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Journal of the American Statistical Association Volume 72, 1977 - Issue 360a
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Invited Paper

Developments in Multiple Comparisons 1966–1976

Rupert G. Miller Jr. Department of Statistics, Stanford University, Stanford, CA, 94305, USA
Pages 779-788 | Received 01 May 1977, Published online: 05 Apr 2012

References

  • Dunn , O. J. 1958 . “Estimation of the Means of Dependent Variables,” . Annals of Mathematical Statistics , 29 : 1095 – 1111 .
  • Efron , B. and Morris , C. 1973 . “Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach,” . Journal of the American Statistical Association , 68 : 117 – 130 .
  • Faith , R. E. 1976 . “Minimax Bayes Set and Point Estimators of a Multivariate Normal Mean,” , Department of Statistics, University of Michigan . Technical Report No. 66
  • Gafarian , A. V. 1964 . “Confidence Bands in Straight Line Regression,” . Journal of the American Statistical Association , 59 : 182 – 213 .
  • Lieberman , G. J. and Miller , R. G. Jr. 1963 . “Simultaneous Tolerance Intervals in Regression,” . Biometrika , 50 : 155 – 168 .
  • Miller , R. G. Jr. 1966 . Simultaneous Statistical Inference , New York : McGraw-Hill Book Co. . (Out of print; for copies contact editor.)
  • Slepian , D. 1962 . “The One-Sided Barrier Problem for Gaussian Noise,” . Bell System Technical Journal , 41 : 463 – 501 .

4. Bibliography 1966–1976: 4.1 Survey Articles

  • Dunnett , C. W. 1970 . “Multiple Comparisons,” . In Statistics in Endocrinology , Edited by: McArthur , J. W. and Colton , T. 79 – 103 . Cambridge , Mass : MIT Press .
  • Games , P. A. 1971 . “Multiple Comparisons of Means,” . American Educational Research Journal , 8 : 531 – 565 .
  • Gill , J. L. 1973 . “Current Status of Multiple Comparisons of Means in Designed Experiments,” . Journal of Dairy Science , 56 : 973 – 977 .
  • O'Neill , R. T. and Wetherill , B. G. 1971 . “The Present State of Multiple Comparisons Methods,” . Journal of the Royal Statistical Society , 33 : 218 – 241 . Ser. B
  • Spjøtvoll , E. 1974 . “Multiple Testing in the Analysis of Variance,” . Scandinavian Journal of Statistics , 1 : 97 – 114 .
  • Thomas , D. A.H. 1973 . “Multiple Comparisons Among Means, A Review,” . The Statistician , 22 : 16 – 42 .

4.2 Probability Inequalities

  • Dykstra , R. L. , Hewett , J. E. and Thompson , W. A. Jr. 1973 . “Events Which Are Almost Independent,” . Annals of Statistics , 1 : 674 – 681 .
  • Esary , J. D. , Proschan , F. and Walkup , D. W. 1967 . “Associated Random Variables with Applications,” . Annals of Mathematical Statistics , 38 : 1466 – 1474 .
  • Halperin , M. 1967 . “An Inequality on a Bivariate Student's” t “Distribution,” . Journal of the American Statistical Association , 62 : 603 – 606 .
  • Jensen , D. R. 1969 . “An Inequality for a Class of Bivariate Chi-Square Distributions,” . Journal of the American Statistical Association , 64 : 333 – 336 .
  • Jogdeo , K. 1970 . “A Simple Proof of an Inequality for Multivariate Normal Probabilities of Rectangles,” . Annals of Mathematical Statistics , 41 : 1357 – 1359 .
  • Khatri , C. G. 1967 . “On Certain Inequalities for Normal Distributions and Their Applications to Simultaneous Confidence Bounds,” . Annals of Mathematical Statistics , 38 : 1853 – 1867 .
  • Khatri , C. G. 1970 . “Further Contributions to Some Inequalities for Normal Distributions and Their Applications to Simultaneous Confidence Bounds,” . Annals of the Institute of Statistical Mathematics , 22 : 451 – 458 .
  • Olkin , I. 1972 . “Monotonicity Properties of Dirichlet Integrals with Applications to the Multinomial Distribution and the Analysis of Variance,” . Biometrika , 59 : 303 – 307 .
  • Scott , A. 1967 . “A Note on Conservative Confidence Regions for the Mean of a Multivariate Normal,” . Annals of Mathematical Statistics , 38 : 278 – 280 . Correction: 39 (1968), 2161
  • Sen , P. K. 1971 . “A Hájek-Rényi Type Inequality for Stochastic Vectors with Applications to Simultaneous Confidence Regions,” . Annals of Mathematical Statistics , 42 : 1132 – 1134 .
  • Šidák , Z. 1967 . “Rectangular Confidence Regions for the Means of Multivariate Normal Distributions,” . Journal of the American Statistical Association , 62 : 626 – 633 .
  • Šidák , Z. 1968 . “On Multivariate Normal Probabilities of Rectangles: Their Dependence on Correlations,” . Annals of Mathematical Statistics , 39 : 1425 – 1434 .
  • Šidák , Z. 1971 . “On Probabilities of Rectangles in Multivariate Student Distributions: Their Dependence on Correlations,” . Annals of Mathematical Statistics , 42 : 169 – 175 .
  • Tong , Y. L. 1970 . “Some Probability Inequalities of Multivariate Normal and Multivariatet,” . Journal of the American Statistical Association , 65 : 1243 – 1247 .

4.3 Tables

  • Beckman , R. J. and Tietjen , G. L. 1973 . “Upper 10% and 25% Points of the Maximum F Ratio,” . Biometrika , 60 : 213 – 214 .
  • Chambers , C. 1967 . “Extension of Tables of Percentage Points of the Largest Variance Ratio, S max 2/S 0 2,” . Biometrika , 54 : 225 – 227 .
  • Dayton , C. M. and Schafer , W. D. 1973 . “Extended Tables of t and Chi-Square for Bonferroni Tests with Unequal Error Allocation,” . Journal of the American Statistical Association , 68 : 78 – 83 .
  • Dudewicz , E. J. , Ramberg , J. S. and Chen , H. J. 1975 . “New Tables for Multiple Comparison with a Control (Unknown Variances),” . Biometrische Zeitschrift , 17 : 13 – 26 .
  • Dunn , O. J. , Kronmal , R. A. and Yee , W. J. 1968 . “Tables of the Multivariate t-Distribution,” , Los Angeles : School of Public Health, University of California .
  • Dutt , J. E. , Mattes , K. D. and Tao , L. C. 1975 . “Tables of the Trivariate t for Comparing Three Treatments to a Control with Unequal Sample Sizes,” , Chicago : Math/Stat Services, G.D. Searle & Co. . Technical Report No. 3
  • Hahn , G. J. and Hendrickson , R. W. 1971 . “A Table of Percentage Points of the Distribution of the Largest Absolute Value of k Student t Variates and Its Applications,” . Biometrika , 58 : 323 – 332 .
  • Hanumara , R. C. and Thompson , W. A. Jr. 1968 . “Percentage Points of the Extreme Roots of a Wishart Matrix,” . Biometrika , 55 : 505 – 512 .
  • Harter , H. L. 1969 . Order Statistics and Their Use in Testing and Estimation, Vol. 1, Tests Based on Range and Studentized Range of Samples from a Normal Population , Aerospace Research Laboratories . (Available from Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.)
  • Krishnaiah , P. R. and Armitage , J. V. 1966 . “Tables for Multivariate t-Distribution,” . Sankhy[abar] , B28 : 31 – 56 .
  • Krishnaiah , P. R. , Armitage , J. V. and Armitage , J. V. 1970 . “On a multivariate F Distribution,” . In Essays in Probability and Statistics , Edited by: Bose , R. C. 439 – 468 . Chapel Hill , N.C. : University of North Carolina Press .
  • Lachenbruch , P. A. 1969 . “Tables of Simultaneous Confidence Limits for the Binomial and Poisson Distributions,” . Biometrika , 56 : 452
  • Pillai , K. C.S. 1967 . “Upper Percentage Points of the Largest Root of a Matrix in Multivariate Analysis,” . Biometrika , 54 : 189 – 194 .
  • Steffens , F. E. 1969 . “Critical Values for Bivariate Student t-Tests,” . Journal of the American Statistical Association , 64 : 637 – 646 .
  • Tietjen , G. L. and Beckman , R. J. 1972 . “Tables for Using the Maximum F-Ratio in Multiple Comparison Procedures,” . Journal of the American Statistical Association , 67 : 581 – 583 .
  • Tobach , E. , Smith , M. , Rose , G. and Richter , D. 1967 . “A Table for Making Rank Sum Multiple Paired Comparisons,” . Technometrics , 9 : 561 – 567 .
  • Trout , J. R. and Chow , B. 1972 . “Table of the Percentage Points of the Trivariate t-Distribution with an Application to Uniform Confidence Bands,” . Technometrics , 14 : 855 – 879 .
  • Vithayasai , C. and Robson , D. S. 1973 . “One-and Two-Tailed Simultaneous Orthogonal Contrasts,” . Communications in Statistics , 1 : 459 – 470 .

4.4 Normal Multifactor Methods: Unbalanced and Heteroscedastic ANOVA

  • Banerjee , S. 1970 . “Simultaneous Confidence Intervals for two Linear Functions of Population Means When Population Variances Are Not Equal,” . Proceedings of the Cambridge Philosophical Society , 67 : 365 – 370 .
  • Brown , M. B. and Forsythe , A. B. 1974 . “The ANOVA and Multiple Comparisons for Data with Heterogeneous Variance,” . Biometrics , 30 : 719 – 724 .
  • Dunn , O. J. 1974 . “On Multiple Tests and Confidence Intervals,” . Communications in Statistics , 3 : 101 – 103 .
  • Hochberg , Y. 1974 . “Some Conservative Generalizations of the T-Method in Simultaneous Inference,” . Journal of Multivariate Analysis , 4 : 224 – 234 .
  • Hochberg , Y. 1975 . “An Extension of the T-Method to General Unbalanced Models of Fixed Effects,” . Journal of the Royal Statistical Society , 37 : 426 – 433 . Ser. B
  • Hochberg , Y. 1976 . “A Modification of the T-Method of Multiple Comparisons for a One-Way Layout with Unequal Variances,” . Journal of the American Statistical Association , 71 : 200 – 203 .
  • Spjøtvoll , E. 1972 . “Joint Confidence Intervals for all Linear Functions of Means in ANOVA with Unknown Variances,” . Biometrika , 59 : 638 – 685 .
  • Spjøtvoll , E. and Stoline , M. R. 1973 . “An Extension of the T-Method of Multiple Comparisons to Include the Cases with Unequal Sample Sizes,” . Journal of the American Statistical Association , 68 : 975 – 978 .
  • Tamhane , A. C. 1977 . “Multiple Comparisons in Model I One-Way Anova with Unequal Variances,” . Communications in Statistics , A6 : 15 – 32 .

Comparison of Procedures

  • Carmer , S. G. and Swanson , M. R. 1971 . “Detection of Differences Between Means: A Monte Carlo Study of Five Pairwise Multiple Comparisons Procedures,” . Agronomy Journal , 63 : 940 – 945 .
  • Carmer , S. G. , Swanson , M. R. and Swanson , M. R. 1973 . “Evaluation of Ten Pairwise Multiple Comparisons Procedures by Monte Carlo Methods,” . Journal of the American Statistical Association , 68 : 66 – 74 .
  • Einot , I. and Gabriel , K. R. 1975 . “A Study of the Powers of Several Methods of Multiple Comparisons,” . Journal of the American Statistical Association , 70 : 574 – 583 .
  • Keselman , H. J. , Toothaker , L. E. and Shooter , M. 1975 . “An Evaluation of Two Unequal nk Forms of the Tukey Multiple Comparisons Statistic,” . Journal of the American Statistical Association , 70 : 584 – 587 .
  • Perlmutter , J. and Myers , J. L. 1973 . “A Comparison of Two Procedures for Testing Multiple Contrasts,” . Psychological Bulletin , 79 : 181 – 184 .
  • Thomas , D. A.H. 1974 . “Error Rates in Multiple Comparisons Among Means—A Simulation,” . Applied Statistics , 23 : 284 – 294 .
  • Ury , H. K. and Wiggins , A. D. 1975 . “A Comparison of Three Procedures for Multiple Comparisons Among Means,” . British Journal of Mathematical and Statistical Psychology , 28 : 88 – 102 .
  • Ury , H. K. and Wiggins , A. D. 1976 . “A Comparison of Four Procedures for Multiple Comparisons Among Means (Pairwise Contrasts) for Arbitrary Sample Sizes,” . Technometrics , 18 : 89 – 97 .

Robustness

  • Brown , R. A. 1974 . “Robustness of the Studentized Range Statistic,” . Biometrika , 61 : 171 – 175 .
  • Games , P. A. 1971 . “The Inverse Relation Between the Risks of Type I and Type II Errors and Suggestions for the Unequal n Case in Multiple Comparisons,” . Psychological Bulletin , 75 : 97 – 102 .
  • Games , P. A. and Howell , J. F. 1976 . “Pairwise Multiple Comparison Procedures with Unequal N's and/or Variances: A Monte Carlo Study,” . Journal of Educational Statistics , 1 : 113 – 125 .
  • Howell , J. F. and Games , P. A. 1973 . “The Robustness of the Analysis of Variance and the Tukey WSD Test Under Various Patterns of Heterogeneous Variances,” . Journal of Experimental Education , 41 : 33 – 37 .
  • Howell , J. F. , Games , P. A. and Games , P. A. 1974 . “The Effects of Variance Heterogeneity on Simultaneous Multiple-Comparison Procedures with Equal Sample Size,” . British Journal of Mathematical and Statistical Psychology , 27 : 72 – 81 .
  • Keselman , H. J. 1976 . “A Power Investigation of the Tukey Multiple Comparison Statistic,” . Educational and Psychological Measurement , 36 : 97 – 104 .
  • Keselman , H. J. , Murray , R. and Rogan , J. 1976 . “Effect of Very Unequal Group Sizes on Tukey's Multiple Comparison Test,” . Educational and Psychological Measurement , 36 : 263 – 270 .
  • Keselman , H. J. , Murray , R. , Rogan , J. and Toothaker , L. E. 1973 . “Error Rates for Multiple Comparison Methods: Some Evidence Concerning the Misleading Conclusions of Petrinovich and Hardyck,” . Psychological Bulletin , 80 : 31 – 32 .
  • Petrinovich , L. F. and Hardyck , C. D. 1969 . “Error Rates for Multiple Comparison Methods: Some Evidence Concerning the Frequency of Erroneous Conclusions,” . Psychological Bulletin , 71 : 43 – 54 .
  • Ramseyer , G. C. and Tcheng , T. 1973 . “The Robustness of the Studentized Range Statistic to Violations of the Normality and Homogeneity of Variance Assumptions,” . American Educational Research Journal , 10 : 235 – 240 .
  • Smith , R. A. 1971 . “The Effect of Unequal Group Size on Tukey's HSD Procedure,” . Psychometrika , 36 : 31 – 34 .

Power Functions

  • David , H. A. , Lachenbruch , P. A. and Brandis , H. P. 1972 . “The Power Function of Range and Studentized Range Tests in Normal Samples,” . Biometrika , 59 : 161 – 168 .
  • Steffens , F. E. 1970 . “Power of Bivariate Studentized Maximum and Minimum Modulus Tests,” . Journal of the American Statistical Association , 65 : 1639 – 1644 .

Conditional Error Rates

  • Bernhardson , C. S. 1975 . “Type I Error Rates When Multiple Comparison Procedures Follow a Significant F Test or ANOVA,” . Biometrics , 31 : 229 – 232 .
  • Olshen , R. A. 1973 . “The Conditional Level of the F-test,” . Journal of the American Statistical Association , 68 : 692 – 698 .

Graphical Techniques

  • Boardman , T. J. and Moffitt , D. R. 1971 . “Graphical Monte Carlo Type I Error Rates for Multiple Comparison Procedures,” . Biometrics , 27 : 738 – 744 .
  • Feder , P. I. 1974 . “Graphical Techniques in Statistical Data Analysis—Tools for Extracting Information from Data,” . Technometrics , 16 : 287 – 299 .
  • Feder , P. I. 1975 . “Studentized Range Graph Paper—A Graphical Tool for the Comparison of Treatment Means,” . Technometrics , 17 : 181 – 188 .
  • Moses , L. E. 1976 . “Charts for Finding Upper Percentage Points of Student's t in the Range .01 to .00001,” , Stanford University . Technical Report No. 24 (5 R01 GM21215–02)
  • Thöni , H. 1968 . “A Nomogram for Testing Multiple Comparisons,” . Biometrische Zeitschrift , 10 : 219 – 221 .
  • Zahn , D. A. 1975 . “Modifications of and Revised Critical Values for the Half-Normal Plot,” . Technometrics , 17 : 189 – 200 .
  • Zahn , D. A. 1975 . “An Empirical Study of the Half-Normal Plot,” . Technometrics , 17 : 201 – 211 .

Bayes Techniques

  • Dixon , D. O. and Duncan , D. B. 1975 . “Minimum Bayes Risk t-Intervals for Multiple Comparisons,” . Journal of the American Statistical Association , 70 : 822 – 831 .
  • Duncan , D. B. 1975 . “t Tests and Intervals for Comparisons Suggested by the Data,” . Biometrics , 31 : 339 – 359 .
  • Waller , R. A. and Duncan , D. B. 1969 . “A Bayes Rule for the Symmetric Multiple Comparisons Problem,” . Journal of the American Statistical Association , 64 : 1484 – 1503 . Corrigenda: 67 (1972), 253–255
  • Waller , R. A. , Duncan , D. B. and Duncan , D. B. 1974 . “A Bayes Rule for the Symmetric Multiple Comparisons Problem II,” . Annals of the Institute of Statistical Mathematics , 26 : 247 – 264 .
  • Waller , R. A. , Duncan , D. B. , Duncan , D. B. and Kemp , K. E. 1975 . “Computations of Bayesian t-Values for Multiple Comparisons,” . Journal of Statistical Computation and Simulation , 4 : 169 – 171 .

Several Treutmenta vs. Control

  • Bechhofer , R. E. 1969 . “Optimal Allocation of Observations When Comparing Several Treatments with a Control,” . In Multivariate Analysis II , Edited by: Krishnaiah , P. R. 463 – 473 . New York : Academic Press .
  • Bechhofer , R. E. and Nocturne , D. J.-M. 1972 . “Optimal Allocation of Observations When Comparing Several Treatments with a Control, II: 2-Sided Comparisons,” . Technometrics , 14 : 423 – 436 .
  • Shaffer , J. P. 1977 . “Multiple Comparisons Emphasizing Selected Contrasts: An Extension and Generalization of Dunnett's Procedure,” . Biometrics , 33 : 293 – 304 .
  • Steffens , F. E. and de Villiers , R. 1973 . “Sample Sizes Required for Two-Sided Comparisons of Two Treatments with a Control,” . Technometrics , 15 : 915 – 921 .

Tests on Interactions

  • Bradu , D. and Gabriel , K. R. 1974 . “Simultaneous Statistical Inference on Interactions in Two-Way Analysis of Variance,” . Journal of the American Statistical Association , 69 : 428 – 436 .
  • Cicchetti , D. V. 1972 . “Extension of Multiple-Range Tests to Interaction Tables in the Analysis of Variance: A Rapid Approximate Solution,” . Psychological Bulletin , 77 : 405 – 408 .
  • Gabriel , K. R. , Putter , J. and Wax , Y. 1973 . “Simultaneous Confidence Intervals for Product-Type Interaction Contrasts,” . Journal of the Royal Statistical Society , 35 : 234 – 244 . Ser. B
  • Harter , H. L. 1970 . “Multiple Comparison Procedures for Interactions,” . American Statistician , 24 : 30 – 32 .
  • Sen , P. K. 1969 . “A Generalization of the T-Method of Multiple Comparisons for Interactions,” . Journal of the American Statistical Association , 64 : 290 – 295 .

Tests on Variances

  • Bechhofer , R. E. 1968 . “Multiple Comparisons with a Control for Multiple-Classified Variances of Normal Populations,” . Technometrics , 10 : 715 – 718 .
  • Broemeling , L. D. 1969 . “Confidence Regions for Variance Ratios of Random Models,” . Journal of the American Statistical Association , 64 : 660 – 664 .
  • Broemeling , L. D. and Bee , D. E. 1976 . “Simultaneous Confidence Intervals for Parameters of a Balanced Incomplete Block,” . Journal of the American Statistical Association , 71 : 425 – 428 .
  • Levy , K. J. 1975 . “A Multiple Range Procedure for Correlated Variances in a Two-Way Classification,” . Biometrics , 31 : 243 – 245 .
  • Levy , K. J. 1975 . “An Empirical Comparison of Several Multiple Range Tests for Variances,” . Journal of the American Statistical Association , 70 : 180 – 183 .
  • Jensen , D. R. and Jones , M. O. 1969 . “Simultaneous Confidence Intervals for Variances,” . Journal of the American Statistical Association , 64 : 324 – 332 .
  • Sahai , H. 1974 . “Simultaneous Confidence Intervals for Variance Components in Some Balanced Random Effects Models,” . Sankhy[abar], B , 36 : 278 – 287 .
  • Sahai , H. and Anderson , R. L. 1973 . “Confidence Regions for Variance Ratios of Random Models for Balanced Data,” . Journal of the American Statistical Association , 68 : 951 – 952 .

General

  • Anderson , D. A. 1972 . “Overall Confidence Levels of the Least Significant Difference Procedure,” . American Statistician , 26 : 30 – 32 .
  • Bhargava , R. P. and Srivastava , M. S. 1973 . “On Tukey's Confidence Intervals for the Contrasts in the Means of the Intraclass Correlation Model,” . Journal of the Royal Statistical Society , 35 : 147 – 152 . Ser. B
  • Bock , J. 1974 . “Planung des Stichproben um Fanges beim Newman-Keuls-Test,” . Biometrische Zeitschrift , 16 : 417 – 422 .
  • Brown , G. H. and Robson , D. S. 1974 . “Joint Confidence Intervals for Linear Combinations of, at most, q of p Means of Normal Distributions,” . Communications in Statistics , 3 : 213 – 222 .
  • Bryant , P. 1972 . “A Short Proof of a Known Lemma,” . American Statistician , 26 : 35 – 36 .
  • Dunnett , C. W. 1970 . “Answer to Query 272: Multiple Comparison Tests,” . Biometrics , 26 : 139 – 140 .
  • Enderlein , G. 1972 . “Die Maximum-Modulus-Methode zum Multiplen Vergleich von Gruppenmitteln mit dem Gesamtmittel,” . Biometrische Zeitschrift , 14 : 85 – 94 .
  • Frank , O. 1966 . “Simultaneous Confidence Intervals,” . Skandinavisk Aktuarietidskrift , 49 : 78 – 84 .
  • Gabriel , K. R. and Putter , J. 1973 . “On the Differences of Equicorrelated Variables with Equal Variances,” . Metron , 31 : 1 – 5 .
  • Gebhardt , F. 1966 . “Approximations to the Critical Values for Duncan's Multiple Range Test,” . Biometrics , 22 : 179 – 182 .
  • Hochberg , Y. 1974 . “The Distribution of the Range in General Balanced Models,” . American Statistician , 28 : 137 – 138 .
  • Hochberg , Y. 1975 . “Simultaneous Inference Under Behrens-Fisher Conditions, A Two Sample Approach,” . Communications in Statistics , 4 : 1109 – 1119 .
  • Johnson , D. E. 1973 . “A Derivation of Scheffé's S-Method by Maximizing a Quadratic Form,” . American Statistician , 27 : 27 – 30 .
  • Klotz , J. 1969 . “A Simple Proof of Scheffé's Multiple Comparison Theorem for Contrasts in the One-Way Layout,” . American Statistician , 23 : 44 – 45 .
  • Marcus , R. and Peritz , E. 1976 . “Some Simultaneous Confidence Bounds in Normal Models with Restricted Alternatives,” . Journal of the Royal Statistical Society , 38 : 157 – 165 . Ser. B
  • Mudholkar , G. S. and Subbaiah , P. 1976 . “Unequal Precision Multiple Comparisons for Randomized Block Designs under Nonstandard Conditions,” . Journal of the American Statistical Association , 71 : 429 – 434 .
  • Schafer , W. D. and Macready , G. B. 1975 . “A Modification of the Bonferroni Procedure on Contrasts Which are Grouped into Internally Independent Sets,” . Biometrics , 31 : 227 – 228 .
  • Sverdrup , E. 1976 . “Significance Testing in Multiple Statistical Inference,” . Scandinavian Journal of Statistics , 3 : 73 – 78 .

4.5 Regression: Confidence Bands

  • Bohrer , R. 1967 . “On Sharpening Scheffé Bounds,” . Journal of the Royal Statistical Society , 29 : 110 – 114 . Ser. B
  • Bohrer , R. 1969 . “On One-Sided Confidence Bounds for Response Surfaces,” . Bulletin of the International Statistical Institute , 43 : 255 – 257 . (Book 2)
  • Bohrer , R. 1973 . “An Optimality Property of Scheffé Bounds,” . Annals of Statistics , 1 : 766 – 772 .
  • Bohrer , R. 1973 . “A Multivariate t Probability Intergral,” . Biometrika , 60 : 647 – 654 .
  • Bohrer , R. and Francis , G. K. 1972 . “Sharp One-Sided Confidence Bounds Over Positive Regions,” . Annals of Mathematical Statistics , 43 : 1541 – 1548 .
  • Bohrer , R. and Francis , G. K. 1972 . “Sharp One-Sided Confidence Bounds for Linear Regression Over Intervals,” . Biometrika , 59 : 99 – 107 .
  • Bowden , D. C. 1970 . “Simultaneous Confidence Bands for Linear Regression Models,” . Journal of the American Statistical Association , 65 : 413 – 421 .
  • Bowden , D. C. and Graybill , F. A. 1966 . “Confidence Bands of Uniform and Proportional Width for Linear Models,” . Journal of the American Statistical Association , 61 : 182 – 198 .
  • Dunn , O. J. 1968 . “A Note on Confidence Bands for a Regression Line Over a Finite Interval,” . Journal of the American Statistical Association , 63 : 1028 – 1033 .
  • Folks , J. L. and Antle , C. E. 1967 . “Straight Line Confidence Regions for Linear Models,” . Journal of the American Statistical Association , 62 : 1365 – 1374 .
  • Graybill , F. A. and Bowden , D. C. 1967 . “Linear Segment Confidence Bands for Simple Linear Models,” . Journal of the American Statistical Association , 62 : 403 – 408 .
  • Halperin , M. and Gurian , J. 1968 . “Confidence Bands in Linear Regression with Constraints,” . Journal of the American Statistical Association , 63 : 1020 – 1027 .
  • Halperin , M. , Gurian , J. , Rastogi , S. C. , Ho , I. and Yang , Y. Y. 1967 . “Shorter Confidence Bands in Linear Regression,” . Journal of the American Statistical Association , 62 : 1050 – 1067 .
  • Hochberg , Y. and Quade , D. 1975 . “One-Sided Simultaneous Confidence Bounds on Regression Surfaces with Intercepts,” . Journal of the American Statistical Association , 70 : 889 – 891 .
  • Trout , J. R. and Chow , B. 1973 . “Uniform Confidence Bands for a Quadratic Model,” . Technometrics , 15 : 611 – 624 .
  • Wynn , H. P. 1975 . “Integrals for One-Sided Confidence Bounds: A General Result,” . Biometrika , 62 : 393 – 396 .
  • Wynn , H. P. and Bloomfield , P. 1971 . “Simultaneous Confidence Bands for Regression Analysis,” . Journal of the Royal Statistical Society , 33 : 202 – 217 . Ser. B

Calibration and Prediction

  • Bowden , D. C. 1968 . “Answer to Query 26: Tolerance Intervals in Regression,” . Technometrics , 10 : 207 – 209 .
  • Chew , V. 1968 . “Simultaneous Prediction Intervals,” . Technometrics , 10 : 323 – 331 .
  • Hahn , G. J. 1972 . “Simultaneous Prediction Intervals for a Regression Model,” . Technometrics , 14 : 203 – 214 .
  • Laubscher , N. F. 1968 . “Single and Multiple Discrimination Regions in Multiple Linear Regression,” . South African Statistical Journal , 2 : 67 – 75 .
  • Lieberman , G. J. , Miller , R. G. Jr. and Hamilton , M. A. 1967 . “Unlimited Simultaneous Discrimination Intervals in Regression,” . Biometrika , 54 : 133 – 145 . Correction: 58 (1971), 687
  • Odén , A. 1973 . “Simultaneous Confidence Intervals in Inverse Linear Regression,” . Biometrika , 60 : 339 – 343 .
  • Scheffé , H. 1973 . “A Statistical Theory of Calibration,” . Annals of Statistics , 1 : 1 – 37 .
  • Steinhorst , R. K. and Bowden , D. C. 1971 . “Discrimination and Confidence Bands on Percentiles,” . Journal of the American Statistical Association , 66 : 851 – 854 .
  • Wilson , A. L. 1967 . “An Approach to Simultaneous Tolerance Intervals in Regression,” . Annals of Mathematical Statistics , 38 : 1536 – 1540 .

General

  • Aitken , M. A. 1974 . “Simultaneous Inference and the Choice of Variable Subsets in Multiple Regression,” . Technometrics , 16 : 221 – 227 .
  • Christensen , L. R. 1973 . “Simultaneous Statistical Inference in the Normal Multiple Linear Regression Model,” . Journal of the American Statistical Association , 68 : 457 – 461 .
  • Duncan , D. B. 1970 . “Answer to Query 273: Multiple Comparison Methods for Comparing Regression Coefficients,” . Biometrics , 26 : 141 – 143 .
  • Spjøtvoll , E. 1972 . “Multiple Comparison of Regression Functions,” . Annals of Mathematical Statistics , 43 : 1076 – 1088 .
  • Steffens , F. E. 1968 . “On Comparing Two Simple Linear Regression Lines,” . South African Statistical Journal , 2 : 33 – 53 .
  • Tarone , R. E. 1976 . “Simultaneous Confidence Ellipsoids in the General Linear Model,” . Technometrics , 18 : 85 – 88 .
  • Thigpen , C. C. and Paulson , A. S. 1974 . “A Multiple Range Test for Analysis of Covariance,” . Biometrika , 61 : 479 – 484 .

4.6 Categorical Data

  • Anderson , D. A. , McDonald , L. L. and Weaver , K. D. 1974 . “Tests on Categorical Data from the Union-Intersection Principle,” . Annals of the Institute of Statistical Mathematics , 26 : 203 – 213 .
  • Bhapkar , V. P. and Somes , G. W. 1976 . “Multiple Comparisons of Matched Proportions,” . Communications in Statistics , A5 : 17 – 25 .
  • Brand , R. J. , Pinnock , D. E. and Jackson , K. L. 1973 . “Large Sample Confidence Bands for the Logistic Response Curve and its Inverse,” . American Statistician , 27 : 157 – 160 .
  • Cohen , J. 1967 . “An Alternative to Marascuilo's “Large-Sample Multiple Comparisons” for Proportions,” . Psychological Bulletin , 67 : 199 – 201 .
  • Gabriel , K. R. 1966 . “Simultaneous Test Procedures for Multiple Comparisons on Categorical Data,” . Journal of the American Statistical Association , 61 : 1081 – 1096 .
  • Goodman , L. A. 1971 . “A Simple Simultaneous Test Procedure for Quasi-Independence in Contingency Tables,” . Applied Statistics , 20 : 165 – 177 .
  • Green , S-O. 1974 . “On Simultaneous Interval Estimation of Multinomial Proportions,” . Statistisktidskrift , 3 : 237 – 245 .
  • Knoke , J. 1976 . “Multiple Comparisons with Dichotomous Data,” . Journal of the American Statistical Association , 71 : 849 – 853 .
  • Renner , M. S. 1969 . “A Graphical Method of Making Multiple Comparisons of Frequencies,” . Technometrics , 11 : 321 – 330 .
  • Rodger , R. S. 1969 . “Linear Hypotheses in 2 × a Frequency Tables,” . British Journal of Mathematical and Statistical Psychology , 22 : 29 – 48 .
  • Shaffer , J. P. 1971 . “An Exact Multiple Comparisons Test for a Multinomial Distribution,” . British Journal of Mathematical and Statistical Psychology , 24 : 267 – 272 .
  • Shaffer , J. P. 1973 . “Defining and Testing Hypotheses in Multidimensional Contingency Tables,” . Psychological Bulletin , 79 : 127 – 141 .

4.7 Nonparametric Techniques

  • Crouse , C. F. 1969 . “A Multiple Comparison Rank Procedure for a One-Way Analysis of Variance,” . South African Statistical Journal , 3 : 35 – 48 .
  • Dunn-Rankin , P. and Wilcoxon , F. 1966 . “The True Distributions of the Range of Rank Totals in the Two-Way Classification,” . Psychometrika , 31 : 573 – 580 .
  • Gabriel , K. R. and Lachenbruch , P. A. 1969 . “Non-Parametric ANOVA in Small Samples: A Monte Carlo Study of the Adequacy of the Asymptotic Approximation,” . Biometrics , 25 : 593 – 596 .
  • Hollander , M. 1966 . “An Asymptotically Distribution-Free Multiple Comparison Procedure—Treatment vs. Control,” . Annals of Mathematical Statistics , 37 : 735 – 738 .
  • Marascuilo , L. A. and McSweeney , M. 1967 . “Nonparametric Post Hoc Comparisons for Trend,” . Psychological Bulletin , 67 : 401 – 412 .
  • McDonald , B. J. and Thompson , W. A. Jr. 1967 . “Rank Sum Multiple Comparisons in One-and Two-Way Classifications,” . Biometrika , 54 : 487 – 497 .
  • Odeh , R. E. 1967 . “The Distribution of the Maximum Sum of Ranks,” . Technometrics , 9 : 271 – 278 .
  • Rhyne , A. L. and Steel , R. G.D. 1967 . “A Multiple Comparisons Sign Test: All Pairs of Treatments,” . Biometrics , 23 : 539 – 549 .
  • Sen , P. K. 1966 . “On Nonparametric Simultaneous Confidence Regions and Tests for the One Criterion Analysis of Variance Problem,” . Annals of the Institute of Statistical Mathematics , 18 : 319 – 336 .
  • Sen , P. K. 1969 . “On Nonparametric T-Method of Multiple Comparisons for Randomized Blocks,” . Annals of the Institute of Statistical Mathematics , 21 : 329 – 333 .
  • Slivka , J. 1970 . “A One-Sided Nonparametric Multiple Comparison Control Percentile Test: Treatments Versus Control,” . Biometrika , 57 : 431 – 438 .

4.8 Multivariate Methods

  • Gabriel , K. R. 1968 . “Simultaneous Test Procedures in Multivariate Analysis of Variance,” . Biometrika , 55 : 489 – 504 .
  • Gabriel , K. R. 1969 . “A Comparison of Some Methods of Simultaneous Inference in MANOVA,” . In Multivariate Analysis-II , Edited by: Krishnaiah , P. R. 67 – 86 . New York : Academic Press .
  • Gabriel , K. R. and Sen , P. K. 1968 . “Simultaneous Test Procedures for One-Way ANOVA and MANOVA Based on Rank Scores,” . Sankhy[abar] A , 30 : 303 – 312 .
  • Grizzle , J. E. 1970 . “An Example of the Analysis of a Series of Response Curves and an Application of Multivariate Multiple Comparisons,” . In Essays in Probability and Statistics , Edited by: Bose , R. C. 311 – 326 . Chapel Hill , N.C. : University of North Carolina Press .
  • Hummel , T. J. and Sligo , J. R. 1971 . “Empirical Comparison of Univariate and Multivariate Analysis of Variance Procedures,” . Psychological Bulletin , 76 : 49 – 51 .
  • Jensen , D. R. 1970 . “The Joint Distribution of Traces of Wishart Matrices and Some Applications,” . Annals of Mathematical Statistics , 41 : 133 – 145 .
  • Jensen , D. R. 1972 . “Some Simultaneous Multivariate Procedures Using Hotelling's T 2 Statistics,” . Biometrics , 28 : 39 – 53 .
  • Jensen , D. R. 1974 . “On the Joint Distribution of Friedman's xr 2 Statistics,” . Annals of Statistics , 2 : 311 – 322 .
  • Krishnaiah , P. R. 1968 . “Simultaneous Tests for the Equality of Covariance Matrices Against Certain Alternatives,” . Annals of Mathematical Statistics , 39 : 1303 – 1309 .
  • Krishnaiah , P. R. 1969 . “Simultaneous Test Procedures Under General MANOVA Models,” . In Multivariate Analysis-II , Edited by: Krishnaiah . 121 – 143 . New York : Academic Press .
  • Krishnaiah , P. R. 1969 . “Further Results on ‘Simultaneous Test Procedures Under General MANOVA Models,’” . Bulletin of the International Statistical Institute , 43 : 288 – 289 . (Book 2)
  • Gabriel , K. R. and Schuurman , F. J. 1974 . “On the Evaluation of Some Distributions That Arise in Simultaneous Tests for the Equality of the Latent Roots of the Covariance Matrix,” . Journal of Multivariate Analysis , 4 : 265 – 282 .
  • Gabriel , K. R. and Waikar , V. B. 1971 . “Simultaneous Tests for Equality of Latent Roots Against Certain Alternatives—I,” . Annals of the Institute of Statistical Mathematics , 23 : 451 – 468 .
  • Gabriel , K. R. and Waikar , V. B. 1972 . “Simultaneous Tests for Equality of Latent Roots Against Certain Alternatives—II,” . Annals of the Institute of Statistical Mathematics , 24 : 81 – 85 .
  • McKay , R. J. 1976 . “Simultaneous Procedures in Discriminant Analysis Involving Two Groups,” . Technometrics , 18 : 47 – 53 .
  • Mudholkar , G. S. 1966 . “On Confidence Bounds Associated with Multivariate Analysis of Variance and Non-Independence Between Two Sets of Variates,” . Annals of Mathematical Statistics , 37 : 1736 – 1746 .
  • Mudholkar , G. S. , Davidson , M. L. and Subbaiah , P. 1974 . “Extended Linear Hypotheses and Simultaneous Tests in Multivariate Analysis of Variance,” . Biometrika , 61 : 467 – 477 .
  • Sen , P. K. and Krishnaiah , P. R. 1974 . “On a Class of Simultaneous Rank Order Rests in MANOCOVA,” . Annals of the Institute of Statistical Mathematics , 26 : 135 – 145 .
  • Tamura , R. 1969 . “Some Multivariate Comparison Procedures Based on Ranks,” . Annals of Mathematical Statistics , 40 : 1486 – 1491 .

4.9 Miscellaneous

  • Aitken , M. A. 1969 . “Multiple Comparisons in Psychological Experiments,” . British Journal of Mathematical and Statistical Psychology , 22 : 193 – 198 .
  • Carmer , S. G. 1976 . “Optimal Significance Levels for Application of the Least Significant Difference in Crop Performance Trials,” . Crop Science , 16 : 95 – 99 .
  • Erlander , S. , Gustavsson , J. and Svensson , A. 1972 . “On Asymptotic Simultaneous Confidence Regions for Regression Planes in a Poisson Model,” . Review of the International Statistical Institute , 40 : 111 – 122 .
  • Gabriel , K. R. 1969 . “Simultaneous Test Procedures—Some Theory of Multiple Comparisons,” . Annals of Mathematical Statistics , 40 : 224 – 250 .
  • Gabriel , K. R. 1970 . “On the Relation Between Union Intersection and Likelihood Ratio Tests,” . In Essays in Probability and Statistics , Edited by: Bose , R. C. 251 – 266 . Chapel Hill , N.C. : University of North Carolina Press .
  • Ghosh , M. and Sen , P. K. 1973 . “On Some Sequential Simultaneous Confidence Intervals Procedures,” . Annals of the Institute of Statistical Mathematics , 25 : 123 – 133 .
  • Hahn , G. J. 1972 . “Simultaneous Prediction Intervals to Contain the Standard Deviations or Ranges of Future Samples from a Normal Distribution,” . Journal of the American Statistical Association , 67 : 938 – 939 .
  • Hahn , G. J. 1975 . “A Simultaneous Prediction Limit on the Means of Future Samples from an Exponential Distribution,” . Technometrics , 17 : 341 – 345 .
  • Hanumara , R. C. 1975 . “Estimating Imprecisions of Measuring Instruments,” . Technometrics , 17 : 299 – 302 .
  • Hopkins , K. D. and Chadbourn , R. A. 1967 . “A Schema for Proper Utilization of Multiple Comparisons in Research and a Case Study,” . American Educational Research Journal , 4 : 407 – 412 .
  • Hurlburt , R. T. and Spiegel , D. K. 1976 . “Dependence of F Ratios Sharing a Common Denominator,” . American Statistician , 30 : 74 – 78 .
  • Jensen , D. R. , Mayer , L. S. and Myers , R. H. 1975 . “Optimal Designs and Large-Sample Tests for Linear Hypotheses,” . Biometrika , 62 : 71 – 78 .
  • Kanofsky , P. 1968 . “Derivation of Simultaneous Confidence Intervals for Parametric Functions from a Parametric Confidence Region,” . Sankhy[abar] A , 30 : 379 – 386 .
  • Krishnaiah , P. R. and Murthy , V. K. 1966 . “Simultaneous Tests for Trend and Serial Correlations for Gaussian Markov Residuals,” . Econometrica , 34 : 472 – 480 . Erratum: 34 (1966), 908–909
  • Levy , K. J. 1975 . “Large-Sample Pair-Wise Comparisons Involving Correlations, Proportions, or Variances,” . Psychological Bulletin , 82 : 174 – 176 .
  • Levy , K. J. 1975 . “Large-Sample Many-One Comparisons Involving Correlations, Proportions, or Variances,” . Psychological Bulletin , 82 : 177 – 179 .
  • Likeš , J. 1968 . “Note on Tukey's Method of Multiple Comparisons,” . Biometrische Zeitschrift , 10 : 19 – 24 .
  • Likeš , J. and Nedělka , S. 1973 . “Note on Studentized Range in Samples from an Exponential Distribution,” . Biometrische Zeitschrift , 15 : 545 – 555 .
  • Mantel , N. 1968 . “Simultaneous Confidence Intervals and Experimental Design with Normal Correlation,” . Biometrics , 24 : 434 – 137 .
  • Marascuilo , L. A. 1966 . “Large-Sample Multiple Comparisons,” . Psychological Bulletin , 65 : 280 – 290 .
  • McCool , J. I. 1975 . “Multiple Comparisons for Weibull Parameters,” . IEEE Transactions on Reliability , R-24 : 186 – 192 .
  • Reading , J. C. 1975 . “A Multiple Comparison Procedure for Classifying All Pairs Out of k Means as Close or Distant,” . Journal of the American Statistical Association , 70 : 832 – 838 .
  • Rodger , R. S. 1967 . “Type I Errors and Their Decision Basis,” . British Journal of Mathematical and Statistical Psychology , 20 : 51 – 62 .
  • Rodger , R. S. 1973 . “Confidence Intervals for Multiple Comparisons and the Misuse of the Bonferroni Inequality,” . British Journal of Mathematical and Statistical Psychology , 26 : 58 – 60 .
  • Rodger , R. S. 1974 . “Multiple Contrasts, Factors, Error Rate and Power,” . British Journal of Mathematical and Statistical Psychology , 27 : 179 – 198 .
  • Rodger , R. S. 1975 . “The Number of Non-Zero, Post Hoc Contrasts from Anova and Error-Rate, I,” . British Journal of Mathematical and Statistical Psychology , 28 : 71 – 78 .
  • Rodger , R. S. 1975 . “Setting Rejection Rate for Contrasts Selected Post Hoc When Some Nulls Are False,” . British Journal of Mathematical and Statistical Psychology , 28 : 214 – 232 .
  • Scheffé , H. 1970 . “Multiple Testing Versus Multiple Estimation, Improper Confidence Sets, Estimation of Directions and Ratios,” . Annals of Mathematical Statistics , 41 : 1 – 29 .
  • Seeger , P. 1968 . “A Note on a Method for the Analysis of Significances en Masse,” . Technometrics , 10 : 586 – 593 .
  • Spjøtvoll , E. 1972 . “On the Optimality of Some Multiple Comparison Procedures,” . Annals of Mathematical Statistics , 43 : 398 – 111 .
  • Srinivasan , R. and Wharton , R. M. 1976 . “Further Results on Simultaneous Confidence Intervals for the Normal Distribution,” . Annals of the Institute of Statistical Mathematics , 28 : 25 – 33 .
  • Ury , H. K. and Wiggins , A. D. 1971 . “Large Sample and Other Multiple Comparisons Among Means,” . British Journal of Mathematical and Statistical Psychology , 24 : 174 – 194 .
  • Ury , H. K. , Wiggins , A. D. and Wiggins , A. D. 1974 . “Use of the Bonferroni Inequality for Multiple Comparisons Among Means with Post Hoc Contrasts,” . British Journal of Mathematical and Statistical Psychology , 27 : 176 – 178 .

4.10 Pre-1966 Articles Missed in 161

  • Balaam , L. N. 1963 . “Multiple Comparisons—A Sampling Experiment,” . Australian Journal of Statistics , 5 : 62 – 84 .
  • Erlander , S. and Gustavsson , J. 1965 . “Simultaneous Confidence Regions in Normal Regression Analysis with an Application to Road Accidents,” . Review of the International Statistical Institute , 33 : 364 – 377 .
  • Krishnaiah , P. R. 1965 . “On the Simultaneous ANOVA and MANOVA Tests,” . Annals of the Institute of Statistical Mathematics , 17 : 35 – 53 .
  • Krishnaiah , P. R. 1965 . “On a Multivariate Generalization of the Simultaneous Analysis of Variance Test,” . Annals of the Institute of Statistical Mathematics , 17 : 167 – 173 .
  • Krishnaiah , P. R. 1965 . “Simultaneous Tests for the Equality of Variances Against Certain Alternatives,” . Australian Journal of Statistics , 7 : 105 – 109 . Correction: 10 (1968), 43
  • Krishnaiah , P. R. 1965 . “Multiple Comparison Tests in Multiresponse Experiments,” . Sankhy[abar] A , 27 : 65 – 72 .
  • Pillai , K. C.S. 1965 . “On the Distribution of the Largest Characteristic Root of a Matrix in Multivariate Analysis,” . Biometrika , 52 : 405 – 414 .
  • Ryan , T. A. 1959 . “Multiple Comparisons in Psychological Research,” . Psychological Bulletin , 56 : 26 – 47 .
  • Ryan , T. A. 1960 . “Significance Tests for Multiple Comparison of Proportions, Variances, and Other Statistics,” . Psychological Bulletin , 57 : 318 – 328 .

4.11 Late Additions

  • Chew , V. 1976 . “Comparing Treatment Means: A Compendium,” . Hortscience , 11 : 348 – 357 .
  • Cima , J. A. and Hochberg , Y. 1976 . “On Optimality Criteria in Simultaneous Interval Estimation,” . Communications in Statistics , A5 : 875 – 882 .
  • Dutt , J. E. , Mattes , K. D. , Soms , A. P. and Tao , L. C. 1976 . “An Approximation to the Maximum Modulus of the Trivariate t with a Comparison to the Exact Values,” . Biometrics , 32 : 465 – 469 .
  • Farebrother , R. W. 1976 . “The Minimum Proportional-Variance Unbiased Linear Estimator of β and Simultaneous Confidence Intervals,” . Journal of the American Statistical Association , 71 : 761 – 762 .
  • Hackl , P. 1975 . “Simultane Inferenz von Abweichungen Zwischen Beobachteten und Erwarteten Häufigkeiten aus Multinomialverteilungen,” . Biometrische Zeitschrift , 17 : 437 – 445 .
  • Hettmansperger , T. P. 1975 . “Non-parametric Inference for Ordered Alternatives in a Randomized Block Design,” . Psychometrika , 40 : 53 – 62 .
  • Hochberg , Y. and Lachenbruch , P. A. 1976 . “Two Stage Multiple Comparison Procedures Based on the Studentized Range,” . Communications in Statistics , A5 : 1447 – 1453 .
  • Jensen , D. R. 1976 . “The Comparison of Several Response Functions with a Standard,” . Biometrics , 32 : 51 – 59 .
  • Johnson , D. E. 1976 . “Some New Multiple Comparison Procedures for the Two-Way AOV Model with Interaction,” . Biometrics , 32 : 929 – 934 .
  • Levy , K. J. 1976 . “The Randomized Response Technique and Large Sample Pairwise Comparisons Among the Parameters of k Independent Binomial Populations,” . British Journal of Mathematical and Statistical Psychology , 29 : 257 – 262 .
  • Reinach , S. G. 1976 . “Multiple Testing Procedures for the k-Sample Runs Test,” . South African Statistical Journal , 10 : 117 – 133 .
  • Waldo , D. R. 1976 . “An Evaluation of Multiple Comparison Procedures,” . Journal of Animal Science , 42 : 539 – 544 .
  • Gupta , Das S. , Eaton , M. L. , Olkin , I. , Perlman , M. , Savage , L. J. and Sobel , M. “Inequalities on the Probability Content of Convex Regions for Elliptically Contoured Distributions,” . Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability . pp. 241 – 265 . II
  • Bryant , J. L. and Paulson , A. S. 1976 . “An Extension of Tukey's Method of Multiple Comparisons to Experimental Designs with Random Concomitant Variables,” . Biometrika , 63 : 631 – 638 .

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