11.3. The Two-Way ANOVA Test http://www.ck12.org
11.3 The Two-Way ANOVA Test
Learning Objectives
- Understand the difference in situations that allow for one-or two-way ANOVA methods.
- Know the procedure of two-way ANOVA and its application through technological tools.
- Understand completely randomized and randomized block methods of experimental design and their relation
to appropriate ANOVA methods.
Introduction
In the previous section we discussed the one-way ANOVA method, which is the procedure for testing the null
hypothesis that the population means and variances of a single independent variable are equal. Sometimes, however,
we are interested in testing the means and variance of more than one independent variable. Say, for example,
that a researcher is interested in determining the effects of different dosages of a dietary supplement on a physical
endurance test in both males and females. The three different dosages of the medicine are (1) low, (2) medium and
(3) high and the genders are (1) male and (2) female. Analyses with two independent variables, like the one just
described, are calledtwo-way ANOVA tests.
TABLE11.6: Mean Scores on a Physical Endurance Test for Varying Dosages and Genders
Dietary Supplement
DosageDietary Supplement
DosageDietary Supplement
Dosage
Low Medium High Total
Female 35. 6 49. 4 71. 8 52. 27
Male 55. 2 92. 2 110. 0 85. 8
Total 45. 2 70. 8 90. 9There are several questions that can be answered by a study like this, for example:
- Does the medication improve physical endurance, as measured by the test?
- Do males and females respond in the same way to the medication?
While there are similar steps in performing one- and two-way ANOVA tests, there are some major differences. In the
following sections we will explore the differences in situations that allow for the one- or two-way ANOVA methods,
the procedure of two-way ANOVA and the experimental designs associated with this method.