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I have a set of data. The data contains 30.000 observations of a set of several variables. One of those variables indicates a nominal segment classification. In total there are six different segments. Another one of those variables is a binary variable with the values 0 and 1. I am now trying to assess, wether the different segments differ in respect to the binary variable, i.e. my hypothesis is that every segment differs from each other in respect to the binary variable. It might be important to note that I have no idea of how the 1´s should be distributed among the entire population/the segments.

Looking at the relative occurence of the binary value 1 within each segment, it looks like the groups really differ in the hypothesized way. But I am trying to put up a statistically valid test to give a valid proof of that hypothesis.

The fact that the variable I am looking at is binary makes me unsure, which kind of test I have/or can use. Any suggestions? Thanks in advance.

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  • $\begingroup$ Why did you split up your dataset into six pieces? Can you tell us a bit more about your data and how it was collected? Are there any independent variables? Just knowing that your data is dichotomous is not really sufficient to provide you with proper guidance on how to proceed. $\endgroup$ Mar 5 '19 at 15:06
  • $\begingroup$ I edited the question accordingly. $\endgroup$
    – shenflow
    Mar 5 '19 at 15:11
  • $\begingroup$ In addition, when you say, "every segment differs from each other in respect to the binary variable," do you mean that you want to know if the proportion of 1's occures equally among the six different segments? Also, I've deleted some of my comments as you've edited your question. Feel free to delete your responses in the comments as well if you've added to your question to keep the question a bit more clean. Thanks. $\endgroup$ Mar 5 '19 at 15:20
  • $\begingroup$ Yes, that is what I want to look at. $\endgroup$
    – shenflow
    Mar 5 '19 at 15:37
  • $\begingroup$ @StatsStudent - do you have an idea? $\endgroup$
    – shenflow
    Mar 7 '19 at 21:44
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I would first start with a 6x2 contingency table. 6 rows for each segment and 2 columns for the binary variable (or vice versa). From here you can look at conditional probabilities to see how the proportions of the binary variable changes across segments. You can also do a chi-square test to statistically test for differences across segments.

If you want to explore further and assess which specific segments are statistically different from each other you can use a logistic regression with the binary variable as the response and the segment variable as a categorical variable. From here you can statistically test each segment group against one another. Be sure to control for multiple comparisons.

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