title: ANCOVA for nonparallel slopes: the Johnson-Neyman technique.
abstract: The Johnson-Neyman (JN) procedure, as originally formulated (Stat Res Mem, 1 (1936) 57-93), applies to a situation in which measurements on 1 dependent (response) variable, X, and 2 independent (predictor) variables, Z1 and Z2, are available for the members of 2 groups. The expected value of X is assumed to be a linear function of Z1 and Z2, but not necessarily the same function for both groups. The JN technique is used to obtain a set of values for the Z variables for which one would reject, at a specified level of significance alpha (e.g., alpha = 0.05), the hypothesis that the 2 groups have the same expected X values. This set of values, or 'region of significance,' may then be plotted to obtain a convenient description of those values of Z1 and Z2 for which the 2 groups differ. The technique can thus be described as a generalization of the analysis of covariance (ANCOVA) which does not make the assumption that the regression coefficients for the regression of X on the covariates, Z1 and Z2, are equal in the groups being compared. In this paper we describe, illustrate and make available a menu-driven PC program (TXJN2) implementing the JN procedure.
authors.affiliation: Department of Biologic and Materials Sciences, Dental School, University of Michigan, Ann Arbor 48109.
authors.forename: C J
authors.initials: CJ
authors.lastname: Kowalski
authors.forename: E D
authors.initials: ED
authors.lastname: Schneiderman
authors.forename: S M
authors.initials: SM
authors.lastname: Willis
mesh_terms: D000704:Analysis of Variance; D003196:Computer Graphics; D016001:Confidence Intervals; D006801:Humans; D007677:Kidney Function Tests; D008103:Liver Cirrhosis / Q000503:physiopathology / Q000601:surgery; D008432:Mathematical Computing; D016032:Randomized Controlled Trials as Topic / Q000379:methods; D012044:Regression Analysis; D012984:Software; D012985:Software Design; D014508:Urea / Q000378:metabolism
chemical_list: D014508:Urea