Significant cost savings can be achieved with the use of matrix sampling in estimating population parameters from psychometric data. The statistical design is intuitively simple, using the framework of the two-way classification analysis of variance technique. For example, the mean and variance are derived from the performance of a certain grade level of students on arithmetic fundamentals. From the matrix of students and proposed test problems in the cell determined by the test and grade level variables, random sampling from both categories will provide efficient estimates of the mean and variance. Formulations for finite and infinite populations are derived. This document reduces the theoretical complexities to readable form; it includes a short literature review, a description of the technique using examples, an extension of the technique to multiple matrix sampling, and a discussion of the negative variance estimate problem using multiple matrix sampling. (LN)