A statistical method has been developed for nested incomplete samples in a longitudinal study in which part of the sample has dropped out in such a way that the data have a nested pattern. A procedure which performed well in a Monte Carlo experiment was extended to a two-factor incomplete design with repeated measures on one factor. Methods designed for this type of analysis included two multivariate techniques--likelihood ratio and step-down procedures with between subjects and within subjects variables--and univariate methods involving use of the EM algorithm in conjunction with restricted maximum likelihood estimation of variance components. Nested data were subjected to analysis of variance and step-down tests. It was concluded that step-down statistics were simple to use and did not require restrictive assumptions--type H covariance matrix--of univariate analysis of variance. They were appropriate for a mixed model, and calculation software was available. Step-down statistics were preferable to analysis of variance when the sample was nested and assumption violations were likely. References and four data tables conclude the document. (GDC)