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.)

### 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.

- 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 detectbefore performing the one-way ANOVA whether your data violate any assumptions.Ways to examineone-way ANOVA results to detect assumption violations.Possible alternativesif 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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