Development of rotation sample designs for the estimation of crop acreages

The idea behind the use of rotation sample designs is that the variation of the crop acreage of a particular sample unit from year to year is usually less than the variation of crop acreage between units within a particular year. The estimation theory is based on an additive mixed analysis of variance model with years as fixed effects, (a sub t), and sample units as a variable factor. The rotation patterns are decided upon according to: (1) the number of sample units in the design each year; (2) the number of units retained in the following years; and (3) the number of years to complete the rotation pattern. Different analytic formulae for the variance of (a sub t) and the variance comparisons in using a complete survey of the rotation patterns.