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Evaluating the treatment effects has become an important topic for manyapplications. However, most existing literature focuses mainly on the averagetreatment effects. When the individual effects are heavy-tailed or have outliervalues, not only may the average effect not be appropriate for summarizing thetreatment effects, but also the conventional inference for it can be sensitiveand possibly invalid due to poor large-sample approximations. In this paper wefocus on quantiles of individual effects, which can be more robust measures oftreatment effects in the presence of extreme individual effects. Moreover, ourinference for quantiles of individual effects are purely randomization-based,which avoids any distributional assumption on the units. We first considerinference for stratified randomized experiments, extending the recent work ofCaughey et al. (2021). The calculation of valid $p$-values for testing nullhypotheses on quantiles of individual effects involves linear integerprogramming, which is generally NP hard. To overcome this issue, we propose agreedy algorithm with a certain optimal transformation, which has much lowercomputational cost, still leads to valid $p$-values and is less conservativethan the usual relaxation by dropping the integer constraint. We then extendour approach to matched observational studies and propose sensitivity analysisto investigate to what extent our inference on quantiles of individual effectsis robust to unmeasured confounding. Both the randomization inference andsensitivity analysis are simultaneously valid for all quantiles of individualeffects, which are actually free lunches added to the conventional analysisassuming constant effects. Furthermore, the inference results can be easilyvisualized and interpreted.

Treatment Effect Quantiles in Stratified Randomized Experiments and Matched Observational Studies