References for ANOVA
    
 

[1]    M. Abramowitz and I.A. Stegun (1970). Handbook of Mathematical functions. U.S. Department of Commerce, National of Standards.

[2]    J. Barnard (1978). "Probability Integral of the Normal Range," Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 27, No. 2, 197-198.

[3]    R.E. Bechhofer and C.W. Dunnett (1988). "Percentage points of multivariate Student t distributions," Selected Tables in Mathematical Studies, Vol.11. American Mathematical Society.

[4]    W.H. Beyer (1987) CRC Standard Mathematical Tables, 28th ed., FL: CRC Press, 462-463.

[5]    D.G. Bonett (2006). "Approximate confidence interval for standard deviation of nonnormal distributions," Computational Statistics & Data Analysis, 50, 775-782.

[6]    D.G. Bonett (2006). "Robust Confidence Intervals for a Ratio of Standard Deviations," Applied Psychological Measurements, 30, 5, 432-439.

[7]    M.B. Brown and A.B. Forsythe (1974). "Robust Tests for the Equality of Variance,"Journal of the American Statistical Association, 69, 364-367.

[8]    H.L. Harter (1970). Order Statistics and Their Uses in Testing and Estimation, Vol.1. U.S. Government Printing Office.

[9]    A.J. Hayter (1984). "A proof of the conjecture that the Tukey-Kramer multiple comparisons procedure is conservative," Annals of Statistics, 12, 61-75.

[10]  D.L. Heck (1960). "Charts of Some Upper Percentage Points of the Distribution of the Largest Characteristic Root," The Annals of Statistics, 625-642.

[11]  C.R. Hicks (1982). Fundamental Concepts in the Design of Experiments, Third Edition. CBC College Publishing.

[12]  Y. Hochberg and A.C. Tamhane (1987). Multiple Comparison Procedures. John Wiley & Sons.

[13]  Y. Hochberg and G. Weiss, S. Hart (1982). "On graphical Procedure for Multiple Comparisons," Journal of the American Statistical Association, Vol. 77, No 380, 767-772.

[14]  J.C. Hsu (1984). "Constrained Two-Sided Simultaneous Confidence Intervals for Multiple Comparisons with the Best," Annals of Statistics, 12, 1136-1144.

[15]  J.C. Hsu (1996). Multiple Comparisons, Theory and methods. Chapman & Hall.

[16]  R. Johnson and D. Wichern (1992). Applied Multivariate Statistical Methods,Third Edition. Prentice Hall.

[17]  M.W.J. Layard (1973). "Robust large-sample tests for homogeneity of variances," Journal of the American Statistical Association, 68, 195-198.

[18]  H. Levene (1960). Contributions to Probability and Statistics. Stanford University Press, CA.

[19]  T.M. Little (1981). "Interpretation and Presentation of Result," HortScience, 19, 637-640.

[20]  R.E. Lund and J.R. Lund (1983). "Probabilities and Upper Quantiles for the Studentized Range," Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 32, No. 2, 204-210.

[21]  G.A. Milliken and D.E. Johnson (1984). Analysis of Messy Data, Volume I. Van Nostrand Reinhold.

[22]  D.C. Montgomery (1991). Design and Analysis of Experiments, Third Edition. John Wiley & Sons.

[23]  D. Morrison (1967). Multivariate Statistical Methods. McGraw-Hill.

[24]  M.K. Nakayama (2009). "Asymptotic Valid Single-Stage Multiple-Comparison Procedures," Journal of Statistical Planning and Inference, 139, 1348-1356.

[25]  L.S. Nelson (1974). "Factors for the Analysis of Means," Journal of Quality Technology, 6, 175-181.

[26]  L.S. Nelson (1983). "Exact Critical Values for Use with the Analysis of Means", Journal of Quality Technology, 15, 40-44.

[27]  P.R. Nelson (1983). "A Comparison of Sample Sizes for the Analysis of Means and the Analysis of Variance," Journal of Quality Technology, 15, 33-39.

[28]  J. Neter, W. Wasserman, and M.H. Kutner (1985). Applied Linear Statistical Models, Second Edition. Irwin, Inc.

[29]  R.A. Olshen (1973). "The conditional level of the F-test," Journal of the American Statistical Association, 68, 692-698.

[30]  E.R. Ott (1983). "Analysis of Means-A Graphical Procedure," Journal of Quality Technology, 15, 10-18.

[31]  E.R. Ott and E.G. Schilling (1990). Process Quality Control-Troubleshooting and Interpretation of Data, 2nd Edition. McGraw-Hill.

[32]  P.R. Ramig (1983). "Applications of the Analysis of Means," Journal of Quality Technology, 15, 19-25.

[33]  E.G. Schilling (1973). "A Systematic Approach to the Analysis of Means," Journal of Quality Technology, 5, 93-108, 147-159.

[34]  S.R. Searle, G. Casella, and C.E. McCulloch (1992). Variance Components. John Wiley & Sons.

[35]  N.R. Ullman (1989). "The Analysis of Means (ANOM) for Signal and Noise," Journal of Quality Technology, 21, 111-127.

[36]  E. Uusipaikka (1985). "Exact simultaneous confidence intervals for multiple comparisons among three or four mean values," Journal of the American Statistical Association, 80, 196-201.

[37]  B.J. Winer (1971). Statistical Principles in Experimental Design, Second Edition. McGraw-Hill.

Additional Resources

[38]  A white paper with simulations and other information about the Multiple Comparisons Method is available from our website at www.minitab.com.

Acknowledgment

We are grateful for assistance in the design and implementation of multiple comparisons from Jason C. Hsu, Department of Statistics, Ohio State University and for the guidance of James L. Rosenberger, Statistics Department, The Pennsylvania State University, in developing the Balanced ANOVA, Analysis of Covariance, and General Linear Models procedures.