PROPHET StatGuide: Compare Samples--Testing equality of means or locations

• If you designate that each sample is sampled from a normal distribution, then Prophet performs the appropriate normal-theory-based test (one-sample t test, paired two-sample t test, unpaired two-sample t test, one-way ANOVA, or one-way blocked ANOVA) based on the number of samples and whether or not the data are paired/blocked.

• If you designate that at least one sample is not sampled from a normal distribution, then Prophet performs the appropriate nonparametric test (one-sample signed rank test, paired signed rank test, rank sum test, Kruskal-Wallis test, or Friedman's test) based on the number of samples and whether or not the data are paired/blocked.

• If you designate that the normality of the population distributions is undetermined, then Prophet first performs a normality test for each of the samples. If one or more of the samples fails the normality test, then Prophet performs the appropriate nonparametric test (one-sample signed rank test, paired signed rank test, rank sum test, Kruskal-Wallis test, or Friedman's test) based on the number of samples and whether or not the data are paired/blocked. Otherwise, Prophet performs the appropriate normal-theory-based test (one-sample t test, paired two-sample t test, unpaired two-sample t test, one-way ANOVA, or one-way blocked ANOVA) based on the number of samples and whether or not the data are paired/blocked.

To properly analyze and interpret results of a Compare Samples analysis, you should be familiar with the following terms and concepts:

• one-sample problem
• paired samples
• two-sample problem
• multi-sample problem
• independent samples
• residuals
• Gaussian (normal) distribution
• equality of variance (homoscedasticity)
• violation of test assumptions
• distribution-free tests
• rank tests
• transformations
• multiplicity of testing
• multiple comparisons
• nominal vs. overall significance level

• 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.
• Neter, J., Wasserman, W., and Kutner, M.H. 1990. Applied Linear Statistical Models. 3rd ed. Homewood, IL: Irwin.
• Sokal, Robert R. and Rohlf, F. James. 1995. Biometry. 3rd. ed. New York: W. H. Freeman and Co.
• Winer, B.J., Brown, D.R., and Michels, K.M. 1991. Statistical Principles in Experimental Design. 3rd ed. New York: McGraw Hill.
• Zar, Jerrold H. 1996. Biostatistical Analysis. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall.

• One-sample tests:

  • t test (test whether population mean is equal to hypothesized value)

  • Wilcoxon signed rank test (test whether population median is equal to hypothesized value)

• Two-sample unpaired tests:

  • t test (test whether two population means are equal)

  • Mann-Whitney rank sum test (test whether two population distribution functions are identical against the alternative that they differ by location)

• Two-sample paired tests:

  • t test (test whether population mean of paired differences is 0)

  • Wilcoxon signed rank test (test whether population median of paired differences is 0)

• Multi-sample (one-way) unblocked tests:

  • One-way ANOVA (unblocked) (test whether several treatment effects (means) are equal)

  • Kruskal-Wallis test (test whether several population distribution functions are identical against the alternative that they differ by location)

• Multi-sample (one-way) blocked tests:

  • One-way ANOVA (blocked) (test whether several treatment effects (means) are equal.)

  • Friedman's test (test whether several treatment effects (locations) are equal.)

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Last modified: March 17, 1997