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I have made a logistic regression model that outputs probabilities over two different time periods(before and after) . I want to test if the difference between the probability of before and after is significant or not.

Which test is best to do so ? t-test? Proportion test? ANOVA? Wald?

My model has about 9 million observations , can i assume the variance of the times periods before and after are equal ?

Thanks , and comments/ suggestion are welcome :)

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    $\begingroup$ If you have an indicator for before/after in your model, how does testing the coefficient being different from zero not achieve that? $\endgroup$ – Glen_b Nov 16 '15 at 0:02
  • $\begingroup$ Do you want to know that for modeling data or for cases unknown to the model? $\endgroup$ – cbeleites unhappy with SX Nov 16 '15 at 0:08
  • $\begingroup$ @Glen_b, for our logistic regression, we've included indicator variables to account for difference in differences of whatever variable we are interested in finding a probability for. $\endgroup$ – a_student Nov 16 '15 at 0:20
  • $\begingroup$ @Glen_b when you say indicator for before and after, do you mean that since we've already included indicator variables in our regression that once we compare probabilities for a variable x before and after, that there is no need to test for significance because we already have indicator varibles included in our logistic regression ? $\endgroup$ – a_student Nov 16 '15 at 0:22
  • $\begingroup$ @cbeleites I want to know for modeling data. ive ran a logistic regression that included indicator variables for variables of interest. For example, after i find a probability for x before, and a probability for x after, and if these 2 probabilities have a difference of lets say, 3% , can I assume that difference is statistically significant? My before and after group have different sample sizes. $\endgroup$ – a_student Nov 16 '15 at 0:24

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