Analysis of Variance Designs

Prerequisites
Introduction to ANOVA

Learning Objectives

1. Be able to identify the factors and levels of each factor from a description of an experiment
2. Determine whether a factor is a between-subjects or a within-subjects factor
3. Define factorial design

There are many types of experimental designs that can be analyzed by ANOVA. This section discusses many of these designs and defines many key terms used.

Factors and Levels

The section on variables defined an independent variable as a variable manipulated by the experimenter. In the case study Smiles and Leniency, the effect of different types of smiles on the leniency showed to a person was investigated. Four different types of smiles (neutral, false, felt, miserable, on leniency) were investigated. In this experiment, "Type of Smile" is the independent variable. In describing an ANOVA design, the term factor is used as a synonym of independent variable. Therefore, "Type of Smile" is the factor in this experiment. Since four types of smiles were compared, the factor "Type of Smile" has four levels.

An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA. If an experiment has two factors, then the ANOVA is called a two-way ANOVA.

Between- and Within-Subject Factors

When different subjects are used for the levels of the factor, the factor is called a between-subjects factor or a between-subjects variable. The term "between subjects" reflects the fact that comparisons are between different groups of subjects.

When the same subjects are used for the levels of the factor, the factor is called a within-subjects factor or within-subjects variable. Within-subjects variables are sometimes referred to as repeated-measures variables since there are repeated measurements of the same subjects.

Multi-Factor Designs

It is common for designs to have more than one factor. For example, consider a hypothetical study of the effects of age and gender on reading speed in which males and females from the age levels of 8 years, 10 years, and 12 years were tested. There would be a total of six different groups as shown in Table 1.

Table 1. Gender x Age Design
 Group Gender Age 1 2 3 4 5 6 Female Female Female Male Male Male 8 10 12 8 10 12

This design has two factors: age and gender. Age has three levels and gender has two levels. When all combinations of the levels are included (as they are here) the design is called a factorial design. A concise way of describing this design is as a Gender (2) x Age (3) factorial design where the numbers in parentheses indicate the number of levels. Complex designs frequently have more than two factors and may have combinations of between- and within-subject factors.