Categorical Independence Tests for Large Sparse R-Way Contingency Tables

2002 ◽  
Vol 95 (2) ◽  
pp. 606-610 ◽  
Author(s):  
Paul W. Mielke ◽  
Kenneth J. Berry
Keyword(s):  
Contingency Tables ◽  
Exact Probability ◽  
Independence Tests ◽  
Chi Squared

A nonasymptotic chi-squared technique is shown to have very useful properties for the analysis of large sparse r-way contingency tables. Examples of analyses of 4 × 5, 5 × 6, 6 × 7. and two 2 × 2 × 2 sparse contingency tables provide comparisons of the nonasymptotic chi-squared technique with asymptotic chi-squared and exact chi-squared techniques. The asymptotic chi-squared analyses yield inflated probability values for the five tables. The nonasymptotic chi-squared technique yields probability values much closer to the exact probability values than the asymptotic chi-squared Technique for the five tables.

scholarly journals Organizational sensory systems of Polish enterprises in the context of cooperative relationships

Management ◽  
2019 ◽  
Vol 23 (1) ◽  
pp. 50-60
Author(s):  
Michał Chomicki
Keyword(s):  
Sensory System ◽  
Sensory Systems ◽  
Economic Environment ◽  
Independence Tests ◽  
Cooperative Relationships ◽  
Theoretical Part ◽  
Chi Squared ◽  
The Relationship

Summary The aim of this paper is to indicate the relationship between the shape of organizational sensory systems of Polish companies and beneficialness of the shape of cooperative relations between these companies with particular kinds of cooperators. The theoretical part of this article was devoted to the identification of the role of cooperative relations in the contemporary economic environment and a brief description of the concept of organizational sensory system, including its influence on cooperation between companies. The survey used the respondents’ indications of frequency of monitoring of elements of organization and its environment and the indication of the beneficialness of the shape of cooperative relationships with suppliers, customers and co-opetitors (in the framework of coopetitive relations). The chi-squared independence tests were used to demonstrate dependencies. In conclusion, it turned out that there are only two statistically significant relations and both of them pertain to relationships with customers.

Asymptotic Log-Linear Analysis: Some Cautions concerning Sparse Frequency Tables

2004 ◽  
Vol 94 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Paul W. Mielke ◽  
Kenneth J. Berry ◽  
Janis E. Johnston
Keyword(s):  
Likelihood Ratio ◽  
Linear Models ◽  
Linear Analysis ◽  
Exact Probability ◽  
Permutation Methods ◽  
Chi Squared ◽  
Asymptotic Probability ◽  
Log Linear ◽  
Likelihood Ratio Statistics ◽  
Hypergeometric Distributions

Traditional asymptotic probability values resulting from log-linear analyses of sparse frequency tables are often much too large. Asymptotic probability values for chi-squared and likelihood-ratio statistics are compared to nonasymptotic and exact probability values for selected log-linear models. The asymptotic probability values are all too often substantially larger than the exact probability values for the analysis of sparse frequency tables. An exact nondirectional permutation method is presented to analyze combined independent multinomial distributions. Exact nondirectional permutation methods to analyze hypergeometric distributions associated with r-way frequency tables are confined to r = 2.

Multiway Contingency Tables: Monte Carlo Resampling Probability Values for the Chi-Squared and Likelihood-Ratio Tests

2010 ◽  
Vol 107 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Michael A. Long ◽  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Monte Carlo ◽  
Likelihood Ratio ◽  
Contingency Table ◽  
Contingency Tables ◽  
Likelihood Ratio Tests ◽  
Ratio Test ◽  
Test Statistics ◽  
Test Statistic ◽  
Resampling Methods ◽  
Chi Squared

Monte Carlo resampling methods to obtain probability values for chi-squared and likelihood-ratio test statistics for multiway contingency tables are presented. A resampling algorithm provides random arrangements of cell frequencies in a multiway contingency table, given fixed marginal frequency totals. Probability values are obtained from the proportion of resampled test statistic values equal to or greater than the observed test statistic value.

Power Anaysis of Independence Testing for Two-Way Contingency Tables Bigger than 2×2

2016 ◽  
Vol 63 (2) ◽  
pp. 191-210 ◽  
Author(s):  
Piotr Sulewski
Keyword(s):  
Monte Carlo ◽  
Statistical Analysis ◽  
Null Hypothesis ◽  
Contingency Tables ◽  
Critical Values ◽  
Simulation Methods ◽  
The Family ◽  
Chi Squared ◽  
Independence Testing

In the statistical literature there are many test measures to study the independence features in the two-way contingency tables. For statistical analysis, the family of six so-called “chi-squared statistic” was selected – including Pearson’s χ2 statistics – and the proposal of the author in the form of modu-lar statistics. In order to free themselves from the limitations of the applicability of the “chi-squared statisti c”, critical values for all analyzed statistics were determined by simulation methods of Monte Carlo. In order to compare the tests, the measure of untruthfulness of H0was proposed and calculated the power of the tests which is the ability of two-way contingency tables to reject null hypothesis which says that between features X and Y there is no relation.

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