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I have data from a randomized survey experiment in which each respondent was assigned to one of 4 groups, one of which can be considered a "control" or "no treatment" group. The key question asked in the survey was a binary one: i.e. each respondent was faced with a choice between two products given some stimulus based on the assigned group. Of course, there are several other questions to be controlled for (demographics, pre-existing preferences, etc.).

I want to know what effect, if any, being in a particular group had on the respondent's choice for that key question, controlling for the other factors. Since my response variable is categorical I can't use ANOVA (at least R doesn't appear willing to let me have a non-numeric response variable). I have tried to do a logistic regression but it seems like the structure of my data means that this would result in the respondents in each group being compared to the rest of the respondents which seems like it would be incorrect.

My data resembles the following in structure:

| Id | Group | Product Chosen | ... (other variables)
| 1  |     1 | A              | ...
| 2  |     4 | B              | ...
| 3  |     3 | B              | ...
| 4  |     2 | B              | ...
| 5  |     1 | A              | ...
| 5  |     2 | B              | ...
| 5  |     4 | A              | ...
| 5  |     3 | B              | ...

etc.

In case it is relevant, I have been using R for my analysis.

Update: Just so it's clear, my working hypothesis is that respondents in non-control groups were more likely to choose product A than B (and less importantly, but similarly, that respondents in group 2 were more likely than those in group 3, and those in group 3 were more likely than those in group 4).

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    $\begingroup$ What are your hypotheses? Since the group factor has 4 levels, there are several possible contrast specifications. $\endgroup$ – Sven Hohenstein Apr 14 '13 at 7:53
  • $\begingroup$ Expanding a bit on @SvenHohenstein 's comment: You can use logistic regression, you just have to tell R which groups you want to compare to which. The way to do this is with contrasts. $\endgroup$ – Peter Flom Apr 14 '13 at 10:53
  • $\begingroup$ Hi-- The hypothesis is that being in one of the three non-control groups correlates with a higher likelihood of choosing product A over B than being in the control does. As a secondary hypothesis I expect group 2 to have more of an effect than 3 and 3 more than 4, but this is less important. $\endgroup$ – Pygmalion Apr 14 '13 at 16:20

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