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Gaining Market Share for Nonparametric Statistics

Gaining Market Share for Nonparametric Statistics. Michael J. Schell Moffitt Cancer Center University of South Florida. Web of Science. Source of count data for this talk Words/phrases found in title or abstract Mainly title only references before 1991

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Gaining Market Share for Nonparametric Statistics

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  1. Gaining Market Share for Nonparametric Statistics Michael J. Schell Moffitt Cancer Center University of South Florida

  2. 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

  3. But is the Market Itself Expanding?

  4. Non-Linear Regression Methods

  5. 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

  6. 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.

  7. 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

  8. Marketing of Pharmaceuticals • Must have the produced the drug and shown its efficacy • Need to produce the drug in mass quantities • Marketing

  9. Marketing of Statistical Ideas • Must have derived the statistic and demonstrated its efficacy • Need to have available software • Need to disseminate the idea

  10. Key Principle In an environment where ideas are not marketed, first on the market wins

  11. First-on-the-market winners T-test, 1905 ANOVA Kolmogorov-Smirnov test, 1937 Duncan’s test, 1950 Kaplan-Meier curves, 1958 Cox regression, 1972

  12. 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.”

  13. 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

  14. Textbook Placement Basic Practice of Statistics, 4th Ed. 2006 David S. Moore (728 pages) Non-parametric tests don’t 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

  15. 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

  16. 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

  17. 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 < Y)

  18. 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

  19. 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

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