Repeated measures ANOVA trend analysis is confusing me

#1
I'm trying to understand how trend analysis works with respect to repeated measures ANOVA, but I'm a bit confused and have some questions. My first question at the bottom of this post is the thing I'm most interested in. I'm using SPSS, but it is unclear what is going on with the outputs and the SPSS docs are not very helpful.

As a perfect example, I saw this pdf while searching, which shows a one-way repeated measures ANOVA testing the hypothesis that depression scores would decrease over time spent in therapy. There is the standard ANOVA results, but SPSS actually outputs the "Tests of Within-Subjects Contrasts" which is a "trend analysis" that compares increasing orders of polynomial models from linear, then quadratic, then cubic, up to n_levels-1 models. I paste from the pdf here, just in case links aren't allowed:



My questions:

1. The tests of within-subjects contrasts table is clearly a regression result (I think?), but what is the point of just reporting that there was a linear/quadratic/cubic effect if it doesn't demonstrate the direction by providing the coefficients? Is it simply a case of reporting the means for each timepoint along with the results of the trends? I don't see any regression coefficients in any of the outputs, nor any information on it in their documentation, so this is pretty confusing to me. All of the "guides" I have found online specifically instruct us to skip this table, which is not very useful.

2. It's really not clear how the violation of independence is handled in this case. For example, I couldn't just take this data and fit a 1st, 2nd, 3rd etc order polynomial model to it since we measure the same subjects across time, so there is going to be a correlation across time points.

3. Maybe it's too much to ask, but how would one go from input data in the shape of N x 6 (in this case), to running these regression models directly?
 

Karabiner

TS Contributor
#2
Possibly you are a researcher who knows whar s/he want to achieve by doing this data analysis.
So if the software "SPSS" for unknown reasons puts out several contrasts by default, what
are you complaining about and why? That is not clear to me, I'm afraid. Maybe you just ignore
those analyses you hadn't intended?

But almost certainly I missed your point
 
#3
Well these are actually what I would like to understand. I know that I want to follow up on my ANOVA, and I expected my DV to show a similar effect to the one in the example. I initially did some pairwise comparisons because I did not know any better, but my supervisor suggested to me that trend analysis is the way to go. From what I've read it makes sense because my design is similar to the example, but I can't seem to understand these outputs and I would like to learn more about them.

For example I can't tell if these are actual results of regression analyses or if they are comparisons between different regression analyses. If the first one, then it seems that the coefficients would be worth getting? If they are, then I don't understand how these regressions were calculated because the design is repeated measures, so I don't think I can simply do a standard regression.