Topic
G-test
About: G-test is a research topic. Over the lifetime, 71 publications have been published within this topic receiving 2186 citations.
Papers published on a yearly basis
Papers
TL;DR: The optimum test policy was found to be analysis by the 'N-1' chi-squared test when the minimum expected number is at least 1, and otherwise, by the Fisher-Irwin test by Irwin's rule (taking the total probability of tables in either tail that are as likely as, or less likely than the one observed).
Abstract: Two-by-two tables commonly arise in comparative trials and cross-sectional studies. In medical studies, two-by-two tables may have a small sample size due to the rarity of a condition, or to limited resources. Current recommendations on the appropriate statistical test mostly specify the chi-squared test for tables where the minimum expected number is at least 5 (following Fisher and Cochran), and otherwise the Fisher-Irwin test; but there is disagreement on which versions of the chi-squared and Fisher-Irwin tests should be used. A further uncertainty is that, according to Cochran, the number 5 was chosen arbitrarily. Computer-intensive techniques were used in this study to compare seven two-sided tests of two-by-two tables in terms of their Type I errors. The tests were K. Pearson's and Yates's chi-squared tests and the 'N-1' chi-squared test (first proposed by E. Pearson), together with four versions of the Fisher-Irwin test (including two mid-P versions). The optimum test policy was found to be analysis by the 'N-1' chi-squared test when the minimum expected number is at least 1, and otherwise, by the Fisher-Irwin test by Irwin's rule (taking the total probability of tables in either tail that are as likely as, or less likely than the one observed). This policy was found to have increased power compared to Cochran's recommendations.
875 citations
TL;DR: In this paper, the authors used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G-test, Fisher's exact test, and an F(ST)-based permutation test.
Abstract: Information on statistical power is critical when planning investigations and evaluating empirical data, but actual power estimates are rarely presented in population genetic studies. We used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G-test, Fisher's exact test, and an F(ST)-based permutation test. Factors considered in the comparisons include the number of samples, their size, and the number and type of genetic marker loci. It is shown that power for detecting divergence may be substantial for frequently used sample sizes and sets of markers, also at quite low levels of differentiation. The choice of statistical method may be critical, though. For multi-allelic loci such as microsatellites, combining exact P values using Fisher's method is robust and generally provides a high resolving power. In contrast, for few-allele loci (e.g. allozymes and single nucleotide polymorphisms) and when making pairwise sample comparisons, this approach may yield a remarkably low power. In such situations chi-square typically represents a better alternative. The G-test without Williams's correction frequently tends to provide an unduly high proportion of false significances, and results from this test should be interpreted with great care. Our results are not confined to population genetic analyses but applicable to contingency testing in general.
237 citations
TL;DR: The theoretical basis of the log likelihood ratio test (the G‐test) is described, and instructions and tables are given for its use as a test of heterogeneity in contingency tables.
Abstract: SUMMAEY
The theoretical basis of the log likelihood ratio test (the G-test) is described, and instructions and tables are given for its use as a test of heterogeneity in contingency tables. There is a marked saving in computation time over the customary Karl Pearson test.
It is a pleasure to thank Miss Mary Wheeler and Miss Madge Wight for the major part of the computations.
193 citations
TL;DR: Two-by-two tables are an important format for expressing data to assess categorical association and can be used for enumerating the numbers of people who were or were not exposed to some causal opportunity or agent and did or did not get a disease.
64 citations
Book•
1 Jan 2007
TL;DR: The Chi-square test for Contingency Tables as discussed by the authors is one of the most commonly used regression test for estimating the Chi-squares test score in statistical testing, along with several others.
Abstract: 1. Introduction to Statistics: Purpose, Measurement, Terminology, and Rounding 2. Tables and Graphs 3. Transformed Scores I: Percentile Ranks 4. Descriptive Statistics: Measuring Central Tendency and Variability 5. Transformed Scores II: Standard Scores and the Normal Distribution 6. Sampling and Confidence Intervals 7. Relationship Tests and Hypothesis Testing: The Pearson Product Moment Correlation Coefficient 8. Interpreting Pearson Product Moment Correlation Coefficients 9. Two-Sample Difference Tests: The Independent-Samples t Test 10. Multiple-Sample Difference Tests I: One-Way Analysis of Variance 11. Multiple-Sample Difference Tests II: Factorial and Repeated-Measures Analysis of Variance 12. The Chi-Square Test for Contingency Tables 13. What Test When: Choosing the Appropriate Statistical Test Appendices Answers to Review Questions Index
64 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 2 |
| 2016 | 1 |
| 2015 | 1 |
| 2014 | 2 |
| 2013 | 1 |
| 2012 | 1 |