(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.
- 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.
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.