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In this paper it is assumed that, using a sample survey, two factors are to be studied, comparisons between the "levels" of the factors are of greatest interest, and there is "interaction" between the factors. Attention is concentrated on situations in which only two levels of each factor are to be compared, but extensions to more complex surveys are discussed. Assuming independent sampling, optimal sample size allocations are obtained. Where these allocations require recourse to programming algorithms, approximate solutions are given. If independent sampling is not feasible, a double sampling procedure is suggested. To indicate how sub-sampling from the first phase sample is to be carried out, a sampling rule (possessing optimal conditional precision properties) is derived. Then, a procedure to determine the optimal first phase sample size is given. Finally, it is demonstrated that this double sampling procedure can be applied to estimation of the (finite) population mean when double sampling with stratification is used. [ABSTRACT FROM AUTHOR]

This paper is devoted to a discussion of an iterative procedure for obtaining the maximum likelihood estimator of the covariance matrix for multivariate experiments in which measurements on certain components of a normal vector random variable are intentionally omitted in corresponding subgroups of the experimental units. The proposed algorithm, which is based on the Newton-Raphson method, is outlined in detail in Section 5. A special design is included to illustrate the procedure and a few areas of application are indicated. [ABSTRACT FROM AUTHOR]