Measures of Association for Cross Classifications*

Goodman, Leo A.; Kruskal, William

doi:10.1080/01621459.1954.10501231

Cited by 622 publications

(623 citation statements)

References 11 publications

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“…The simple matching coefficient has been used traditionally as a measure of similarity or proximity between two ordered variables. However, it has been criticized by a number of researchers, including Goodman and Kruskal (1954) and Nelson (1984), for two reasons. One is that it does not provide a measure of bivariate ordinal association between two variables.…”

Section: Accuracy Versus Associationmentioning

confidence: 99%

“…He concluded that gamma (i.e. y) a measure of association developed by Goodman and Kruskal (1954), provided the best summative index of feeling-of-knowing performance. Specifically, y provides a measure of association between two ordered, symmetric responses of two or more levels each.…”

mentioning

confidence: 99%

“…Specifically, y provides a measure of association between two ordered, symmetric responses of two or more levels each. Responses are ordered when they can be ranked along a single dimension; they are symmetric when there is no implied causal or temporal relation between them (Goodman and Kruskal, 1954).…”

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confidence: 99%

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Measures of feeling‐of‐knowing accuracy: A new look at an old problem

Schraw

1995

Applied Cognitive Psychology

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Two ordinal measures of feeling-of-knowing performance appropriate for n x n data arrays are reviewed. Goodman and Kruskal's gamma provides a measure of association between recognition performance and feeling-of-knowing judgements. The Hamann coefficient provides a measure of agreement accuracy. The relative strengths and weaknesses of each measure are compared at length. A proof is provided, which reveals a lack of one-to-one relation between the two and suggests that they may be independent under most circumstances. It is concluded that both measures should be reported together as complementary indices as each captures a different facet of feeling-of-knowing performance. Alternative measures for gamma and the Hamann coefficient are considered and a number of recommendations are made for future research.

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Section: Accuracy Versus Associationmentioning

confidence: 99%

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confidence: 99%

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Measures of feeling‐of‐knowing accuracy: A new look at an old problem

Schraw

1995

Applied Cognitive Psychology

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“…Kendall-Gibbons' τ b [13] and Goodman-Kruskal's γ g [14] are two important association measures based on concordance. Two pairs (X, Y ) and (X , Y ) are concordant if X > X and Y > Y , or X < X and Y < Y .…”

Section: Association Measures For Discrete Random Variablesmentioning

confidence: 99%

Measuring degree-degree association in networks

2010

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The Pearson correlation coefficient is commonly used for quantifying the global level of degreedegree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy-tailed degree distributions. Theoretical arguments together with our numerical study indicate that Pearson's coefficient often depends on the size of networks with equal association structure, impeding a systematic comparison of real-world networks. In contrast, Kendall-Gibbons' τ b is a considerably more robust measure of the degree-degree association.

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“…Accurately determining cluster numbers is dif®cult (see, for example, Meloun et al, 2000). We used estimates based on the eigenanalysis of the correlation and related matrices integrated with techniques based on cluster analysis, developed by Goodman & Kruskal (1954), Calins Ïki & Harabasz (1974 and Milligan & Cooper (1985) (see paper II). The individual estimates of cluster numbers are shown in Table 2(a).…”

Section: Unshifted Datamentioning

confidence: 99%

High-throughput powder diffraction. III. The application of full-profile pattern matching and multivariate statistical analysis to round-robin-type data sets

et al. 2004

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Powder pattern matching techniques, using all the experimentally measured data points, coupled with cluster analysis, fuzzy clustering and multivariate statistical methods are used, with appropriate visualization tools, to analyse a set of 27 powder diffraction patterns of alumina collected at seven different laboratories on different instruments as part of an International Center for Diffraction Data Grant-in-Aid program. In their original form, the data factor into six distinct clusters. However, when a non-linear shift of the form Á 2 a 0 a 1 sin (where a 0 and a 1 are re®nable constants) is applied to optimize the correlations between patterns, clustering produces a large 25-pattern set with two outliers. The ®rst outlier is a synchrotron data set at a different wavelength from the other data, and the second is distinguished by the absence of K 2 lines, i.e. it uses Ge-monochromated incident X-rays. Fuzzy clustering, in which samples may belong to more than one cluster, is introduced as a complementary method of pinpointing problematic diffraction patterns. In contrast to the usual methodology associated with the analysis of round-robin data, this process is carried out in a routine way, with minimal user interaction or supervision, using the PolySNAP software.

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Measures of Association for Cross Classifications*

Cited by 622 publications

References 11 publications

Measures of feeling‐of‐knowing accuracy: A new look at an old problem

Measures of feeling‐of‐knowing accuracy: A new look at an old problem

Measuring degree-degree association in networks

High-throughput powder diffraction. III. The application of full-profile pattern matching and multivariate statistical analysis to round-robin-type data sets

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