PROPHET StatGuide: One-way analysis of variance (ANOVA)

One-way analysis of variance (ANOVA) is used to test the null hypothesis that multiple population means are all equal.

Assumptions:

• Within each sample, the values are independent, and identically normally distributed (same mean and variance).

• The samples are independent of each other.

• The different samples are all assumed to come from populations with the same variance, allowing for a pooled estimate of the variance.

• For a multiple comparisons test of the sample means to be meaningful, the populations are viewed as fixed, so that the populations in the experiment include all those of interest.

Guidance:

• Ways to detect before performing the one-way ANOVA whether your data violate any assumptions.

• Ways to examine one-way ANOVA results to detect assumption violations.

• Possible alternatives if your data or one-way ANOVA results indicate assumption violations.

To properly analyze and interpret results of one-way analysis of variance (ANOVA), you should be familiar with the following terms and concepts:

• multi-sample problem
• independent samples
• residuals
• Gaussian (normal) distribution
• equality of variance (homoscedasticity)
• 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.
• Daniel, Wayne W. 1995. Biostatistics. 6th ed. New York: John Wiley & Sons.
• Lindman, Harold R. 1992. Analysis of Variance in Experimental Design. New York: Springer-Verlag.
• 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.
• Rosner, Bernard. 1995. Fundamentals of Biostatistics. 4th ed. Belmont, California: Duxbury Press.
• Winer, B.J., Brown, D.R., and Michels, K.M. 1991. Statistical Principles in Experimental Design. 3rd ed. New York: McGraw Hill.
• 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: February 21, 1997