Thanks you for your insight, this is a huge help. I actually already have a variable with the number of months that a student was in the program, so that saves me a step!
Your assumptions are correct, all scores are columns in a row for each student (total_tpm_1, total_tpm_2, ect), and cells with no data have been left blank.
As for the "aside" variable, I think I was a bit unclear. Sorry about that! I was actually explaining my reasoning for averaging the first three month's scores and averaging the last three month's scores. I do not think I need a variable that averages the first and last score together.
That being said, does it seem like a wise statistical decision to take the average of the first three month and the average of the last three months, and then look at the change in those average scores? Time series are a bit new to me, and I want to make sure I do not miss step my analysis.
I should probably explain the scores a little more. They are assessments in a sense, but are more so just a count of occurrences within a given time (one month). We are looking for change in these occurrences over time, with one month being the unit of measurement. I used the student example in the original post because it seemed easier to explain.
On a final note, aside from z-scores, is there a good way to standardize scores like this? The scores vary drastically, as some students go from scoring 40 to scoring 5 over time, while others go from scoring 1 to scoring 0 over time, and they are not normally distributed. I think this will complicate the analysis. We are looking for the average % change per student, and looking at variables that may influence someone's rate of change or amount of change.
Thanks for your help, I hope this makes sense.