Analysis of variance (ANOVA) is a statistical technique that is used to compare groups on possible differences in the average (mean) of a quantitative (interval or ratio, continuous) measure. Variables that allocate respondents to different groups are called factors; an ANOVA can involve one factor (a one-way design) or multiple factors (a multi-way or factorial design). The term analysis of variance refers to the partitioning of the total variation in the outcome variable into parts explained by the factor(s)—related to differences between groups, so-called explained or between variation—and a part that remains after taking the factor(s) into account, the so-called unexplained, residual, or within variation.

Consider a one-factor example in which the target population contains respondents from four different ethnic backgrounds (e.g. Chinese, Japanese, Korean, Vietnamese) ...