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R by Example pp 243-253 | Cite as

Randomization Tests

  • Jim AlbertEmail author
  • Maria Rizzo
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Part of the Use R! book series (USE R)

Abstract

If the model assumptions for ANOVA do not hold, then the ANOVA F-test is not necessarily valid for testing the hypothesis of equal means. However, one can compute an ANOVA table and a F statistic; what is in doubt is whether the “F” ratio has a F distribution.

Keywords

Permutation Test Randomization Test Waste Data Rank Base Measure Ization Test 
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.
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References

  1. 1.
    Albert, J. (2009), Bayesian Computation with R, Springer, New York.Google Scholar
  2. 2.
    Agresti, A. and Coull, B. (1998), “Approximate is better than ‘exact’ for interval estimation of binomial proportions", The American Statistician, 52, 119–126.MathSciNetGoogle Scholar
  3. 3.
    Ashenfelter, O. and Krueger, A. (1994), “Estimates of the economic return to schooling from a new sample of twins", The American Economic Review, 84, 1157–1173.Google Scholar
  4. 4.
    Bolstad, W. (2007), Introduction to Bayesian Statistics, Wiley-Interscience.Google Scholar
  5. 5.
    Box, G. E. P., Hunter W. G. and Hunter J. S. (1978), Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, Wiley, New York.Google Scholar
  6. 6.
    Cameron E. and Pauling L. (1978), “Experimental studies designed to evaluate the management of patients with incurable cancer", Proc. Natl. Acad. Sci. USA, 75, 4538–4542.CrossRefGoogle Scholar
  7. 7.
    Canty, A. and Ripley. B. (2010), boot: Bootstrap R Functions, R package version 1.2–43.Google Scholar
  8. 8.
    Casella, G., and George, E. (1992), “Explaining the Gibbs sampler", The American Statistician, 46, 167–174.Google Scholar
  9. 9.
    Chib, S., and Greenberg, E. (1995), “Understanding the Metropolis-Hastings algorithm", The American Statistician, 49, 327–335.Google Scholar
  10. 10.
    Cleveland, W. (1979), “Robust locally weighted regression and smoothing scatterplots", Journal of the American Statistical Association, 74, 829–83.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Carmer, S. G. and Swanson, M. R. (1973), “Evaluation of ten pairwise multiple comparison proceedures by Monte Carlo methods", Journal of the American Statistical Association, 68, 66–74.CrossRefGoogle Scholar
  12. 12.
    DASL: The Data and Story Library, http://lib.stat.cmu.edu/DASL/.
  13. 13.
    Davison, A. C. and Hinkley, D. V. (1997), Bootstrap Methods and Their Applications. Cambridge University Press, Cambridge.Google Scholar
  14. 14.
    Efron, B. and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, Chapman & Hall/CRC, Boca Raton, FL.Google Scholar
  15. 15.
    Everitt, B. S., Landau, S., And Leese, M. (2001), Cluster Analysis, 4th edition, Oxford University Press, Inc. New York.Google Scholar
  16. 16.
    Faraway, J. (2002), “Practical regression and ANOVA Using R", Contributed documentation in PDF format available at http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf.
  17. 17.
    Friendly, M. (2002), “A brief history of the mosaic display", Journal of Computational and Graphical Statistics, 11, 89–107.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Fienberg, S. E. (1971), “Randomization and social affairs: The 1970 draft lottery", Science, 171, 255–261.Google Scholar
  19. 19.
    Gelman, A., Carlin, J., Stern, H. and Rubin, D. (2003), Bayesian Data Analysis, second edition, Chapman and Hall, New York.Google Scholar
  20. 20.
    Gentle, J. E. (2003), Random Number Generation and Monte Carlo Methods, second edition, Springer, New York.Google Scholar
  21. 21.
    Hand D. J., Daly F., Lunn A. D., McConway K. J., Ostrowski E. (1994), A Handbook of Small Data Sets, Chapman and Hall, London.Google Scholar
  22. 22.
    Hoaglin, D., Mosteller, F., and Tukey, J. (2000), Understanding Robust and Exploratory Data Analysis, Wiley-Interscience.Google Scholar
  23. 23.
    Hoff, P. (2009), A First Course in Bayesian Statistics, Springer, New York.Google Scholar
  24. 24.
    Hogg, R. and Klugman, S. (1984), Loss Distributions, Wiley, New York.Google Scholar
  25. 25.
    Hollander. M. and Wolfe, D. (1999), Nonparametric Statistical Methods, second edition, Wiley, New York.Google Scholar
  26. 26.
    Hornik, K (2009). R FAQ: Frequently Asked Questions on R, Version 2.13.2011-04-07, http://cran.r-project.org/doc/FAQ/R-FAQ.html.
  27. 27.
    Hothorn, T., Hornik, K., van de Wiel, M. and Zeileis, A. (2008), “Implementing a class of permutation tests: The coin package", Journal of Statistical Software, 28, 1–23.CrossRefGoogle Scholar
  28. 28.
    Koopmans, L. (1987), Introduction to Contemporary Statistical Methods, Duxbury Press.Google Scholar
  29. 29.
    Labby, Z. (2009), “Weldon’s dice, automated” Chance, 22, 258–264.Google Scholar
  30. 30.
    Larsen, R. J. and Marx, M. L. (2006), An Introduction to Mathematical Statistics and Its Applications, 4th edition, Pearson Prentice Hall, Saddle River, New Jersey.Google Scholar
  31. 31.
    Leisch, F. (2007), bootstrap: Functions for the Book “An Introduction to the Bootstrap", R package version 1.0-22.Google Scholar
  32. 32.
    Meyer, D., Zeileis, A., and Hornik, K. (2010), vcd: Visualizing Categorical Data, R package version 1.2-9.Google Scholar
  33. 33.
    Montgomery, D. G. (2001), Design and Analysis of Experiments, 5th edition., Wiley, New York.Google Scholar
  34. 34.
    Moore, G. (1965), “Cramming more components onto integrated circuits", Electronics Magazine, April, 114–117.Google Scholar
  35. 35.
    Mosteller, F. (2010), The Pleasures of Statistics, Springer, New York.Google Scholar
  36. 36.
    Mosteller, F. and Wallace, D. L. (1984), Applied Bayesian and Classical Inference: The Case of the Federalist Papers, Springer-Verlag, New York.Google Scholar
  37. 37.
    Murrell, P. (2006), R Graphics, Chapman and Hall, Boca Raton, Florida.Google Scholar
  38. 38.
    OzDASL, Australian Data and Story Library, http://www.statsci.org/data/index.html.
  39. 39.
    Pearson, K. (1900), “On the criterion that a given system of derivations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling", Philosophical Magazine, 5, 157–175.zbMATHGoogle Scholar
  40. 40.
    R Development Core Team (2011), “R: A language and environment for statistical computing," R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/.
  41. 41.
    The R Development Core Team (2011), “R: A Language and Environment for Statistical Computing, Reference Index.” Version 2.13.0 (2011-04-13)Google Scholar
  42. 42.
    Ross, S. (2007), Introduction to Probability Models, 9th edition, Academic Press, Burlington, MA.Google Scholar
  43. 43.
    Sarkar, D. (2008), Lattice: Multivariate Data Visualization with R, Springer, New York.Google Scholar
  44. 44.
    Smith, J. M. and Misiak, H. (1973), “The effect of iris color on critical flicker frequency (CFF)", Journal of General Psychology 89, 91–95.CrossRefGoogle Scholar
  45. 45.
    Snell, L. (1988), Introduction to Probability, Random House, New York.Google Scholar
  46. 46.
    Starr, N. (1997), Nonrandom risk: the 1970 draft lottery. Journal of Statistics Education, 5, http://www.amstat.org/publications/jse/v5n2/datasets.starr.html
  47. 47.
    Tukey, J. (1977), Exploratory Data Analysis, Addison-Wesley.Google Scholar
  48. 48.
    “Campaign 2004: Time-tested formulas suggest both Bush and Kerry will win on Nov. 2", USA Today, http://www.usatoday.com/news/politicselections/nation/president/2004-06-23-bush-kerry-cover_x.htm.
  49. 49.
    Venables, W. N., Smith, D. M. and the R Development Core Team (2011). “An Introduction to R”, Version 2.13.0 (2011-04-13).Google Scholar
  50. 50.
    Venables, W. N. and Ripley, B. D. (2002), Modern Applied Statistics with S, 4th edition. Springer, New York.Google Scholar
  51. 51.
    Verzani, J. (2010), UsingR: Data sets for the text Using R for Introductory Statistics, R package version 0.1-13.Google Scholar
  52. 52.
    Wickham, H. (2009), ggplot2: Elegant Graphics for Data Analysis, Springer, New York.Google Scholar
  53. 53.
    The Washington Post (2007) “Heads and Shoulders above the Rest”, http://blog.washingtonpost.com/44/2007/10/11/head_and_shoulders_above.html.
  54. 54.
    Wikipedia, “Heights of Presidents of the United States and presidential candidates”, retrieved June 28, 2011.Google Scholar
  55. 55.
    Wilkinson, L. (2005), The Grammar of Graphics, second edition, Springer, New York.Google Scholar
  56. 56.
    Willerman, L., Schultz, R., Rutledge, J. N., and Bigler, E. (1991), “In vivo brain size and intelligence", Intelligence, 15, 223–228.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA

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