A Comparison of Minimum Logit Chi-Square Estimation and Maximum Likelihood Estimation in 2×2×2 and 3×2×2 Contingency Tables: Tests for Interaction

References

• Bartlett , M. S. 1935 . “Contingency Table Interactions,” . Journal of the Royal Statistical Society, Supplement , 2 : 248 – 52 .
   Google Scholar
• Bartlett , M. S. 1937 . “Some Examples of Statistical Methods of Research in Agriculture and Applied Biology,” . Journal of the Royal Statistical Society, Supplement , 4 : 137 – 71 .
   Google Scholar
• Berkson , J. 1944 . “Application of the Logistic Function to Bioassay,” . Journal of the American Statistical Association , 39 : 357 – 65 .
   Web of Science ®Google Scholar
• Berkson , J. 1955 . “Maximum Likelihood and Minimum χ2 Estimates of the Logistic Function,” . Journal of the American Statistical Association , 5 : 130 – 62 .
   Google Scholar
• Berkson , J. 1968 . Application of Minimum Logit χ2 Estimate to a Problem of Grizzle with a Notation on the Problem of No Interaction,” . Biometrics , 24 : 75 – 95 .
   PubMed Web of Science ®Google Scholar
• Bliss , C. I. 1935 . “The Calculation of the Dosage-Mortality Curve,” . The Annals of Applied Biology , 22 : 134 – 67 .
   Google Scholar
• Finney , D. J. 1964 . Statistical Method in Biological Assay, , 2nd ed. , London : Charles Griffin & Company Limited .
   Google Scholar
• Fix , E. , Hodges , J. L. Jr. and Lehmann , E. L. 1959 . “The Restricted Chi Square Test,” . In Probability and Statistics , Edited by: Grenander , U. New York : John Wiley & Sons, Inc. .
   Google Scholar
• Gart , J. J. and Zweifel , J. R. 1967 . “On the Bias of Various Estimators of the Logit and Its Variance with Application to Quantal Bioassay,” . Biometrika , 54 : 181 – 7 .
   PubMed Web of Science ®Google Scholar
• Goodman , L. A. 1963 . “On Plackett's Test for Contingency Table Interactions,” . Journal of the Royal Statistical Society , 25 : 179 – 88 . Series B
   Google Scholar
• Goodman , L. A. 1964 . “Simple Methods for Analyzing Three-Factor Interaction in Contingency Tables,” . Journal of the American Statistical Association , 59 : 319 – 52 .
   Web of Science ®Google Scholar
• Plackett , R. L. 1962 . “A Note on Interactions in Contingency Tables,” . Journal of the Royal Statistical Society , 24 : 162 – 6 . Series B
   Google Scholar
• Neyman , J. “Contributions to the Theory of the χ2 Test,” . Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability . Berkeley : University of California Press .
   Google Scholar
• Norton , H. W. 1945 . “Calculation of Chi Square for Complex Contingency Tables,” . Journal of the American Statistical Association , 40 : 251 – 58 .
   Web of Science ®Google Scholar
• Roy , S. N. and Kastenbaum , M. A. 1956 . “On the Hypothesis of No ‘Interaction’ in a Multi-Way Contingency Table,” . The Annals of Mathematical Statistics , 27 : 749 – 57 .
   Google Scholar
• Scheffé , H. 1959 . The Analysis of Variance , New York : John Wiley & Sons, Inc. .
   Google Scholar
• Snedecor , G. W. and Cochran , W. G. 1967 . Statistical Methods, , 6th ed. , Ames , Ia. : The Iowa State University Press .
   Google Scholar
• Taylor , W. F. 1953 . “Distance Functions and Regular Best Asymptotically Normal Estimates,” . The Annals of Mathematical Statistics , 24 : 85 – 92 .
   Google Scholar
• Woolf , B. 1955 . “On Estimating the Relation between Blood Group and Disease,” . Annals of Human Genetics, London , 19 : 251 – 53 .
   PubMed Web of Science ®Google Scholar
• Yates , F. 1934 . “The Analysis of Multiple Classifications with Unequal Numbers in the Different Classes,” . Journal of the American Statistical Association , 29 : 51 – 66 .
   Web of Science ®Google Scholar