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We study ratio metrics in A/B testing at the presence of correlation amongobservations coming from the same user and provides practical guidanceespecially when two metrics contradict each other. We propose new estimatingmethods to quantitatively measure the intra-user correlation (within segments).With the accurately estimated correlation, a uniformly minimum-varianceunbiased estimator of the population mean, called correlation-adjusted mean, isproposed to account for such correlation structure. It is proved theoreticallyand numerically better than the other two unbiased estimators, naive mean andnormalized mean (averaging within users first and then across users). Thecorrelation-adjusted mean method is unbiased and has reduced variance so itgains additional power. Several simulation studies are designed to show theestimation accuracy of the correlation structure, effectiveness in reducingvariance, and capability of obtaining more power. An application to the eBaydata is conducted to conclude this paper.

Dealing With Ratio Metrics in A/B Testing at the Presence of Intra-User Correlation and Segments