# Definition of Anova (analysis of variance)

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**Anova (analysis of variance)**Definition from Science & Technology Dictionaries & Glossaries

Common Concepts in Statistics

A test for significant differences between means by comparing variances. It concerns a normally distributed response (outcome) variable and a single categorical explanatory (predictor) variable which represents treatments or groups. ANOVA is a special case of multiple regression where indicator variables (or orthogonal polynomials) are used to describe the discrete levels of factor variables. The term analysis of variance refers not to the model but to the method of determining which effects are statistically significant. Major assumptions of ANOVA are the normality of the response variable (the response variable should be normally distributed within each group), and homogeneity of variances (it is assumed that the variances in the different groups of the design are equal). Under the null hypothesis (that there are no mean differences between groups or treatments in the population), the variance estimated from the within-group (treatment) random variability (

**residual sum of squares**= RSS) should be about the same as the variance estimated from between-groups (treatments) variability (**explained sum of squares**= ESS). If the null hypothesis is true, there should be no difference between within and between groups variability, and their ratio (variance ratio), mean ESS / mean RSS should be equal to 1. This is known as the**F test**or variance ratio test (see also**one-way**and**two-way ANOVA**). The ANOVA approach is based on the partitioning of sums of squares and degrees of freedom associated with the response variable. ANOVA interpretations of main effects and interactions are not so obvious in other regression models. An accumulated ANOVA table reports the results from fitting a succession of regression models to data from a factorial experiment. Each main effect is added on to the constant term followed by the interaction(s). At each level an F test result is also reported showing the extra effect of adding each variable so it can be worked out which model would fit best. In a two-way ANOVA with equal replications, the order of terms added to the model does not matter, whereas, this is not the case if there are unequal replications. When the assumptions of ANOVA are not met, its non-parametric equivalent**Kruskal-Wallis test**may be used. (A tutorial on ANOVA )