Goodman and Kruskal's Tau b: Multiple and Partial Analogs

Gray, Louis N.; Williams, J. Sherwood

doi:10.1177/004912418101000105

Cited by 26 publications

(18 citation statements)

References 6 publications

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“…It also allows an evaluation of the contiibution of age to this prediction when the contribution of size is known and vice versa for size and age. The second analysis is based on the Goodman-Kruskal T a u coefficient, a measure of association (Goodman & Kruskal 1954) and partial association developed by Gray & Williams (1975). This evaluates quantitatively the relative contribution of either age or size to predicting the reproductive event when the other state variable is taken into account.…”

Section: Methodsmentioning

confidence: 99%

Natural dynamics of a Fucus distichus (Phaeophyceae, Fucales) population: reproduction and recruitment

Ang¹

1991

Mar. Ecol. Prog. Ser.

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ABSTRACT. Various phenomena related to reproduction and recruitment in a population of Fucus distichus L. emend. Powell in Vancouver, British Columbia. Canada were evaluated. Using log linear analysis and tests for simple, multiple and partial associations, a g e and size were both found to b e significant, but size slightly more so than age, as descriptors of reproductive events. Reproductive plants were found throughout the sampling period, from September 1985 to November 1987, but peaked in fall and winter of each year. Potential egg production, based on number of eggs produced per conceptacle and number of conceptacles per unit area of receptacle, is size-dependent. However, estimated monthly egg production, calculated by observed number of eggs in clusters extruded from the receptacle, is independent of plant size. Two types of recruits were monitored Microrecruits (< 1 mo-old of microscopic size) are germlings developed from fertilized eggs. Their numbers were assessed using settling blocks. Macrorecruits are detectable by the unaided eye and are plants appearing in the permanent quadrats for the first time. They can first be detected when about 3 to 4 mo old. The recruitment pattern of microrecruits is significantly correlated with reproductive phenology and patterns of potential and estimated monthly egg production. The pattern of recruitment of macrorecruits is negatively correlated with reproductive phenology and that of the estimated monthly egg production. Peaks in microrecruitment are not always followed by peaks in macro-recruitment. This apparent discrepancy is probably due to a differential survivorship of microrecruits over time or to the possible existence of a 'germling bank'. Patterns of survival and emergence of macrorecruits may b e independent of those of microrecruits or may be unrelated to the prevailing reproductive phenology.

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Section: Methodsmentioning

confidence: 99%

Natural dynamics of a Fucus distichus (Phaeophyceae, Fucales) population: reproduction and recruitment

Ang¹

1991

Mar. Ecol. Prog. Ser.

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“…(τ A is sometimes called multiple τ (Gray and Williams (1981) because it represents the total predictability of two or more predictor variables.) The CATANOVA test may be used to test the significance of the τ index.…”

Section: The Proposed Methodsmentioning

confidence: 99%

“…(τ B is simply the basic τ index for the marginal table (Table 2), while τ E is sometimes called partial τ (Gray and Williams 1981).) The CATANOVA test statistic can also be analogously decomposed into two parts.…”

Section: The Proposed Methodsmentioning

confidence: 99%

Tests of ignoring and eliminating in nonsymmetric correspondence analysis

Takane

Jung

2009

Adv Data Anal Classif

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Nonsymmetric correspondence analysis (NSCA) aims to examine predictive relationships between rows and columns of a contingency table. The predictor categories of such tables are often accompanied by some auxiliary information. Constrained NSCA (CNSCA) incorporates such information as linear constraints on the predictor categories. However, imposing constraints also means that part of the predictive relationship is left unaccounted for by the constraints. A method of NSCA is proposed for analyzing the residual part along with the part accounted for by the constraints. The CATANOVA test may be invoked to test the significance of each part. The two tests parallel the distinction between tests of ignoring and eliminating, and help gain some insight into what is known as Simpson's paradox in the analysis of contingency tables. Two examples are given to illustrate the distinction.

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“…One may also consider either of the Gray-Williams measures. Refer to Equations (3.2) or (4.2), and their discussion, of Gray and Williams [14] for description of these measures.…”

Section: A Measure Of Deviation From Complete Independencementioning

confidence: 99%

“…When contingency tables consist of three or more variables, multi-variate extensions of the Goodman-Kruskal tau can be considered. In particular, one may consider using the Gray-Williams [14] index, the Marcotorchino [16][17][18] index or the Simonetti [21] delta index.…”

Section: Introductionmentioning

confidence: 99%

Partitioning a non-symmetric measure of association for three-way contingency tables

Beh

Simonetti

D’Ambra

2007

Journal of Multivariate Analysis

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The Goodman-Kruskal tau index is a popular measure of asymmetry for two-way contingency tables where there is a one-way relationship between the variables. Numerous extensions of this index for multi-way tables have been considered in the statistical literature. These include the Gray-Williams measures, Simonetti's delta index and the Marcotorchino index. This paper looks at the partition of the Marcotorchino index for a three-way contingency table with one, two and three ordered categorical variables. Such a partition makes use of orthogonal polynomials and identifies two-way measures of asymmetry (akin to the Goodman-Kruskal tau index) and three-way measures generalisation. These partitions provide information about the structure of the asymmetric relationship between the categories in terms of location, dispersion and higher order moments

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Goodman and Kruskal's Tau b: Multiple and Partial Analogs

Cited by 26 publications

References 6 publications

Natural dynamics of a Fucus distichus (Phaeophyceae, Fucales) population: reproduction and recruitment

Natural dynamics of a Fucus distichus (Phaeophyceae, Fucales) population: reproduction and recruitment

Tests of ignoring and eliminating in nonsymmetric correspondence analysis

Partitioning a non-symmetric measure of association for three-way contingency tables

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