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Facet theory is a metatheory for the multivariate behavioral sciences that posits that replicable research and meaningful measurements can be advanced by discovering relationships between classifications of observations and partitions of suitable data-representation spaces. These spaces may depict either similarity measures (e.g., correlations) or partially ordered sets, derived from the data. Facet Theory was initiated by Louis Guttman and has been further developed and applied in a variety of disciplines of the behavioral sciences including psychology, sociology, and business administration. Variables as statistical units. Facet theory acknowledges that, in behavioral research, observed variables typically form but a sample from an infinite number, or a very large number of variables that make up the investigated attribute (the content universe). Consequently, facet theory proposes techniques for sampling variables for observation from the entire content universe; and for making inferences, from the sample of observed variables to the entire content universe, as follows: (a) Sampling variables from the content universe. This is done with the aid of a mapping sentence, essentially a function whose domain consists of the respondents and of the stimuli as arguments, and whose image consists of the cartesian product of the ranges of responses to the stimuli, where each response-range is similarly ordered from high to low with respect to a concept common to all stimuli. When stimuli are classified a priori by one or more content criteria, the mapping sentence facilitates stratified sampling of content universe. See Section 1 below. A classification of the stimuli by their content is called a content facet; and the pre-specified set of responses to a stimulus (classifying respondents by their response to that stimulus) is called a range facet. (b) Making inferences from the sample of observed variables to the entire content universe. Such inferences require a specification of the kind of research-outcomes with respect to which inferences are to be made. Facet theory posits that scientifically stable (reproducible) outcomes would result from regional hypotheses; hypotheses about correspondences between the definitional (content- or range-) facets on the one hand, and empirical partitionings into regions of certain geometric spaces, on the other hand. Thus, a regional hypothesis specifies a one-to-one correspondence between facet-elements (classes) and disjoint regions in space.

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facemark, facepiece, faceplate, facer, facet, facete, faceted, facetely, faceteness, facetiae

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