Analysis of Variance (ANOVA)

ANOVA (Analysis of Variance) is a statistical method used to compare means among two or more groups to determine if there are significant differences. It works by analyzing the variance within groups and between groups, partitioning the total variance into components attributable to different sources. 

The most common types are one-way ANOVA, used for one independent variable, and two-way ANOVA, used when there are two factors or independent variables. ANOVA helps determine whether the observed differences in means are due to the independent variables or simply random chance. 

If you were only comparing the means of two groups, then it would be appropriate to employ a t-Test.  When you have more than one group means to compare, it might be tempting to employ a t-Test between each group.  However, this approach will lead to incorrectly rejecting the null hypothesis (called a Type 1 Error).  When you are comparing the means of several groups, the null hypothesis to be tested will be that the means of all groups are equal.  Only the ANOVA test provides you with the tools you need to compare means across multiple groups without making a Type 1 Error. 

A one-way ANOVA tests the effect of a single independent variable (factor) on a dependent variable, comparing means across different levels of that factor to see if they are significantly different. For example, comparing test scores between three teaching methods.

The following video provides an example of a scenario employing a one-way ANOVA: 

The calculations required for a complete ANOVA can be quite daunting, so the use of some kind of spreadsheet with appropriate extensions or dedicated statistical analysis software is highly recommended.  In the following video, a one-way ANOVA is demonstrated using a spreadsheet and using Rstudio. 

A two-way ANOVA assesses the effects of two independent variables (factors) on a dependent variable, while also examining the interaction between these factors. For example, it can analyze the impact of teaching method and study time on test scores, considering both individual effects and how the factors interact. This analysis provides insights into the main effects of each factor as well as their combined interaction effects, offering a more comprehensive understanding of the relationships.

The results of a two-way ANOVA are explored in the following video: 

In the following video, a two-way ANOVA is demonstrated using a spreadsheet and using Rstudio. 

For you convenience, here are the complete notes for all the ANOVA resources and examples covered on this page: