Order Restricted Cluster Randomized Block Design

Music City Center 

This research introduces a novel two-stage cluster randomized design, the order restricted cluster randomized block design (ORCRBD). The ORCRBD 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 the ORCRBD under a suitable linear model, develop an approximate F-test for the treatment effect, assess ranking quality, calculate optimal sample sizes for a given cost model, formulate multiple comparison procedures, and apply the design to an educational setting.

order restricted randomization

ranked set sampling

intracluster correlation coefficient

Latin square

optimal design 

Section on Statistics and Data Science Education