Order restricted randomized designs and two sample inference

This paper develops a new design that relies on subjective judgment ranking to compare subsets of experimental units. This judgment ranking is used along with restricted randomization to improve statistical inference for the contrast between two levels of a treatment. The new design assigns the judgment ranked units in a subset to different treatments. Such an assignment translates the positive dependence among units within each subset into negative dependence for the estimators of treatment means, and hence leads to a reduction in variance for the contrast. For the proposed design, a test for the difference in means of two treatment levels is developed along with an associated confidence interval. It is shown that the null distribution of the proposed test is approximated reasonably well with the Student’s t-distribution for sample sizes as small as 6. A simulation study indicates that the proposed design is advantageous compared to its competitors in the literature for both high and low quality rankings. The new design’s advantage increases with the quality of rankings.