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?