If I understand correctly: all of your students took an entry course, then they had to take one course in each category of mid-level courses, and then each of those mid-level courses opened up the choice & requirement to take one (or more) courses in a set of high-level courses?  If so, it seems like your courses follow a flow-chart.  If your courses are perfectly structured with prerequisites, then it's possibly a tree diagram.  I recommend you begin by drawing that diagram with all the course names.  Many software programs like PowerPoint facilitate drawing flow charts.  Next tabulate the number of students who take each course; add those to the diagram.  Depending on how you have the data set up, you might use "sort" and "countifs" in Excel or use "split file" and "frequencies" in SPSS.  Calculate conditional probabilities of taking each course given you took the prerequisite; add those.  Now you have an intuitive graph that summarizes your students' progress.

If you are trying to figure out if certain courses are more commonly chosen by students then make a table for each "branch" in the tree.  Make a column called "course" and on each row below write a course from the part of the "menu" students chose from.  In the second column call it "actual" and write the number who chose each course.  In the third column label it "expected" and divide the total students by the number of courses and write that number in each cell (that would be the number of students taking each course if they chose at random).  To statistically determine if the actual students took some courses more/less frequently than others, use a goodness-of-fit chi square.  SPSS can do this (if your data is set up properly) but it's probably easier to just type your numbers into one of the many online stats calculators. I put a link to a good one below.  Just use caution in interpreting your results.  For example, just because students chose a course more often does not necessarily mean students want more of that course offered.  It could simply be a consequence of how many sections of the course you've offered in the past (and students' desire to graduate on time).

Hope this helps some Jim.

Kevin

http://vassarstats.net/csfit.html

Hello Jim,

I did a somewhat similar study on analysis of public choices for ecological solid waste management using discrete choice experiment technique. I used multinomial logit regression for analysis which is possible using SPSS. Please find the attached publications. Hope this will help. Best......... 

Conference Paper ANALYSIS OF PUBLIC PREFERENCES FOR ECOLOGICAL SOLID WASTE MA...

Conference Paper Analysis of Public Preferences on Ecological Solid Waste Man...

I think Kevin has provided good suggestions. But I think you will need to keep track of those who succeed in the first round of classes v. simply taking the courses. And one of the locations I would think you want is that they dropped out of school.  You don't mention the size of your data base which limits any advice w can give you.

Hi, mostly in the presented case: multinomial logit regression is the best test

good luck

Thank you all for your responses.  Very helpful.  I am, of course, trying to avoid doing all the hand-work that Kevin Grobman's suggestion would entail. As Kevin probably knew, I have not been able to find any alternative, although this seems like a very common question in the analysis of choices over time.

As this is a census and a descriptive study, I am not very interested in tests of significance (gasp!).  To restate:  I am trying to trace the actual patterns of choices of students entering a menu based curriculum through 12 academic periods (4 academic years). I will have data on every student who took a course in that curriculum any time during the most recent four years.  We have 127 courses in our curriculum, about a third of which are offered every semester and the others on a regular or irregular rotation. About 60 courses are offered per academic period. We have 1,500 majors with another 150 visitors with an average headcount enrollments of 750 per regular semester (maybe half that in the summer).  Consequently over the 12 academic periods, people will drop in and out and courses will drop in and out.

To begin I will have 12 sets of data, each containing all the enrollments for the given academic period.  These will be merged across students to produce one record of all the courses taken for every student who took a course in our curriculum any time during the 4-year span. (The data could also be pivoted and merged across courses.) I'm guessing 2,500 records, but no one knows at this point.

Therefore, I have N students engaging up to12 choice points, each resulting in 0-4 selections from the N courses offered from the curriculum at that point  Each choice point occurs at a different time.  This being public education, rules and prerequisites are more recommendations than not. The student becomes the final actor in the curriculum development process. 

My initial thought was cluster analysis with a dendrogram display. However, I would really like to get the "flow" of numbers as students move through the curriculum.  (I envision them as multi-colored currents in a river of enrollments.) I am not sure if I can extract those numbers out of regression. Knowing that 20% of those enrolled in course A at time 1 takes course B at time 2 seems much more valuable than a relational coefficient.

The opportunity to write this all out has had great value in and of itself.  Your further comments will be even better.  Thanks.

One thing I missed is that each student will select at least 14 courses to complete a major.

Reading your details, Jim, I'm even more convinced it's a giant number-crunching exercise instead of an inferential statistic.  Regression seems like overkill, in that you would effectively be running each to get the conditional probabilities anyway.  Cluster analysis would tell you which courses tend to be taken together, but basically your results will just show you that students tend to follow the curriculum for the major, like they're supposed to.  Joseph makes a good point about not equating taking the course with completing it, so that would make it even more complicated.  It's not quite as bad as it seems.  Excel is a much more powerful and flexible program than most researchers realize.  In fact, I manage all of my data and do any calculations in Excel, and then import a refined spreadsheet into SPSS for statistics.  Try this.  In a single workbook on a single spreadsheet, organize your data about students.  I'm imagining each row is a student and then you have a column for each course indicating if it's completed or not.  On the next worksheet (tab), create a matrix with every course in the top row and the same courses in every column (paste special -> transpose).  This will be a conditional probability matrix.  Pick any cell in the matrix you would like to begin with.  Manually enter a formula to calculate the probability that a student took ROW course given he or she took COL course.  In the process you'll click the course in the row, course in the column, and highlight an array on your raw data sheet.  You'll probably use the COUNTIFS function.  Put dollar signs in to fix your rows & columns as needed.  Now copy & paste your formula throughout the entire matrix.  In seconds you'll have all the data that you need to make the tree diagram and you might discover some unexpected patterns (e.g., students who took a certain upper-level course in one menu were more likely to take a certain upper-level course in another menu, possibly because its taught by the same inspiring professor).  Best wishes with your project, Kevin