Interpretation of Adjusted Treatment Means and Regressions in Analysis of Covariance

Statistical with several variates or variables has become loosely classified into multivariate analysis, regression and of covariance. Most workers have more or less definite ideas about what is implied by each term, but few would agree with any specific definition of their boundaries. Most multivariate work is in one sense or another analysis; but, since its introduction by Fisher 1934 as an adjunct to of variance, the term analysis of covariance has had a special connotation, although the restriction may not always be maintained. Analysis of variance has itself acquired multiple connotations. In line with the comment by Eisenhart 1947 its etymological sense might be taken to imply detection and estimation of components of random variation associated with a composite population niow often referred to as variance component analysis. In a wider sense some have thought it might more accurately have been described as of a sum of squares, particularly when the model specifies only one variance derived from random sources, and the parts of the are compounds of this with constants by which class means are supposed to differ. In this form it is primarily an algorithm for tests of significance for estimates of certain constants, estimands of location. The associated model is conveniently called a regression model because the constants to be estimated can be formulated as regression coefficients. (See, for example, Anderson and Bancroft 1952). When classifications (treatments) are qualitative the estimands can be regarded as regression