we assume that the first factor has 2 levels and the second factor has 3 levels. Define if and if , i.e. is the one-hot encoding of the first factor and is the one-hot encoding of the second factor. With that, where the last term is an intercept term. For a more concrete example suppose that Then, See also ANOVA on ranks ANOVA-simultaneous component analysis Analysis of covariance (ANCOVA) Analysis of molecular variance (AMOVA) Analysis of rhythmic variance (ANORVA) Expected mean squares Explained variation Linear trend estimation Mixed-design analysis of variance Multivariate analysis of covariance (MANCOVA) Permutational analysis of variance Variance decomposition Footnotes Notes References Pre-publication chapters are available on-line. Cohen, Jacob (1988). Statistical power analysis for the behavior sciences (2nd ed.). Routledge Cox, David R. (1958). Planning of experiments. Reprinted as Freedman, David A.(2005). Statistical Models: Theory and Practice, Cambridge University Press. Lehmann, E.L. (1959) Testing Statistical Hypotheses. John Wiley & Sons. Moore, David S. & McCabe, George P. (2003). Introduction to the Practice of Statistics (4e). W H Freeman & Co. Rosenbaum, Paul R. (2002). Observational Studies (2nd ed.). New York: Springer-Verlag. Further reading Cox, David R. & Reid, Nancy M. (2000). The theory of design of experiments. (Chapman & Hall/CRC). Freedman, David A.; Pisani, Robert; Purves, Roger (2007) Statistics, 4th edition. W.W. Norton & Company Tabachnick, Barbara G. & Fidell, Linda S. (2007). Using Multivariate Statistics (5th ed.). Boston: Pearson International Edition. External links SOCR: ANOVA Activity Examples of all ANOVA and ANCOVA models with up to three treatment factors, including randomized block, split plot, repeated measures, and Latin squares, and their analysis in R (University of Southampton) NIST/SEMATECH e-Handbook of Statistical Methods, section 7.4.3: "Are the means equal?" Analysis of variance: Introduction Design of experiments Statistical tests Parametric statistics