"Analysis of variance" (or ANOVA) is designed to test hypotheses about the equality of two or more group means, and gets its name from the idea of judging the apparent differences among the means of the groups of observations relative to the variance of the individual groups.

The basic underlying idea is to compare the variability of the observations among groups, to that within groups:

• if the variability among groups is small (relative to the variability within groups), this lends support to a null hypothesis that the means of the different groups are identical; but
• if the variability among groups is large, (relative to the variability within groups), this discredits the null hypothesis, and lends support for the alternative hypothesis.

There are some assumptions that underlie the application of analysis of variance, and which, if violated, add uncertainty to the results. The assumptions are:

• there are three or more independent groups of data
• within each group, the values of the variables are normally distributed
• the variances of each group are equal
• dependent or response variables are measured on an interval or ratio scale

Analysis of variance for testing for the equality of k mean values is a special case of a set of techniques known as linear modeling, which also includes regression analysis, a future topic.

• analysis of variance examples
• the null and alternative hypothesis

Readings:

Owen (The R Guide):  section 7.3; Rogerson (Statistical Methods):  Ch. 4; Rossiter (Introduction ... ITC):  section 4.20