Order Restricted Cluster Randomized Block Design

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