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ON A CERTAIN TYPE OF PARTIAL HIGHER‐ORDERED METRIC SCALING 1
Author(s) -
Phillips J. P. N.
Publication year - 1966
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1966.tb00356.x
Subject(s) - metric (unit) , scaling , mathematics , object (grammar) , type (biology) , multidimensional scaling , identification (biology) , value (mathematics) , scale (ratio) , combinatorics , computer science , statistics , artificial intelligence , geometry , physics , ecology , operations management , botany , quantum mechanics , economics , biology
When a subject makes a number of discriminations between pairs of reference objects, each time saying which of the pair is closer in value to a test object, there arise two problems: (1) deciding which patterns of responses are internally consistent and (2) scaling the consistent response patterns. This paper generalizes Shapiro's solution for the case of three reference objects. (1) The identification of consistent response patterns requires a certain partial higher‐ordered metric scaling of the reference objects; however, if certain incomplete sets of judgements are used, then only an ordinal scaling of the reference objects is demanded. (2) The consistent response patterns can be ordinally scaled, but only a rudimentary partial higher‐ordered metric scale can be established.