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I am performing an A(control) vs B(variant) test twice. I want to know if the difference of A/B change between the 2 runs is statistically significant.

Example:

1st run: 
both A and B have 100 data points each
conversion(A)=12% , conversion(B)=15% => change=25%

2nd run: 
both A and B have 80 data points each
conversion(A)=10%, conversion(B)=12% => change=20%

What test to apply to know if the difference between 25% and 20% is significant?

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  • $\begingroup$ Do you have the raw data? Counts? $\endgroup$ Aug 7, 2019 at 13:12
  • $\begingroup$ This sounds almost like a difference in difference design. $\endgroup$ Aug 7, 2019 at 13:14
  • $\begingroup$ I have only the data provided in the example. $\endgroup$
    – Anton
    Aug 7, 2019 at 13:25

1 Answer 1

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Assume that the conversion in groups A and B is binomially distributed with parameters $p_1$ and $p_2$, respectively. If you have the exact data, but not only the counts i.e. whether each datapoint belongs to A or not and to B or not, then I could suggest an approach which is probably not the best one, but it might be of some use:

  • Take an estimates for $p_1 = 0.12$ and $p_2 = 0.15$, coming from run 1, which gives also an estimate for the difference $p_2 - p_1 = 0.03$. Then, use the Fisher's exact test(https://www.statsdirect.com/help/proportions/unpaired.htm), to get a confidence interval for the same difference , when using the data from run 2. If the obtained interval does not contain 0.03, then you might say that the difference between the 2 differences you have, for the proportions in groups A and B is significant.
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