One-way analysis of variance (ANOVA)

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

(For two samples, one-way ANOVA is equivalent to the two-sample (unpaired) t test.)


A one-way analysis of variance (ANOVA) tests whether any of the population means differ from each other. A multiple comparisons test may be used to answer the question of which population means differ from which other means, a question the ANOVA itself will not answer.


  • 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:

Failure to understand and properly apply one-way analysis of variance (ANOVA) may result in drawing erroneous conclusions from your data. If you are not familiar with these terms and concepts, you are advised to consult with a statistician. Additionally, you may want to consult the following references:

  • 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. 1996. Beyond ANOVA, Basics of Applied Statistics. 2nd. ed. London: Chapman & Hall.
  • 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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