Covariance Analysis, Factorial Experiments and Marginality

Abstract

The use of covariates introduces non-orthogonality into factorial analyses that would otherwise be orthogonal; in particular, non-orthogonality is induced between one treatment effect and another. Recent discussions on the general principles of non-orthogonal analyses and on the principle of marginality might therefore be thought relevant to factorial covariance analyses. The present paper examines these matters and tries to assesstheir importance in practice. Published analyses are re-examined and criticized, to illustrate the points at issue. Covariance analysis for split-plot experiments and for variates with missing values is not discussed.

Donald Arthur Preece: A life in statistics, mathematics and music

“…He compiled a bibliography of randomization, and kept it up to date, but never published it. He did publish expository articles [40,42,44,65,69] in the Statistician about simple parts of statistics and how to teach them, as well as some rants [47,51,58,64,71] about statistical practice in the design of real experiments and the subsequent data analysis. These may have been motivated by poor practice that he found in experimental stations on his overseas trips or by the struggles of his junior colleagues.…”