PROPHET StatGuide: Nonparametric Tests--Tests that do not assume normality

• one-sample sign test (test the hypothesis that the probability of a random value from the population being above the specified value is equal to the probability of a random value being below the specified value)
• two-sample paired sign test (test the hypothesis that the probability of a paired difference being above 0 is equal to the probability of a paired difference being below 0)
• Wilcoxon one-sample signed rank test (test whether population median is equal to hypothesized value)
• Wilcoxon two-sample paired signed rank test (test whether population median of paired differences is 0)
• Mann-Whitney rank sum test (test whether two population distribution functions are identical against the alternative that they differ by location)
• Kruskal-Wallis test (test whether several population distribution functions are identical the alternative that they differ in location)
• Friedman's test (test whether several treatment effects ( locations) are equal for data in a two-way layout)
• Ansari-Bradley test (test whether two population distribution functions are identical vs the alternative that they differ by dispersion (scale))
• Cochran's Q (test whether several treatment effects ( locations) are equal --dichotomous outcome variable)
• McNemar's Q (test whether population median of paired differences is 0 --dichotomous outcome variable, counted data arranged in "contingency" table)

• violation of test assumptions
• distribution-free tests
• rank tests

• Brownlee, K. A. 1965. Statistical Theory and Methodology in Science and Engineering. New York: John Wiley & Sons.
• Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed. New York: John Wiley & Sons.
• Daniel, Wayne W. 1978. Applied Nonparametric Statistics. Boston: Houghton Mifflin.
• Daniel, Wayne W. 1995. Biostatistics. 6th ed. New York: John Wiley & Sons.
• Hollander, M. and Wolfe, D. A. 1973. Nonparametric Statistical Methods. New York: John Wiley & Sons.
• Lehmann, E. L. 1975. Nonparametrics: Statistical Methods Based on Ranks. San Francisco: Holden-Day.
• Miller, Rupert G. Jr. 1986. Beyond ANOVA, Basics of Applied Statistics. New York: John Wiley & Sons.
• Rosner, Bernard. 1995. Fundamentals of Biostatistics. 4th ed. Belmont, California: Duxbury Press.
• Sokal, Robert R. and Rohlf, F. James. 1995. Biometry. 3rd. ed. New York: W. H. Freeman and Co.
• Zar, Jerrold H. 1996. Biostatistical Analysis. 3rd ed. Upper Saddle River, NJ: Prentice-Hall.

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Last modified: March 17, 1997