Hello Diana,

I think the most challenging part of your query is, how to set suitable values for what should be considered as the "expected value" for any one one count in your model (e.g., pre_product #1 users who change to post_product #2 users).

Isolating just the instances of pre_product #1 users as an example, you could establish some hypothesis as to what the "expected" distribution of choices (1, 2, 3, 4, or none) at post_measurement should be, then use a chi-square goodness-of-fit test to compare observed frequencies with expected frequencies. This could be applied to all 4 products.

A variant of McNemar's test might be closer to what you're after: ignoring the cases that remain the same with respect to choice, is there an inequality in the choices among those who changed from pre to post?

The minute you propose to add covariates to the model, though, things become more challenging (especially if these are continuous variables, and not categories, like your pre and post choices. If all were converted to categories, log-linear models might be one way to proceed.

If this seems not to address your intended goals, perhaps you could elaborate your query a bit.

Good luck with your work.

Thank you so much, David. Your comments have been very helpful.

Can you recommed me a textbook easy to understand with examples of these tests?

According to your comments, I ran a chi-square goodness-of-fit test with the expectation that consumers would buy the same amount of brand A in both pretest and posttest, to see if the flow to buying brand A in pretest to buying brand A in postest is significant. A made a dichotomous variables (yes/no) where I have 196 consumers that buy brand A in both pretest and postest and 24 who switch from buying brand A in pretest to buying another brand. The expected is that the 220 consumers who buy brand A in pretest continue buying it in postest. Then I will do the same with all the flows. What do you think about this?

Regarding the McNemar's test, I think it's useful but I don't know which 2 variables I can compare. Maybe the consumers buying brand A in pretest and another one in postest and consumers buying another brand in pretest and brand A in posttest?

Thank you again. You're so kind.

What I mean in the last comment is if I use the chi-square goodness of fit test with a table like:

Observed Expected

Yes 196 220

No 24 0

Can I use a 0 in expected frequencies? It doesn't seem appropriate.

Hello again Diana,

1. If your null hypothesis is that there is no change from pre to post choice, then you may indeed set expected frequencies as per your last post (e.g., 100% same; 0% different). Here, the zero expected frequency isn't a concern because this is a goodness of fit test. In the (perhaps more common) chi-square test of independence, expected cell frequencies should be 5 or more for the sample statistic to conform well to the theoretical chi-square distribution...which only means that marginal frequencies (row or column totals in an X by Y table) are not tiny or zero.

2. For evaluating instances of responses that changed, if your hypothesis was that each of four other options was equally likely, then your expected cell frequencies for those option categories would be nc / 4, where nc is the number of persons who changed their selection from the pre occasion (for a given brand).

Of course, if few people change from one specific brand, the low counts in the cells will mean that the test of equality (among competing brands or no brand options) will not be very powerful.

Good luck with your work.

If I understand correctly this is a square table, and often used in social mobility research and elsewhere. These are usually examined within a log-linear framework, and do, like David Morse suggests, compare observed values with various sets of expected values. It will be covered in most categorical data analysis books (for examples, Agresti's CDA has a chapter "Models for matched pairs." As you add more time points the models become more involved, but there are also methods for these (google categorical with longitudinal or time series).

I'm going to try with your recommendations.

Thank you very much David Morse and Daniel Wright