ANALYSIS OF VARIANCE BASICS
An ANOVA test is a way to find out if survey or experiment results are significant. In other words, they
help you to figure out if you need to reject the null hypothesis or accept the alternate hypothesis.
Basically, you are testing groups to see if there is a difference between them. Examples of when
you might want to test different groups:
• A group of psychiatric patients are trying three different therapies: counseling, medication
and biofeedback. You want to see if one therapy is better than the others.
• A manufacturer has two different processes to make light bulbs. They want to know if one
process is better than the other.
• Students from different colleges take the same exam. You want to see if one college
outperforms the other.
What Does “One-Way” or “Two-Way Mean?
One-way or two-way refers to the number of independent variables (IVs) in your Analysis of
Variance test.
• One-way has one independent variable (with 2 levels). For example: brand of cereal,
• Two-way has two independent variables (it can have multiple levels). For example: brand of
cereal, calories.
What are “Groups” or “Levels”?
Groups or levels are different groups within the same independent variable. In the above example,
your levels for “brand of cereal” might be Lucky Charms, Raisin Bran, Cornflakes — a total of three
levels.
Your levels for “Calories” might be: sweetened, unsweetened — a total of two levels.
Let’s say you are studying if an alcoholic support group and individual counseling combined is the
most effective treatment for lowering alcohol consumption. You might split the study participants into
three groups or levels:
• Medication only,
• Medication and counseling,
• Counseling only.
Your dependent variable would be the number of alcoholic beverages consumed per day. If your
groups or levels have a hierarchical structure (each level has unique subgroups), then use a nested
ANOVA for the analysis.
What Does “Replication” Mean?
It’s whether you are replicating (i.e. duplicating) your test(s) with multiple groups. With a two-way
ANOVA with replication, you have two groups and individuals within that group are doing more than
one thing (i.e. two groups of students from two colleges taking two tests). If you only have one group
taking two tests, you would use without replication.
