Abstract
Abstract Some properties of and extensions to Tukey's method of median polish, an exploratory robust additive decomposition of a two-way table, are presented using the low median. If the table entries are rational numbers, then the iteration process must stop after a finite number of steps. However, even for tables of bounded dimension the number of iterations can be arbitrarily large. For 3 by 3 tables, the sum of absolute residuals is often minimized by median polish. Minimization conditions are identified that are likely to occur in practice. A method to supplement the polishing process by increasing the number of zero residuals is developed.
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