Small-sample study of the use of mid-p power divergence goodness-of-fit tests

References

• Baglivo , J. , Olivier , D. and Pagano , M. 1987 . Applications of Fast Fourier Transform Methods to Exact Goodness-of-Fit Tests . Unpublished technical report presented at the Joint Statistical Meetings . August 1987 , San Francisco. pp. 17 – 20 .
   Google Scholar
• Baglivo , J. , Olivier , D. and Pagano , M. 1992 . Methods for Exact Goodness-of-Fit Tests . Journal of the American Statistical Association , 87 August : 464 – 469 .
   Web of Science ®Google Scholar
• Baglivo , J. , Olivier , D. and Pagano , M. 1993 . Analysis of Discrete Data: Rerandomization Methods and Complexity . Computational Statistics and Data Analysis , 16 August : 175 – 184 .
   Web of Science ®Google Scholar
• Barnard , G.A. 1989 . On Alleged Gains in Power From Lower P–values . Statistics in Medicine , 8 August : 1469 – 1477 .
   PubMed Web of Science ®Google Scholar
• Berry , G. and Armitage , P. 1995 . mid–P Confidence Intervals: A Brief Review . The Statistician , 44 August : 417 – 423 .
   Google Scholar
• Cressie , N. and Read , T.R.C. 1984 . Multinomial Goodness–of–Fit Tests . Journal of the Royal Statistical Society B, Ser. , B46 August : 440 – 464 .
   Google Scholar
• Formann , A.K. 1995 . Small–Sample Comparison of the Exact and Asymptotic Upper Tail Probabilities of the Chi–Squared Goodness–of–Fit Statistics: Pearson’s χ2, Likelihood Ratio, and Power–Divergence Statistic . Journal of Statistical Computation and Simulation , 51 August : 369 – 384 .
   Google Scholar
• Good , I.J. 1981 . The Fast Calculation of the Exact Distribution of Pearson’s Chi–Squared and of the Number of Repeats Within the Cells of a Multinomial by Using a Fast Fourier Transform . Journal of Statistical Computation and Simulation , 14 August : 71 – 78 .
   Google Scholar
• Good , I.J. 1982 . The Fast Calculation of the Exact Distribution of Pearson’s Chi–Squared and of the Number of Repeats Within the Cells of a Multinomial by Using a Fast Fourier Transform: An Addendum . Journal of Statistical Computation and Simulation , 15 August : 336 – 337 .
   Web of Science ®Google Scholar
• Good , I.J. 1983 . An Improved Algorithm for the Fast Calculation of the Exact Distribution of Pearson’s Chi–Squared . Journal of Statistical Computation and Simulation , 17 August : 236 – 242 .
   Web of Science ®Google Scholar
• Good , I.J. and Crook , J.F. 1978 . Correction to ’Exact Distribution for χ2 and for the Likelihood–Ratio Statistic for the Equiprobable Multinomial Distribution’ . Journal of the American Statistical Association , 73 ( 900 ) August
   Google Scholar
• Good , I.J. , Gover , T.N. and Mitchell , G.J. 1970 . Exact Distribution for χ2 and for the Likelihood–Ratio Statistic for the Equiprobable Multinomial Distribution . Journal of the American Statistical Association , bf65 ( 900 ) August : 267 – 283 .
   Google Scholar
• Good , I.j. , Gover , T.N. and Mitchell , G.J. 1971 . Correction to ‘Exact Distribution for χ2 and for the Likelihood–Ratio Statistic for the Equiprobable Multinomial Distribution’ . Journal of the American Statistical Association , 66 ( 229 ) August
   Google Scholar
• Haberman , S.J. 1988 . A Warning on the Use of Chi–Squared Statistics with Frequency Tables with Small Expected Cell Counts . Journal of the American Statistical Association , 83 ( 229 ) August : 555 – 560 .
   Google Scholar
• Hirji , K.F. 1997 . A Review and a Synthesis of the Fast Fourier Transform Algorithms for Exact Analysis of Discrete Data . Comuutational Statistics and Data Analysis , 25 ( 229 ) August : 321 – 336 .
   Google Scholar
• Hirji , K.F. and Johnson , T.D. 1996 . A Comparison of Algorithms for Exact Analysis of Unordered 2✗K Conting–ency. Tables . Comuutational Statistics and Data Analysis , 21 ( 229 ) August : 419 – 429 .
   Google Scholar
• Lancaster , H.O. 1952 . Statistical Control of Counting Experiments . Biometrika , 39 ( 229 ) August : 419 – 422 .
   Google Scholar
• Lancaster , H.O. 1961 . Significance Tests in Discrete Distributions . Journal of the American Statistical Association , 56 ( 229 ) August : 223 – 234 .
   Google Scholar
• Larntz , K. 1978 . Small–Sample Comparisons of Exact Levels for Chi–Squared Goodness–of–Fit Statistics . Journal of the American Statistical Association , 73 ( 229 ) August : 253 – 263 .
   Google Scholar
• Lawal , H.B. 1984 . Comparisons of the X 2 Y 2, Freeman–Tukey and Williams’ Improved G 2 Test Statistics in Small Samples of One–Way Multinomials . Biometrika , 71 ( 229 ) August : 415 – 418 .
   Google Scholar
• Lawal , H.B. 1989 . Comparing Power Behaviors For Some Goodness–of–Fit Statistics in Sparse Multinomials . Biometrical Journal , 3 ( 229 ) August : 297 – 306 .
   Google Scholar
• Lawal , H.B. 1992 . A modified χ2 Test When Some Cells Have Small Expectations in the Multinomial Distribution . Journal of Statistical Computation and Simulation , 40 ( 229 ) August : 15 – 27 .
   Google Scholar
• Lawal , H.B. 1993 . Comparisons of Some Chi–Squared Goodness–of–Fit Test Statistics in Sparse One–Way Multinomials . Biometrical Journal , 5 ( 229 ) August : 589 – 599 .
   Google Scholar
• Read , T.R.C. 1984 . Small–Sample Comparisons for the Power Divergence Goodnessof– Fit Statistics . Journal of the American Statistical Association , 79 ( 229 ) August : 929 – 935 .
   Google Scholar
• Read , T.R.C. and Cressie , N.A.C. 1988 . Goodness–of–Fit Statistics for Discrete Multivariate Data , New York : Springer .
   Google Scholar
• West , E.N. and Kempthorne , O. 1971 . A Comparison of the chi2 and Likelihood Ratio Tests for Composite Alternatives . Journal of Statistical Computation and Simulation , 1 : 1 – 33 .
   Google Scholar
• Zelterman , D. 1987 . Goodness–of–Fit Tests for Large Sparse Multinomial Distributions . Journal of the American Statistical Association , 82 : 624 – 629 .
   Web of Science ®Google Scholar