Nonorthogonal Analysis of Variance Using Iterative Improvement and Balanced Residuals

A method is developed for computing an exact nonorthogonal analysis of variance using cell means. This is accomplished without forming or using computer storage for X 0, or X′0 X 0, or an orthogonal transformation of X 0, where X 0 is the N × p nonorthogonal design matrix. The method is a convergent iterative method which utilizes balanced analysis-of-variance estimates and residuals iteratively in solving the relevant normal equations and conducting tests of hypotheses. A monotonicity property of the method is derived to minimize iteration for nonsignificant factors or interactions in hypothesis testing.