# 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:

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.

### 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:

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. 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

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