Chapter 13

One-Way Within-Groups ANOVA

327

One-Way Within-Groups ANOVA

  • The Benefits of Within-Groups ANOVA
  • The Six Steps of Hypothesis Testing

Beyond Hypothesis Testing for the One-Way Within-Groups ANOVA

  • R2, the Effect Size for ANOVA
  • Tukey HSD

Next Steps: Matched Groups

BEFORE YOU GO ON

  • You should be able to differentiate between between-groups designs and within-groups designs (Chapter 1).
  • You should be able to conduct the six steps of hypothesis testing for a one-way between-groups ANOVA (Chapter 12).
  • You should understand the concept of effect size (Chapter 8) and know how to calculate R2 for a one-way between-groups ANOVA (Chapter 12).
  • You should understand the concept of post hoc testing and be able to calculate a Tukey HSD test for a one-way between-groups ANOVA (Chapter 12).

328

Within-Groups Design Whenever researchers have people provide ratings of several items—such as here, with different types of coffee—they are using a within-groups design.
REUTERS/Jose Miguel Gomez

“What’s in a name?” Juliet asks Romeo. “That which we call a rose/By any other name would smell as sweet.” A group of Canadian researchers decided to test Juliet’s assertion (Djordjevic et al., 2007). They assigned names associated with positive, negative, or neutral odors to 15 different odors and then presented them to participants, who were asked to rate the pleasantness and the intensity of the aroma. Positive names for aromas included “cinnamon stick” and “jasmine tea.” Negative names for odors included “rotten fish” and “dry vomit.” Neutral names were 2-digit numbers such as “36.”

The researchers used a within-groups design, which means that each participant smelled the same odor with a positive name, a negative name, and a neutral name. Having each participant experience each level of the independent variable is one of the advantages of using a within-groups design: Researchers require fewer participants. The research team found that participants generally rated aromas with positive names as more pleasant and odors with negative names as more intense.

This odor study also demonstrates why this chapter is divided into two parts. The first part discusses the one-way within-groups ANOVA, which shows how to determine the probability that any differences are real (such as the differences between odor ratings based on a positive, negative, or neutral name). The second part takes us beyond hypothesis testing and discusses how to calculate the size of those differences.