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The American Statistician Volume 30, 1976 - Issue 1
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Original Articles

Actual Type 1 Error Probabilities for Various Tests in the Homogeneity Case of the 2 × 2 Contingency Table

G. R. Garside Univ. of Bradford, Bradford, West Yorkshire, BD7 1DP, England
&
C. Mack Univ. of Bradford, Bradford, West Yorkshire, BD7 1DP, England
Pages 18-21 | Published online: 12 Mar 2012

References

  • Barnard , G. A. 1947 . “Significance Tests for 2 × 2 Tables” . Biometrika , Vol. 34 : 123 – 138 .
  • Boschloo , R. D. 1970 . “Raised conditional level of significance for the 2 × 2 table when testing for the equality of two probabilities” . Statistica Neerlandica , Vol. 21 ( No. 1 ) : 1 – 35 .
  • Conover , W. J. “Some Reasons for Not Using the Yates Continuity Correction on 2 × 2 Contingency Tables” . J. Amer. Stat. Ass. , Vol. 69 ( No. 345 ) 374 – 382 . with Comments by (i) Starmer, F., Grizzle, J. E., and Sen, P. K., and (ii) Miettinen, O. S.
  • Fisher , R. A. 1974 . “The Design of Experiments”, , First Edition , Edinburgh : Oliver and Boyd . 1925
  • Garside , G. R. 1971 . “An accurate corrrection for the χ2-test in the homogeneity case of 2 × 2 contingency tables” . N.J. Statist. Op. Res. , Vol. 7 : 1 – 26 . Pt. 1
  • Garside , G. R. 1972 . “Further tables of an accurate correction for the χ2-test in the homogeneity case of the 2 × 2 contingency table” . N.J. Statist. Op. Res. , Vol. 7 : 1 – 21 . Pt. 3, and Vol. 8, Pt. 1, pp. 6–25
  • Garside , G. R. and Mack , C. 1970 . “A quantitative analysis of all sources of correction in the homogeneity case of the 2 × 2 contingency table” . N. J. Statist. Op. Res. , Vol. 6 : 16 – 25 . Pt. 1
  • Grizzle , J. 1967 . “Continuity correction in the χ2-test for 2 × 2 tables” . The American Statistician , Vol. 21 ( No. 4 ) : 28 – 32 .
  • Kurtz , T. E. 1968 . “A Role of Time-Sharing Computing in Statistical Research” . The American Statistician , Vol. 22 ( No. 5 ) : 19 – 21 .
  • Mack , C. 1966 . “Confidence limits for the cross-product ratio in 2 × 2 tables fully correct to the second order (first part)” . N.J. Statist. Op. Res. , Vol. 2 : 15 – 28 . Pt. 2
  • Mantel , N. and Greenhouse , S. W. 1968 . “What is the Continuity Correction?” . The American Statistician , Vol. 22 ( No. 5 ) : 27 – 30 .
  • Pearson , E. S. 1947 . “The Choice of a Statistical Test Illustrated on the Interpretation of Data Classed in a 2 × 2 Table” . Biometrika , Vol. 34 : 139 – 167 .
  • Plackett , R. L. 1964 . “The continuity correction in 2 × 2 tables” . Biometrika , Vol. 51 : 327 – 337 .
  • Tocher , K. D. 1950 . “Extension of the Neyman-Pearson Theory of Tests to Discontinuous Variates” . Biometrika , Vol. 37 : 130 – 144 .
  • Yates , F. 1934 . “Contingency tables involving small numbers and the χ2-test” . J. Roy. Statist. Soc. Suppl. , 1 : 217 – 235 .

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