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      Fisher’s exact approach for post hoc analysis of a chi-squared test

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      PLoS ONE

      Public Library of Science

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          Abstract

          This research is motivated by one of our survey studies to assess the potential influence of introducing zebra mussels to the Lake Mead National Recreation Area, Nevada. One research question in this study is to investigate the association between the boating activity type and the awareness of zebra mussels. A chi-squared test is often used for testing independence between two factors with nominal levels. When the null hypothesis of independence between two factors is rejected, we are often left wondering where does the significance come from. Cell residuals, including standardized residuals and adjusted residuals, are traditionally used in testing for cell significance, which is often known as a post hoc test after a statistically significant chi-squared test. In practice, the limiting distributions of these residuals are utilized for statistical inference. However, they may lead to different conclusions based on the calculated p-values, and their p-values could be over- o6r under-estimated due to the unsatisfactory performance of asymptotic approaches with regards to type I error control. In this article, we propose new exact p-values by using Fisher’s approach based on three commonly used test statistics to order the sample space. We theoretically prove that the proposed new exact p-values based on these test statistics are the same. Based on our extensive simulation studies, we show that the existing asymptotic approach based on adjusted residual is often more likely to reject the null hypothesis as compared to the exact approach due to the inflated family-wise error rates as observed. We would recommend the proposed exact p-value for use in practice as a valuable post hoc analysis technique for chi-squared analysis.

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          Most cited references 34

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          The Analysis of Residuals in Cross-Classified Tables

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            Note on an exact treatment of contingency, goodness of fit and other problems of significance.

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              Ecological and Genetic Studies onDreissena polymorpha(Pallas): a New Mollusc in the Great Lakes

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                Author and article information

                Contributors
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: InvestigationRole: MethodologyRole: SoftwareRole: Writing – original draftRole: Writing – review & editing
                Role: ConceptualizationRole: Data curationRole: Project administrationRole: SoftwareRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2017
                20 December 2017
                : 12
                : 12
                Affiliations
                School of Community Health Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154, United States of America
                University of Pittsburgh, UNITED STATES
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Article
                PONE-D-17-19167
                10.1371/journal.pone.0188709
                5737889
                29261690
                © 2017 Shan, Gerstenberger

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                Page count
                Figures: 1, Tables: 8, Pages: 12
                Product
                Funding
                GS’s research is partially supported by grants from the National Institute of General Medical Sciences from the National Institutes of Health: P20GM109025, P20GM103440, and 5U54GM104944. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Research and Analysis Methods
                Mathematical and Statistical Techniques
                Statistical Methods
                Test Statistics
                Physical Sciences
                Mathematics
                Statistics (Mathematics)
                Statistical Methods
                Test Statistics
                Physical Sciences
                Mathematics
                Statistics (Mathematics)
                Contingency Tables
                Research and Analysis Methods
                Mathematical and Statistical Techniques
                Statistical Methods
                Statistical Hypothesis Testing
                Chi Square Tests
                Physical Sciences
                Mathematics
                Statistics (Mathematics)
                Statistical Methods
                Statistical Hypothesis Testing
                Chi Square Tests
                Biology and Life Sciences
                Organisms
                Eukaryota
                Animals
                Invertebrates
                Molluscs
                Bivalves
                Mussels
                Biology and Life Sciences
                Anatomy
                Head
                Medicine and Health Sciences
                Anatomy
                Head
                Biology and Life Sciences
                Anatomy
                Neck
                Medicine and Health Sciences
                Anatomy
                Neck
                Research and Analysis Methods
                Simulation and Modeling
                Medicine and Health Sciences
                Oncology
                Cancers and Neoplasms
                Melanomas
                Custom metadata
                All relevant data are within the paper and its Supporting Information files.

                Uncategorized

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