One-level rotation design balanced on time in monthly sample and in rotation group

We introduce the two-way balanced one-level rotation design for which balancing is done on interview time in sample and in rotation group and provide the necessary and sufficient condition for the two-way balancing and an algorithm to construct such design. Using this design, we obtain generalized composite estimators (GCE) and the minimum variance linear unbiased estimator (MVLUE). We then calculate their variance and mean squared error (MSE) when there exist two types of correlations and the rotation group bias. Minimizing the weighted sum of variances (or MSEs), we derive one set of the compromise coefficients for all important estimators and characteristics to retain the consistency in total. We compared the GCE with the compromise coefficients to MVLUE and other GCEs with the previous coefficients. We show that the second-order correlations have very significant effects on the variance and MSE. We also investigate the design efficiencies for some selected two-way balanced designs.