Analysis of variance (ANOVA)--Testing equality of means

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• One-way Unblocked ANOVA (test whether multiple population means are all equal)
• One-way Blocked ANOVA (test whether factor level means are all equal, allowing for block effects)
• Multi-factor ANOVA (for each of multiple factors/effects, test whether each effect's level means are all equal)

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To properly analyze and interpret results of one-way analysis of variance, 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

In addition, to properly analyze and interpret results of one-way blocked analysis of variance you should also be familiar with the following terms and concepts:

• two-way layout
• randomized block design
• matched samples (blocking)

In addition, to properly analyze and interpret results of multi-factor analysis of variance you should also be familiar with the following terms and concepts:

• factors
• levels within factors
• two-way layout
• randomized block design
• interaction

If you are not familiar with these terms and concepts, you are advised to consult with a statistician. Failure to understand and properly apply one-way analysis of variance and multi-factor analysis of variance (ANOVA) may result in drawing erroneous conclusions from your data. 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.
• Miller, Rupert G. Jr. 1996. Beyond ANOVA, Basics of Applied Statistics. 2nd. ed. London: Chapman & Hall. of variance.)
• 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.
• Sokal, Robert R. and Rohlf, F. James. 1995. Biometry. 3rd. ed. New York: W. H. Freeman and Co.
• Winer, B.J., Brown, D.R., and Michels, K.M. 1991. Statistical Principles in Experimental Design. 3rd ed. New York: McGraw Hill.
• Zar, Jerrold H. 1996. Biostatistical Analysis. 3rd ed. Upper Saddle River, NJ: Prentice-Hall.

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