median polish

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A robust method suggested by Tukey for estimating the mean μ, row parameters r1, r2,…, rj, column parameters c1, c2,…, ck, and residuals εjk for the model


with j=1, 2,…, J and k=1, 2,…, K. This iterative algorithm alternates row and column operations. Considering the rows first, for each row the row median is subtracted from every element in that row. For each column, the median of the revised numbers is then subtracted from every element in that column. This continues until all medians are 0. The outcome may vary slightly depending on whether rows or columns are considered first. In the example, μ is estimated as 30, with r1=−12, c4=−7, and ε1, 4=7 (so that 30−12−7+7=18, the original value).

Subjects: Probability and Statistics.

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