Post-Stratified Inference for Pairwise Treatment Comparisons in Randomized Block Designs

Abstract In this study, we introduce a novel approach to statistical inference for multiple comparison procedures in a generalized randomized complete block design (RCBD) by employing post-stratification of experimental units. After completing the experiment, our method involves randomly pairing within-block experimental units (EUs) subjected to two different treatments, t and $$t'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>t</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> . Each pair of experimental units is then ranked based on pre-treatment auxiliary (covariate) information, assuming no treatment effects. These ranked sets are subsequently divided into two distinct categories, which serve as an additional blocking factor based on the ranking of within-set experimental units. The first ranking block contains the sets where the lower rank corresponds to treatment t and the higher rank to treatment $$t'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>t</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> , while the second ranking block contains the reverse treatment allocation. This post-stratification is performed for all possible pairs of treatments with $$t&lt;t'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msup> <mml:mi>t</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:math> . Based on this post-stratified data, we develop a multiple comparison procedure for all pairwise contrast parameters. The proposed procedure demonstrates superior statistical power and yields narrower confidence intervals for multiple pairwise contrast inferences when the assumptions of the analysis of covariance model are not satisfied. The application of the proposed procedure is illustrated using experimental data.