Meta-Analysis Calculator For A/B Tests

apples
For meta-analyzing and combining two or more a/b tests together.
Good for apples, red, green, orange-like, pink or simply honey crisps. Your call.
Test 1
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vs
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1.75%
0.2718
1.099
Your A/B Test
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vs
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Calculate
Meta Inverse Variance-weighted Method Total z-score 1.099 | Sum of weights 3,935.65 | Total sample 1,242,470
Stouffer Method: value 1.109 | p-value 0.2676 | z-score 1.109
+1.75%
0.2718
1.099

α = 0.05 (two-sided)

QUICK SUMMARY OF APPROACH
  1. We take an inverse variance-weighted (precision-weighted) average of the lifts from each experiment to estimate the "true" lift that's assumed common to all experiments. This is also the maximum-likelihood estimate.
  2. Because we're working with RELATIVE lifts, we estimate the variance of the lift using the standard approach derived using the delta method.

CREDITS
A big thanks to the following indivduals for making this little project possible:
Ron Kohavi for guidance and input on weighing of p-values and inspring this project with his own meta-analysis spreadsheet.
Simon Dhala from whom I took the cumnormdist PHP function.
Tyler Buffington for multiple discussions and input about various meta analysis approaches.
Ryan Thomas for finding that the initial p-values were not being properly calculating upon the initial release.

Thanks,
Jakub Linowski