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I have a need to analyze an experiment that had a binomial outcome and categorical predictors. For context we sent out an email to our customers and encouraged them to register their account online (did register or did not register online). There are different nine groups that received the email. The groups are segmented based on their account opening date with our firm (1 week ago, 2 weeks ago, 3 weeks ago, etc...).

What method would I use to determine if the response from each of the nine groups is significantly different? We have used R and ran ANOVA in the past when our dependent is continuous but I am not sure how to apply the same procedure with a binomial.

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The model you re looking for is called a logistic regression. Look at the glm function in R and use family=binomial().

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As @fabians noted, this can be done with logistic regression. You should investigate the inclusion of your predictor as an ordinal variable (not categorical) because with 9 levels you likely could model it that way and gain power. Then you can test for a linear effect or a quadratic effect etc. instead of ignoring the ordering of the "categories".

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