By Clyde Coombs

A few facets of the methatheory of dimension -- the matter of mental dimension -- Definitions and postulates -- Genotypic parameters -- Phenotypic parameters -- the world of joint scales -- The unfolding approach -- a few implications for the legislations of comparative judgment.

"This monograph describes the development of a mental conception which defines the data inside the responses of people to stimuli. This has been comprehensive by way of abstracting yes homes of habit that are invariant over content material. those were categorised and quantified in a conception of information which, with the quasi-formal foundation hypothesized the following, determines the genotypic inferences that could be made up of appear habit. at the foundation provided the following sure theoretical strategies and interpretations are constructed and in addition yes new experimental methods and experimental kinfolk presented"--Preface. (PsycINFO Database checklist (c) 2015 APA, all rights reserved). Read more...

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Also Ref. 11, 45 Chapter V I THE AREA OF JOINT SCALES Certain interrelations between the genotypic and phenotypic parameters w i l l be studied in this chapter. The problem here is what the data, when collected by a given method, look like, for various characteristics of the genotypic level. This is an immense problem. The theory developed here, however, makes possible, in principle, the theoretical analysis of such relationships. Certain segments of this problem have been studied and the results w i l l be presented.

2. = J - ? 2 ( P h i j - P , j ) ^ (43) f^,. = i r f (p-ij-p-j)''-'^ (44) V . = D ^ ; + ff2 . ••I ••) . p .. 1 -1) Following the same reasoning as that used in developing the phenotypic parameters for individuals but this time reversing the roles of stimuli and individuals gives: (45) T?. = (1-^2 ) . p .. p .. 1-1) (46) 1 ' ^ • i ) . -a V . = D^ • + T ^ ••) ••) + 77^ ••) (7^ . P .. . P .. 1 1 -ij. 1) In the simplest case in which the sole source of controlled variance of the phenotypic scores (difficulties) of a stimulus over individuals is the spread of abilities of the individuals on the phenotypic level.

This quantity, t_^j_ , will be fundamental to the quantitative definition of a trait. Substituting Equation (11) in (8), the total variance of an individual's ^ h i j ^^1*^^^ over a group of stimuli becomes: (12) v.. = d f . + t2. i, Equation (12) is in some respects a more general case than is required for most experiments involving scaling on a single continuum. Because measurement problems are classifiable on the basis of relations between Q and C values and because this relation is the most common single source of the variance of the C values of an individual over a group of stimuli, the expression for t j ^ may be simplified by taking into account only this one source of variance.