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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Facet theory | 2/8 | https://en.wikipedia.org/wiki/Facet_theory | reference | science, encyclopedia | 2026-05-05T09:54:10.375224+00:00 | kb-cron |
An initial framework for observing intelligence could be Mapping Sentence 1. The mapping sentence serves as a unified semantic device for specifying the system of intelligence test items, according to the present conceptualization. Its content facet, the material facet, may now serve as a classification of intelligence test items to be considered. Thus, in designing observations, a stratified sampling of items is afforded by ensuring an appropriate selection of items from each of the material facet elements; that is, from each class of items: the verbal, the numerical and the spatial.
=== Enriching the mapping sentence === The research design can be enriched by introducing to the mapping sentence an additional, independent classification of the observations in the form of an additional content-facet, thereby facilitating systematic differentiations of the observations. For example, intelligence items may be classified also according to the cognitive operation required in order to respond correctly to an item: whether rule-recall (memory), rule-application, or rule-inference. Instead of the three sub-content-universes of intelligence defined by the material facet alone, we now have nine sub-content-universes defined by the cartesian multiplication of the material and the mental-operation facets. See mapping sentence 2.
Another way of enriching a mapping sentence (and the scope of the research) is by adding an element (a class) to an existing content facet; for example, by adding Interpersonal material as a new element to the extant material facet. See Mapping Sentence 3.
=== Content profiles === A selection of one element from each of the two content facets defines a content profile which represents a sub-content-universe of intelligence. For example, the content profile (c2, q2) represents the application of rules for performing mathematical computations, such as performing long division. The 3x4=12 sub-content-universes constitute twelve classes of intelligence items. In designing observations, the researcher would strive to include a number of varied items from each of these 12 classes so that the sample of observed items would be representative of the entire intelligence universe. Of course, this stratified sampling of items depends on the researchers' conception of the studied domain, reflected in their choice of content-facets. But, in the larger cycle of the scientific investigation (which includes Faceted SSA of empirical data, see next section), this conception may undergo adjustments and remolding, converging to improved choices of content-facets and observations, and ultimately to robust theories in research domain. In general, mapping sentences may attain high levels of complexity, size and abstraction through various logical operations such as recursion, twist, decomposition and completion.
=== Cartesian decomposition and completion: an example === In drafting a mapping sentence, an effort is made to include the most salient content-facets, according to the researcher's existing conception of the investigated domain. And for each content facet, attempt is made to specify its elements (classes) so that they be exhaustive (complete) and exclusive (non-overlapping) of each other. Thus, the element 'interpersonal' has been added to the incumbent 3-element material facet of intelligence by a two-step facet-analytic procedure. Step 1, cartesian decomposition of the 3-element material facet into two binary elementary facets: The Environment Facet, whose elements are 'physical environment' and 'human-environment'; and the Symbolization Facet whose elements are 'symbolic' (or high symbolization), and 'concrete' (or low symbolization). Step 2, cartesian completion of the material facet is then sought by attempting to infer the missing material classifiable as 'human environment' and 'concrete'.
In facet theory, this 2×2 classification of intelligence-testing material may now be formulated as an hypothesis to be tested empirically, using Faceted Smallest Space Analysis (SSA).
=== Complementary topics concerning the mapping sentence === Despite its seemingly rigid appearance, the mapping sentence format can accommodate complex semantic structures such as twists and recursions, while retaining its essential cartesian structure. In addition to guiding the collection of data, mapping sentences have been used to content-analyze varieties of conceptualizations and texts—such as organizational quality, legal documents and even dream stories.
== Concepts as spaces: faceted SSA ==
=== Description of Faceted Smallest Space Analysis (Faceted SSA) === Facet theory conceives of a multivariate attribute as a content-universe defined by the set of all its items, as specified by the attribute mapping-definition, illustrated above. In facet-theoretical data analysis, the attribute (e.g., intelligence) is likened to a geometric space of suitable dimensionality, whose points represent all possible items. Observed items are processed by Faceted SSA, a version of Multidmensional Scaling (MDS) which involves the following steps: