How would I compare a set of discrete data before and after treatment? What type of statistical test would you use to examine the difference in these tests to see if there is a difference between the before and after sample?




Treatment A results
Grade 8
Grade 9
Grade 10
Grade 11
Grade 12




Before Treatment Count (week0)
0
11
33
34
22


After Treatment Count (week12)
4
18
35
26
17




Thanks ahead of time! I'm having trouble wrapping my head around this one for some reason...
 A: A $2 \times 5$ contingency (multiway) table analysis, based on a chi-squared test.  It's essentially a test of proportions of the frequencies (count data) to determine if anything "tracks" between the two factors, before/after and grade.  Contingency table analysis can be complex, however, wherein different hypotheses can be employed surrounding questions about independence, correlation, trends, patterns.
Since you do have before and after data, where subjects are their own controls, there may be within-subject correlation issues that need to be taken into account.  In other words, there can be some predictability between the before and after data, since the frequencies in the after data are not independent of the frequencies in the before data, because they are correlated.
If your before and after categories were drug vs. placebo, and different subjects were evaluated for grade in these two categories, then the frequencies would be independent.  For $2 \times 2$ tables with before and after vs. e.g. disease/no disease, or low grade vs high grade, look at the McNemar test.   Otherwise, the analysis may be attacked from a longitudinal data analysis perspective.
