Premium
Development and Analysis of Modified Paired Comparisons by Use of Linearized Nonlinear Regression
Author(s) -
Walsh John E.
Publication year - 1969
Publication title -
biometrische zeitschrift
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0006-3452
DOI - 10.1002/bimj.19690110204
Subject(s) - mathematics , flexibility (engineering) , nonlinear regression , statistics , nonlinear system , probabilistic logic , regression , set (abstract data type) , confidence interval , paired comparison , regression analysis , interval (graph theory) , basis (linear algebra) , linear regression , computer science , programming language , physics , geometry , quantum mechanics , combinatorics
The linearized nonlinear regression method (Walsh, 1963) has substantial curve‐fitting flexibility. It also permits isolation and probabilistic investigation of pertinent effects, and can be used for developing paired comparisons for persons, animals, or plants (“items” of a given type). Here, an item is identified by the values for specified characteristics, and two kinds of “treatment” (e. g., exposure and nonexposure to radiation) are compared with respect to observed values for a given characteristic. Ideally, two items being compared for treatment effect should be the same with regard to the other characteristics (those not used for comparison). That is, they should have the same set of values for these other characteristics. This ideal situation seldom occurs. However, by suitable use of the linearized nonlinear regression model, composite items can be constructed (for given treatment) that are the same with respect to the other characteristics. Modified paired comparisons are obtained on the basis of these composite items. The probability properties of modified paired comparisons can be very heterogeneous, so that special concepts and statistical techniques are needed. Two approaches for development of tests and confidence intervals are given. Some applications involving exposure to radiation are discussed.