# ANOVA

An acronym for Analysis of Variance (**AN**alysis **O**f **VA**riance) developed by statistician and evolutionary biologist Ronald Fisher.

ANOVA is a statistical analysis of the variation between group means of factors or variables in a data set. ANOVA provides a statistical significance test of whether the estimated population means of 2 or more groups within each factor are equal.

To perform an ANOVA, you must have a continuous response variable and at least one categorical factor with two or more levels.

The procedure works by comparing the variance between group means versus the variance within groups (error or noise in the experiment) as a way of determining whether the groups are all part of one larger population, or are separate (statistically different) populations with different characteristics.

Here is an example of the ANOVA summary results. An organization would like to know whether the differences in delivery times between the three shipping centers (Central, Eastern and Western) are statistically significant.

The variation being analyzed is the delivery times, which is the dependent response variable. The factor (independent variable) being evaluated is the shipping center. A One-way ANOVA is performed, since there is only one factor used in the analysis.

In this simple example provided by Minitab, there is a statistical difference between the shipping centers, since the P-value is less than a standard threshold of 0.05 (5% risk of being wrong).

The analysis also shows that there are other factors missing that could help explain the variation in delivery times, as the R-sq(adj) is only 20.24% (where 100% is a perfect model).

Links

Books

- Statistical Methods for Research Workers by Ronald Fisher
- Lean Six Sigma and Minitab
- The Six Sigma Handbook
- Six Sigma For Dummies