# SAGE Journal Articles

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**Summary/Abstract: **This is the second in a series on design of experiments that started in the last issue. Here we introduce the basic idea of a factorial design using an invented, but at least qualitatively realistic, example about baking bread.

#### Questions to Consider

1. What are the fundamental differences between a single factor experimental design and a factorial design?

2. When we say that there is an interaction between two factors, this means that the effect on the response of changing one factor depends on:

- the type of experimental design.
- the level of the other one.
- one level of the other one.
- an average of the other one.

3. What are some advantages of the factorial experiment?

- The main effects provide efficient estimates of quantities.
- You can see if there is an interaction.
- A and B.
- None of the above.

**Summary/Abstract: **The authors provide a cautionary note on reporting accurate eta-squared values from multifactor analysis of variance (ANOVA) designs. They reinforce the distinction between classical and partial eta-squared as measures of strength of association. They provide examples from articles published in premier psychology journals in which the authors erroneously reported partial eta-squared values as representing classical eta-squared values. Finally, they discuss broader impacts of inaccurately reported eta-squared values for theory development, meta-analytic reviews, and intervention programs.

#### Questions to Consider

1. Compare and contrast classical eta-squared and partial eta-squared.

2. Which is not a measure of strength of association when using ANOVA to analyze data?

- eta-squared
- omega-squared
- beta-squared
- epsilon-squared

3. Assuming nonerror sources accounted for 100% of the total variation, the authors believe that the classical eta-squared values were inflated by ___.

- 34%
- 46%
- 53%
- 65%