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A modified $χ^2$-test for uplift models with applications in marketing performance measurement

Uplift, essentially being the difference between two probabilities, is a central number in marketing performance measurement. A frequent question in applications is whether the uplifts of two campaigns are significantly different. In this article we present a new $χ^2$-statistic which allows to answer this question by performing a statistical test. We show that this statistic is asymptotically $χ^2$-distributed and demonstrate its application in a real life example. By running simulations with this new and alternative approaches, we find our suggested test to exhibit a better decisive power.