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One Way Anova

  • David J. Olive
Chapter

Abstract

Chapters  5 9 consider experimental design models. These models are linear models, and many of the techniques used for multiple linear regression can be used for experimental design models. In particular, least squares, response plots, and residual plots will be important. These models have been used to greatly increase agricultural yield, greatly improve medicine, and greatly improve the quality of manufactured goods. The models are also good for screening out good ideas from bad ideas (e.g., for a medical treatment for heart disease or for improving the gas mileage of a car).

Keywords

Anova Model Residual Plot Identity Line ANOVA Table Location Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, B, 26, 211–246.MathSciNetzbMATHGoogle Scholar
  2. Box, G. E. P, Hunter, J. S., & Hunter, W. G. (2005). Statistics for experimenters (2nd ed.). New York, NY: Wiley.zbMATHGoogle Scholar
  3. Brown, M. B., & Forsythe, A. B. (1974a). The ANOVA and multiple comparisons for data with heterogeneous variances. Biometrics, 30, 719–724.Google Scholar
  4. Brown, M. B., & Forsythe, A. B. (1974b). The small sample behavior of some statistics which test the equality of several means. Technometrics, 16, 129–132.Google Scholar
  5. Cobb, G. W. (1998). Introduction to design and analysis of experiments. Emeryville, CA: Key College Publishing.zbMATHGoogle Scholar
  6. Cook, R. D., & Olive, D. J. (2001). A note on visualizing response transformations in regression. Technometrics, 43, 443–449.MathSciNetCrossRefGoogle Scholar
  7. Cook, R. D., & Weisberg, S. (1999a). Applied regression including computing and graphics. New York, NY: Wiley.Google Scholar
  8. Dean, A. M., & Voss, D. (2000). Design and analysis of experiments. New York, NY: Springer.zbMATHGoogle Scholar
  9. Ernst, M. D. (2009). Teaching inference for randomized experiments. Journal of Statistical Education, 17 (online).Google Scholar
  10. Fox, J. (1991). Regression diagnostics. Newbury Park, CA: Sage Publications.CrossRefGoogle Scholar
  11. Haenggi, J. C. (2009). Plots for the Design and Analysis of Experiments. Master’s Research Paper, Southern Illinois University, at http://lagrange.math.siu.edu/Olive/sjenna.pdf Google Scholar
  12. Hoaglin, D. C., Mosteller, F., & Tukey, J. W. (Eds.). (1991). Fundamentals of exploratory analysis of variance. New York, NY: Wiley.zbMATHGoogle Scholar
  13. Hoeffding, W. (1952). The large sample power of tests based on permutations of observations. The Annals of Mathematical Statistics, 23, 169–192.MathSciNetCrossRefzbMATHGoogle Scholar
  14. Kirk, R. E. (1982). Experimental design: Procedures for the behavioral sciences (2nd ed.). Belmont, CA: Brooks/Cole Publishing Company.zbMATHGoogle Scholar
  15. Kirk, R. E. (2012). Experimental design: Procedures for the behavioral sciences (4th ed.). Thousand Oaks, CA: Sage Publications.zbMATHGoogle Scholar
  16. Kuehl, R. O. (1994). Statistical principles of research design and analysis. Belmont, CA: Duxbury.zbMATHGoogle Scholar
  17. Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear statistical models (5th ed.). Boston, MA: McGraw-Hill/Irwin.Google Scholar
  18. Ledolter, J., & Swersey, A. J. (2007). Testing 1-2-3 experimental design with applications in marketing and service operations. Stanford, CA: Stanford University Press.Google Scholar
  19. Maxwell, S. E., & Delaney, H. D. (2003). Designing experiments and analyzing data (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.zbMATHGoogle Scholar
  20. McKenzie, J. D., & Goldman, R. (1999). The student edition of MINITAB. Reading, MA: Addison Wesley Longman.Google Scholar
  21. Montgomery, D. C. (1984). Design and analysis of experiments (2nd ed.). New York, NY: Wiley.Google Scholar
  22. Montgomery, D. C. (2012). Design and analysis of experiments (8th ed.). New York, NY: Wiley.Google Scholar
  23. Moore, D. S. (2007). The basic practice of statistics (4th ed.). New York, NY: W.H. Freeman.Google Scholar
  24. Oehlert, G. W. (2000). A first course in design and analysis of experiments. New York, NY: W.H. Freeman.Google Scholar
  25. Olive, D. J. (2004b). Visualizing 1D regression. In M. Hubert, G. Pison, A. Struyf, & S. Van Aelst (Eds.), Theory and applications of recent robust methods (pp. 221–233). Basel, Switzerland: Birkhäuser.Google Scholar
  26. Olive, D. J. (2014). Statistical theory and inference. New York, NY: Springer.CrossRefzbMATHGoogle Scholar
  27. SAS Institute (1985). SAS user’s guide: Statistics. Version 5. Cary, NC: SAS Institute.Google Scholar
  28. Snedecor, G. W., & Cochran, W. G. (1967). Statistical methods (6th ed.). Ames, IA: Iowa State College Press.zbMATHGoogle Scholar
  29. Tukey, J. W. (1957). Comparative anatomy of transformations. Annals of Mathematical Statistics, 28, 602–632.MathSciNetCrossRefzbMATHGoogle Scholar
  30. Welch, B. L. (1947). The generalization of Student’s problem when several different population variances are involved. Biometrika, 34, 28–35.MathSciNetzbMATHGoogle Scholar
  31. Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330–336.MathSciNetCrossRefzbMATHGoogle Scholar
  32. Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing (3rd ed.). New York, NY: Academic Press, Elsevier.zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • David J. Olive
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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