
Dissertation Defense: Dalton Hopper, Statistics Ph.D. Candidate
Title: Order Restricted Cluster Randomized Design (ORCRD)
Abstract: This dissertation develops inference for the order restricted cluster randomized design (ORCRD). For H treatment levels, this design consists of H blocks, each of which contains m sets of H ranked cluster units. These cluster units are then organized into a row-column structure. In this structure, rows are indexed by two variables: block and set. Columns are indexed by rank only. The block and rank indices define H2 cells. The H treatments are then randomly allocated to these H2 cells with the restriction that each treatment appears only once in each block and column (rank). All cluster units in each cell receive the same treatment. The data is collected from subsampling in each cluster unit by using either simple random sampling or ranked set sampling. For the ORCRD, we fit a linear model that accounts for the correlation structure among cluster units in the same set, calculate EMS expressions, develop inference for the treatment effect, assess ranking quality, and estimate model parameters. We also compare the efficiency of the ORCRD to competitive designs in the literature, calculate optimal cluster and within-cluster sample sizes, and present asymptotic results for treatment contrast estimators. Finally, we apply the ORCRD to an educational setting.
Advisor: Omer Ozturk