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This book summarizes the methods and concepts of Statistical
Implicative Analysis (SIA), created by Régis Gras in the 1980s to
study, in a new way, the behavioural responses of French pupils to
mathematics tests. Using a multidimensional, non-symmetrical data
analysis method, SIA crosses a set of subjects or objects with a
set of variables. It effectively complements traditional
correlational and psychometric methods. SIA, through its various
extensions, is today presented as a broad Artificial Intelligence
method aimed at extracting trends and possible causalities in the
form of rules, from a set of variables. It is based on the
unlikeliness of the existence of these relationships, i.e. on the
relative weakness of their counter-examples compared to what chance
alone would produce. It establishes a dual topological relationship
between the set of subjects and the set of variables. Many
applications of this approach, driving forces or crucibles for the
development of SIA, have concerned and still concern various fields
such as didactics, evaluation and assessment, psychology,
sociology, medicine, biology, economics, art history, and others.
Key Features: Presents the foundations and representations of SIA.
Provides extensions of variable sets and subjects. Includes a bonus
exercise.
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