## Stat Colloquium: Dr. Omer Ozturk

#### The Ohio State University

**Title**: Order Restricted Randomization
in Agricultural Field Experiments

**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 randomised 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 model. It also provides approximate 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 trial illustrates the
use of the method in a split-plot experiment.