Order restricted row‐column cluster randomized design

Abstract This research introduces a novel two‐stage cluster randomized design, the order restricted row‐column cluster randomized design. The new design builds upon the cluster randomized block design by incorporating a second layer of blocking, achieved through ranking cluster units that are randomly sampled from the population. This approach creates a two‐way layout, with blocks and ranking groups, and employs restricted randomization to enhance the accuracy of treatment contrast estimation. We calculate the expected mean square for each source of variation in this new design under a suitable linear model, develop an approximate ‐test for the treatment effect, assess the impact of ranking quality, calculate optimal sample sizes for a given cost model, formulate multiple comparison procedures, and apply the design to an educational setting.