control group where people were provided with attention and positive regard, but no specific therapy

**4) Waiting List (WL) control** – no therapy, just measurement.

Assignment?

In the actually study, there were many outcome variables. For our purposes we will only look PTSD Severity, which was the total number of symptoms endorsed by the subject (the sum of the subject’s ratings on about 15 variables related to PTSD—e.g. flashbacks, nightmares, memory difficulties, etc.) Higher scores represent more PTSD symptoms.

People were measured on 3 occasions: Pre-treatment, Post-treatment, and one month following treatment.

To Summarize:

- Independent Variables
- Between Subjects conditions–therapy type (4 conditions)
- Within Subjects conditions—repeated measures (3 times)

- Dependent Variable = PTSD Severity

To begin, open the data file. (FOA.sav, click on SAVE AS, once downloaded, open the file with SPSS)

Once the data is open in SPSS, notice the tabs at the bottom, there is a variable view and a data view.

- The data view allows you to see all the data (this is where you would enter new data).
- The variable view allows you to see the variables (this is where you would create new variables).

INFERENTIAL STATISTICS

Our first inferential statistic we will use is a t-test. We want to compare pre-treatment scores to post-treatment scores (we are going to collapse across the treatments to see whether there is an overall change in all people).

**t-test**

Run a repeated measures t-test to determine whether there is a overall change between pre and post PTSD symptoms

- Click on ANALYZE/COMPARE MEANS/PAIRED SAMPLES t-test
- In the dialog box, we will first click on ‘pre’ then on ‘post’ (below the variables, there is a box that is labeled current selections)
- move the paired variables to the PAIRED VARIABLES box
- Click on OK

**Q1) **For this analysis, what is H_{0}:

**Q2)** Based on the paired t-test results, what can you say about an overall treatment effect? Do people get better over time? Make sure you use the APA notation when describing the statistics (e.g., A significant effect was found for… (t (23) = 2.97, *p* < .05); ASK in the discussion if you are unsure how to do this.).

Assignment?

One-Way ANOVA

Our first ANOVA will be comparing the 4 groups on the first time point. We want to see whether the groups have a different amount of PTSD before they start treatment. We randomly assigned people to groups, so we hope they do not differ, but we need to check it anyway. If they do differ before we start treatment, we will have a difficult time disentangling the results (e.g., maybe one treatment had people with more severe PTSD symptoms).

**Q3) **What is H_{0}: for the ANOVA comparing 4 groups at pretreatment?

- Click on ANALYZE/COMPARE MEANS/ONE-WAY ANOVA
- In the dialog box:
- our dependent variable is ‘pre’
- our factor is ‘group’

- we can also get a graph of the means of our groups, if we click on OPTIONS and then MEANS PLOT in the next dialog box (note: it is interesting to see how SPSS will automatically generate the y-axis range according to the data, this feature can make a nonsignificant result look significant and a significant result look nonsignificant depending on your data).
- Click on OK

**Q4) **What can you say about the groups prior to beginning treatment?

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**Q5)** Is there a need to do Post Hoc tests (i.e., do we have an overall difference between groups, where we will need to find which individual groups are different)?

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Repeated Measures ANOVA

Now, we want to look at how people change over time. Our first step will be to see whether there is improvement across time for everyone (collapsing all groups and ignoring the different types of therapy).

**Q6)** We already investigate whether there was an overall effect from pre to post treatment with a repeated measures t-test. We could use another repeated measures t-test to determine whether there is a change from post to follow-up. And then we could use another repeated measures t-test to determine whether there was a difference between pre and follow-up. There might be some merit in this approach, but what would be one problem?

Instead of multiple repeated measures t-tests, we will use a repeated-measures ANOVA to determine whether there was an overall effect across time.

- Click on ANALYZE/GENERAL LINEAR MODEL/REPEATED MEASURES to open the dialog box
- the first dialog box is asking you to name your factor and tell it how many levels there are. We have three levels (pre, post, follow-up).
- name the factor ‘time’ (it will make your output make more sense)
- in the number of levels box, type in 3
- click on the ADD button and then click on DEFINE
- A new dialog box will open
- we want to move ‘pre,’ ‘post,’ and ‘followup’ over to the top box (make sure they are in order)
- It is also nice to see change over time with a plot.
- Click on PLOT
- move time over to HORIZONTAL AXIS
- click on ADD and CONTINUE
- Click on OK

There is a lot of output. One of the first items that is outputted, “Multivariate Tests,” combine ‘pre,’ ‘post,’ and ‘followup’ into a linear combination (a sort of super variable) and determines how much of the variance in symptoms can be explained by time. That is, does time (all time combined) predict PTSD symptoms? In our example, these tests do not make much sense. So we can save our jokes about Roy’s Largest Root until later.

Another issue with repeated measure ANOVA is whether the variance changes across time. If it does it can lead to significant problems (similar to the homogeneity of variance problem in the t-test). Thus, SPSS will check for this problem (called sphericity) and provide many corrections. Thus, the next bit of output is a test of sphericity (to determine whether we have this problem).

The most important box for our purposes is labeled “Tests of Within-Subjects Effects.” Here are many different F-ratios (some contain correction factors if the data does not meet the sphericity assumption, such as Greenhouse-Geisser, Huynh-Feldt, etc. If you can create another correction you could get your name in SPSS.). In this table, we can see whether time was a significant factor. That is, do the people in our study change over time.

**Q7) **Can we reject the null hypothesis and say that there was a significant change over time (Our H_{0} for this test is that all time points are equal).

The profile plot is also good to look at to see the change in means over time.

**Q8) **Based on the profile plot and the F-test, what can you say about change over time? Be sure to include the profile plot AND the results of the F-test.

One problem with the last analysis is that we can’t differentiate how the different treatments affected PTSD symptoms. All we could say was that overall there was a change in symptoms. We need to look at the Repeated Measures ANOVA again, but look at the different treatments. To accomplish this goal, we will again use the GLM procedure, but add group as a between subjects variable (thus, the first seven steps below are exactly the same).

- Click on ANALYZE/GENERAL LINEAR MODEL/REPEATED MEASURES to open the dialog box
- the first dialog box is asking you to name your factor and tell it how many levels there are. We have three levels (pre, post, follow-up).
- name the factor ‘time’ (it will make your output make more sense)
- in the number of levels box, type in 3
- click on the ADD button and then click on DEFINE
- A new dialog box will open
- we want to move ‘pre,’ ‘post,’ and ‘followup’ over to the top box (make sure they are in order)

- move group over to the BETWEEN SUBJECTS FACTOR
- Click on PLOT
- move group over to the SEPARATE LINES box
- move time over to HORIZONTAL AXIS
- click on ADD and CONTINUE
- Click on OK

Again, the most important output box of which we are interested is the “Tests of Within-Subjects Effects.” We have F-ratios for ‘time’ as we did above. Now we add an interaction effect of time by group. This interaction term is used to determine whether there was a different effect over time for each group. If it is significant, we can say that there was a difference in how the different treatments changed over time (group by time interaction).

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**Q9) **Is there a significant interaction over time (i.e., do the groups differ from each other over time)? Be sure to include the figure and label it per APA guidelines.

**Q10) **We can use post hoc analysis to determine whether there are treatment group differences across time. Using only the profile plot, what might you say about how the treatment effects differ? Be sure to include the profile plot and label it per APA guidelines.

**Q11) **Write up the results section as if you were writing a manuscript. Describe what you have found so far in your study (include the descriptive). The final analysis described in question 9 and 10 is the most important. Thus, you do not have to discuss the previous t-tests, but focus on the final analysis. Make sure you use tables and/or figures to describe the results. (this question is most important part of this assignment; please use proper APA formatting on this question). Make sure you use the APA notation when describing the statistics (e.g., A significant effect was found for… (t (23) = 2.97, *p* < .05); ASK in the discussion if you are unsure how to do this.).