Analysis of Variance Tutorial
Analysis of variance (ANOVA) refers to a collection of statistical methods that researchers use to
determine whether mean scores differ significantly across
treatment groups.
About the Tutorial
This tutorial explains how to use analysis of variance
to assess the effect of one or more
factors on a single
interval or
ratioscale variable.
The tutorial focuses on four classic
experimental designs:
 Singlefactor independent groups design.
 Full factorial independent groups design.
 Randomized block design with independent groups.
 Repeated measures design (aka, withinsubjects design).
Who Is This For?
This tutorial is designed for students and researchers who have some familiarity with introductory statistics (e.g., a high school statistics course or
Advanced Placement Statistics).
What Will You Learn?
By the end of the
tutorial, you will be able to judge whether analysis of variance is the right tool for the study you are conducting.
You will be able to choose the right design for your research.
You will be able to conduct an appropriate analysis of variance for the design you have chosen,
by hand or with software.
And, most important, you will be able to correctly interpret the outputs you produce.
Note: In the real world, you will most likely use a software package (e.g., SAS, SPSS, Excel) to
generate outputs from
analysis of variance. Examples in this tutorial use Excel, since it is widely available.
Outputs from Excel are similar to outputs from other statistical packages;
so if you can interpret outputs from Excel, you should be able to interpret similar outputs from other packages.
How to Use This Tutorial
Individual lessons are accessible through the table of contents, which can be
found in the vertical column on the left side of the page. You should work through lessons
in the order in which they appear; because some lessons build on
previous lessons.
Individual lessons are accessible through the table of contents, which can be
accessed by tapping the "Analysis of Variance: Table of Contents" button at the top of the page. You should work through lessons
in the order in which they appear; because some lessons build on previous lessons.
Additional Helpful Resources
As you progress through the tutorial, take advantage of the following helpful resources.

Online calculators. The
F distribution calculator, the
chisquare calculator,
and the Bartlett's test calculator
are useful for interpreting outputs from analysis of variance.
They can be found in the table of contents.

Sample problems. Many of the lessons include sample problems and solutions.
The sample problems expand your knowledge. The solutions explain how to correctly interpret analytical outputs.

Online help. Stat Trek's online
Statistics Dictionary takes the mystery out of statistical jargon. If any term or
concept is unclear, visit the dictionary for additional explanation.
Note: The dictionary can be accessed by clicking the Help tab in the main menu (located at the top of this web page).