An Exploratory Graphical Method for Identifying Associations in r x c Contingency Tables (original) (raw)
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We present a unified approach to describing and linking several methods for representing categorical data in a contingency table. These methods include: correspondence analysis, Hellinger distance analysis, the log-ratio alternative, which is appropriate for compositional data, and the non-symmetrical correspondence analysis. We also present two solutions working with cummulative frequencies.
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We propose and illustrate a new graphical method to perform diagnostic analyses in two-way contingency tables. In this method, one observation is added or removed from each cell at a time, whilst the other cells are held constant, and the change in a test statistic of interest is graphically represented. The method provides a very simple way of determining how robust our model is (and hence our conclusions) to small changes introduced to the data. We illustrate via four examples, three of them from real-world applications, how this method works.
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The American Statistician, 2001
This article has been written in recognition of the 100th aniversary of introduction of the concept of association between categorical variables by Yule and Pearson. The most popular among the contingency coe cients, Pearson's chi-squared, estimates the bias of a cross-classi cation from the statistical independence. Also, it measures association per se between the row and column variables. The purpose of this article is to present a collection of eleven de nitions for the chisquared coe cient related to either of these goals. One of the quoted de nitions of the chi-squared coe cient seems especially appealing as an association measure: the averaged relative Quetelet index of category-to-category associations.
Advances in Methodology and Statistics, 2011
Spearman and Pearson correlation coefficient, Gamma coefficient, Kendall's tau-b, Kendall's tau-c, and Somers' d are the most commonly used measures of association for doubly ordered contingency tables. So far there has been no study expressing a priority on those measures of association. The aim of this study is to compare those measures of association for several types and different sample sizes of generated squared doubly ordered contingency tables and determine which measures of association are more efficient. It is found that both the sample sizes and the dimension of the doubly ordered contingency tables play a significant role on the effect of those measures of association.
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2000
This paper presents a new software package designed to aid in the creation and analysis of two-way contingency (or Burt) tables and is a continuation of previous work relating to the multimedia-aided instruction of a similar subject. The software we have created, allows for a better understanding of the twoway table concept, since it creates clear, concise and well perceived results, all in the friendly, windowed GUI of Excel. The two part software package was built using Visual Basic for Applications and is supplemented with an on-line help system. Key-Words: Statistical Software, Data Analysis Software, Contingency Tables, Two-Way Tables,
An information measure of association in contingency tables
Information and control, 1971
Linfoot (1957) introduced an informational measure r! of correlation between two random variables X and Y. The measure r 1 is based on the information gain r0 in knowing that X and Y are mutually dependent with a given bivariate density function as compared with the original knowledge that X and Y are statistically independent. In the present paper, an asymptotic form of the information measure rl, denoted by rl, is derived in terms of Pearson's (1904) chi-square for contingency tables. Hence ~l is suggested as an information measure of association in contingency tables. On comparing fl with Pearson's classical coefficient of contingency P, it is found that ~I /> P. This is a desirable property of rI, since Lancaster and Hamdan (1964) demonstrated that P underestimates the product-moment correlation coefficient in contingency tables with broad categories. The asymptotic variance of rl is derived and compared with the asymptotic variance of P.
Measures of association for contingency tables
2012
The most general term for this type of measure is size of effect. Effect sizes allow us to make descriptive statements about samples. Traditionally, experimentalists have referred to ‘large’, ‘medium’ and ‘small’ effects, which is rather imprecise. Nonetheless, it is possible to employ statistically sound methods for comparing different sizes of effect by inverting a Gaussian interval (Bishop, Fienberg and Holland 1975) or by comparing contingency tables for the difference of differences (Wallis 2019).