PSY 2060 Assignment: ANOVA Design

Factorial ANOVA

Consider the following senario:

    • A researcher is interested in how reading to children affects those kids own reading ability. The researcher thinks that the age of the child being read to and how long each reading session is might be important variables. So the researcher designs the following experiment.

Three groups of children are selected: 3 yr olds, 8 yr olds, & 14 yr olds. Each group is read a Dr. Seuss story. Within each group, individuals are randomly assigned to one of three reading conditions. Reading sessions for group 1 only last 5 mins; 15 mins for group 2; and 30 mins for group 3. After two weeks the kids’ reading ability is measured (with age appropriate standardized books).

 

 

Reading session duration
5 mins 15 mins 30 mins
Age 3 yrs
8 yrs
14 yrs

So we have not two samples, but 3 X 3 samples (that’s 9). How do we analyze the data?

So far our Analysis of Variance (ANOVA) models have had only 1 factor (that’s the “one-way” part). Often researchers aren’t interested only in a single factor, but how multiple factors (independent variables) work together. The way the factors work together are called interaction effects.

In analysis of variance, a factor is an independent variable. A study that invloves only one independent variable is called a single-factor design. A study with more than one independent variable is called a factorial design.

The individual treatment conditions that make up a factor are called levels of the factor.

 

      • So the study described above is a factorial design, with two between groups factors, and each factor has 3 levels (sometimes described as a 3 by 3 between groups design).

For the most part we will focus on a 2-Factor between groups ANOVA, although there are many other designs that use the same basic underlying concepts.

 

Factorial – multiple factors

 

    • A factorial design is an experiment with two or more factors (independent variables).

      • 2 x 4 design means two independent variables, one with 2 levels and one with 4 levels
      • “condition” or “groups” is calculated by multiplying the levels, so a 2×4 design has 8 different conditions

Results

    • Main effects
    • Interaction effects* One should always consider the interaction effects before trying to interpret the main effects. Sometimes the interaction effects are the “cause” of the apparent main
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