Order Restricted Randomized Block Designs

Abstract

Field experiments are run under two competing objectives, high precision and minimal cost. The precision can be increased either by using sound experimentation techniques that account for the sources of variation with reasonable statistical models or by increasing the sample size. Large sample sizes usually increase the cost of the experiment and may not be feasible. This paper uses order restricted randomized designs (ORRD) to increase the precision while keeping the sample size and cost of the experiment minimal. The ORRD described here starts with a randomized block design but adds a second layer of blocking by ranking plots within each block. This creates a two-way lay-out, blocks and ranking groups, and uses a restricted randomization to improve the precision of estimation of the treatment parameters. Ranking groups create a correlation structure for within-block units. The restricted randomization uses this correlation structure to reduce the error variance of the experiment. The paper computes the expected mean square for each source of variation in the ORRD design under a suitable linear model. It also provides approximate F-tests for treatment and ranking group effects. The efficiency of the ORRD is investigated through empirical power studies. Finally, an example based on a uniformity field trial illustrates the use of the method in a split-plot experiment. Supplementary material to this paper is provided online.