10.1 : What is an ANOVA?

The Analysis of Variance or ANOVA is a statistical test developed by Ronald Fisher in 1918. It is performed on three or more samples to check for equality between their means.

Before performing ANOVA, one must ensure that the samples used for this analysis have three crucial characteristics or statistical assumptions. The first assumption states that the samples should be drawn from normally distributed samples, while the second requires that all the drawn samples should be randomly and independently selected. The third and last assumption states that the samples should be drawn from populations with equal variances.

There are two commonly used types of ANOVA: one-way ANOVA and two-way ANOVA. One-way ANOVA is used for the samples categorized by one factor, whereas two-way ANOVA is used when two factors categorize the samples.

Further, ANOVA is a helpful method that has broad practical applications. It can help a consumer select a washing machine or refrigerator after comparing different models or help a sociologist discern whether a person's income depends on their upbringing. ANOVA is used in environmental sciences to determine the variation in average pollution levels among several water bodies. Hence, ANOVA is widely applicable in fields such as life science, business administration, social science, forensic science, etc.

This text is adapted from Openstax, Introductory Statistics, Section 13.1 One way ANOVA