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A partial correlation test for the Goodman‐Kruskal λ on a dichotomy
Author(s) -
Suich Ronald C.,
Turek Richard J.
Publication year - 1989
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.2044-8317.1989.tb00909.x
Subject(s) - categorical variable , mathematics , statistics , measure (data warehouse) , test (biology) , partial correlation , variable (mathematics) , correlation , correlation coefficient , mathematical analysis , data mining , paleontology , geometry , biology , computer science
Goodman & Kruskal (1954) introduced a measure λ of predictive association when predicting the category of a variable A from a category of a variable B. The measure λ is such that 0≤λ≤1 with a zero value meaning no predictive gain, while λ=1 indicates a perfect predictive association between A and B. Turek & Suich (1983) developed an exact test of H 0 :λ = 0 versus H 1 :λ>0 where the variable A is dichotomous. This test is analogous to a test for the significance of the correlation coefficient. This paper analyses the partial λ coefficient in order to answer the question of whether knowledge of a third (fourth, fifth, etc.) classification results in a significant increase in ability to predict the dichotomous variable A. This test, developed for qualitative categorical variables, is analogous to the test for partial correlation coefficients for quantitative variables.