# Self-selected groups categorical breakdown test

I have a population of people, and one group who was self-selected (group A), and the remainder of the population (group B), and each group is broken into a group of n nominal categories (categories are identical for each group)

I want to track their follow-on behavior, and at a time in the future, I have a subset of group A who made a repeat behavior (say group A', who is self-selected), and a similar subset of group B (B', again, self-selected). I again have these groups broken down into the same n nominal categories as in the first stage.

I want to determine if the subset A' is significantly different than subset B', but am having trouble finding an appropriate statistical test to determine this, given the self-selection occurring at the original point in time (A vs B), and again for the repeat behavior (A' vs B').

Essentially I want to see if the categorical distribution of A' and B' are statistically different, given what we know about their initial distribution in A and B. Any ideas and the appropriate methodology to go about this? It seems McNemar's test is not appropriate, given the effect being measured (A vs B) happened before the original segmenting.

Example dataset:

|Group A    | CustomerCount|        | Group B   | CustomerCount|
|-----------|--------------|        |-----------|--------------|
| Channel 1 | 54           |        | Channel 1 | 2112         |
| Channel 2 | 34           |        | Channel 2 | 1332         |
| Channel 3 | 65           |        | Channel 3 | 2641         |


|Group A'   | CustomerCount|        |Group B'   | CustomerCount|
|-----------|--------------|        |-----------|--------------|
| Channel 1 | 16           |        | Channel 1 | 380          |
| Channel 2 | 12           |        | Channel 2 | 288          |
| Channel 3 | 41           |        | Channel 3 | 1234         |

• This is hard to follow. Can you make this more concrete? Can you provide a small, example dataset? – gung - Reinstate Monica Oct 28 '15 at 1:03
• Sure - essentially I have a group of customers who purchased product A, and a group who purchased product B. A subset of those who purchased product A, will at some point in the future repeat purchase any product (call that subset A'), and the same will happen with those who originally purchased product B (subset B' is those who purchased anything else again). Of those subsets, they can purchase via multiple channels. I'm trying to determine if the breakdown of those multiple channels is statistically different for those in group A' and those in group B'. – Nathan B. Oct 28 '15 at 16:24