Gaining Market Share for Nonparametric Statistics

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Gaining Market Share for Nonparametric Statistics

• Michael J. Schell
• Moffitt Cancer Center
• University of South Florida

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Web of Science

• Source of count data for this talk
• Words/phrases found in title or abstract
• Mainly title only references before 1991
• The number of articles has increased over the
  years, thus the need for benchmarking

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• But is the Market Itself Expanding?

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• Non-Linear Regression Methods

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Article Counts and Growth Rate of Regression
Sub-Fields

• Sub-Field 1990-94 2005-07 GR
• Non-linear 1469 2494 3.4
• Wavelets 1025 6114 11.9
• Linear 4360 8281 3.8
• Logistic 4291 16,728 7.8
• Mixed models 750 2817 7.5
• Data mining 11 2979 542
• Bioinformatics 14 4194 599
• Estimated 5-year rate obtained by doubling the
  count
• GR Growth Rate

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How Many Discoveries Have Been Lost by Ignoring
Modern Statistical Methods?Rand R. Wilcox,
American Psychologist, 1998

• Arbitrarily small departures from normality
  result in low power even when distributions are
  normal, heteroscedasticity can seriously lower
  the power of standard ANOVA and regression
  methods.
• most quantitative articles tend to be too
  technical for applied researchers.
• If the goal is to avoid low power, the worst
  method is the ANOVA F test.
• the Theil-Sen estimator deserves consideration
  as well.

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British Medical Journal articles by Doug Altman

• The scandal of poor medical research, 1994
• Why are errors so common? Put simply, much poor
  research arise because researchers feel compelled
  for career reasons to carry out research that
  they are ill equipped to perform, and nobody
  stops them.
• Statistics and ethics in medical research. The
  misuse of statistics is unethical, 1980

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Marketing of Pharmaceuticals

1. Must have the produced the drug and shown its
   efficacy
2. Need to produce the drug in mass quantities
3. Marketing

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Marketing of Statistical Ideas

1. Must have derived the statistic and demonstrated
   its efficacy
2. Need to have available software
3. Need to disseminate the idea

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Key Principle

• In an environment where ideas are not marketed,
  first on the market wins

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First-on-the-market winners

• T-test, 1905
• ANOVA
• Kolmogorov-Smirnov test, 1937
• Duncans test, 1950
• Kaplan-Meier curves, 1958
• Cox regression, 1972

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Hodges and Lehmann , 19614th Berkeley Symposium

• Chernoff and Savage (1958) proved that the ARE of
  the normal scores test is at least 1
• The above results suggest that on the basis of
  power, at least for large samples, both the
  Wilcoxon and normal scores tests are preferable
  to the t-test for general use.

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First Simulation on Robustness of t-testCA
Boneau, 1960

• 320 citations
• Conclusion t-test is fine, exponential
  distribution simulation was done wrong
• Highest citation count on any subsequent
  simulation study (39 thru 2000) 96

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Textbook Placement

• Basic Practice of Statistics, 4th Ed. 2006 David
  S. Moore (728 pages)
• Non-parametric tests dont make the book they
  appear in the virtual appendix.
• Statistics A Biomedical Introduction, 1977
• Hollander and Wolfe
• T-test in Chapter 5 Wilcoxon in Chapter 13
• Biostatistics, 2nd Ed. van Belle, Fisher, et al.,
  2004
• T-test in Chapter 5 Wilcoxon in Chapter 8

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One-Way Layout for Books of Psalms

• Book N Mn SD Sk Kurt Range Md
• 1 41 15.0 9.3 1.9 4.6 5-50 12
• 2 31 15.0 8.0 1.1 0.9 5-36 12
• 3 17 21.1 16.7 2.3 5.4 7-72 18
• 4 17 18.9 13.2 1.2 0.5 5-48 15
• 5 44 15.9 26.1 5.6 34.5 2-43,176 9
• 150

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Results

• ANOVA p .7015
• ANOVA on logged data p .0586
• Kruskal-Wallis p .0458
• Normal scores p .0378
• AD sum for data 14 2.2 1.0 2.0
  0.9 7.9
• AD sum for log data 1.9 0.3 0.3 0.5 0.2
  0.6

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Deciding Between ANOVA and KW on Principle

• If one is convinced that the metric of the values
  is what one wants, then ANOVA is fine
• ANOVA political kin is the monarchy
• KW political kin is democracy
• Power assessed as P(X lt Y)

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Cancer Research

• It has been my experience as a statistician in
  cancer research, that we are
• rarely sure of the metric for the data,
• typically interested in answering the democratic
  question
• Thus, nonparametric analysis has predominated in
  my applied articles

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Ethical Considerations

• Applied statistical work is very important in
  decision-making
• Educators have an ethical responsibility to
  properly train their tool user students in best
  practices
• Tool user statisticians have an ethical
  responsibility to seek best practice information