ANOVA

Analysis of Variance (ANOVA) is a collection of statistical models and their associated procedures used to analyze the differences among group means in a sample. ANOVA was developed by Ronald Fisher in the early 20th century and is a fundamental tool in the field of statistics, allowing comparisons among three or more groups for statistical significance.

Overview

ANOVA tests the hypothesis that the means of several groups are equal. It calculates the ratio of the variance between groups to the variance within groups (the F-ratio). A significant F-ratio suggests that at least some of the group means are significantly different from each other. This test is highly useful in experimental design and is often used in conjunction with other statistical techniques that identify which specific groups differ from each other.

Types of ANOVA

There are several types of ANOVA depending on the design of the experiment and the type of data:

• One-way ANOVA: Used when comparing more than two groups based on one independent variable. It assesses whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

• Two-way ANOVA: Used when comparing groups based on two independent variables. This type of ANOVA not only evaluates the effect of each independent variable on the dependent variable but also whether there is an interaction between the two independent variables.

• Repeated measures ANOVA: Used when the same subjects are used for each treatment (i.e., repeated measures on the same subjects), which means that this type of ANOVA is useful for analyzing longitudinal data.

• Multivariate analysis of variance (MANOVA): Extends the ANOVA to cover cases where there is more than one dependent variable.

Assumptions

ANOVA has several assumptions that must be met for the F-ratio to be valid:

• Independence of cases: the samples must be independent of each other.
• Normality: the data should follow a normal distribution.
• Homogeneity of variance: all groups must have the same variance.
• The observations are sampled randomly and are roughly equal in size.

Applications

ANOVA is widely used in many fields such as psychology, medicine, engineering, and agriculture to analyze experimental data. It is particularly useful in the analysis of experimental results where several different groups are compared.

See also

• F-test
• Variance
• Statistical hypothesis testing
• Experimental design