Chapter 11 Introduction

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CHAPTER 11

One-Way ANOVA

Using the F Distributions with Three or More Samples

Type I Errors When Making Three or More Comparisons

The F Statistic as an Expansion of the z and t Statistics

The F Distributions for Analyzing Variability to Compare Means

The F Table

The Language and Assumptions for ANOVA

One-Way Between-Groups ANOVA

Everything About ANOVA but the Calculations

The Logic and Calculations of the F Statistic

Making a Decision

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

R2, the Effect Size for ANOVA

Post Hoc Tests

Tukey HSD

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

BEFORE YOU GO ON

  • You should understand the z distribution and the t distributions. You should also be able to differentiate among distributions of scores (Chapter 6), means (Chapter 6), mean differences (Chapter 9), and differences between means (Chapter 10).

  • You should know the six steps of hypothesis testing (Chapter 7).

  • You should understand what variance is (Chapter 4).

  • You should be able to differentiate between between-groups designs and within-groups designs (Chapter 1).

  • You should understand the concept of effect size (Chapter 8).

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Here’s the bad news: You are not very good at multitasking. Here’s some additional bad news: You probably think you’re pretty good at multitasking—especially when it comes to using your mobile phone while driving.

Usually, nothing bad happens when you drive and talk on your mobile phone, so many people probably conclude that they are pretty good at multitasking while driving. But here’s a simple research question: Are we worse drivers when we talk on a hands-free device or when we have a conversation with the person in the passenger seat? A simple, two-group design analyzed with a t test will answer that question. But reality is often more complicated than a simple two-group design and people drive while holding a conversation in a variety of ways.

To address the variety of conversations, researchers used a driving simulator with eight surrounding projection screens to create a series of dangerous driving situations, such as merging into traffic (Gaspar & colleagues, 2014). Participants experienced all four different experimental conditions: (1) driving alone, (2) driving and talking with a passenger seated next to them, (3) driving and talking on a videophone with a “remote passenger” in a separate room, and (4) driving and talking on a hands-free mobile phone. The third condition–with the videophone–used two projection screens that allowed the “remote passenger” to see both what the driver saw (the road ahead) and the driver’s face—just like a real passenger. Remember, everyone in the experiment experienced all four conditions. Which condition do you think was most dangerous (Figure 11-1)?

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Figure 11.1: FIGURE 11-1
Comparing Three or More Groups
Researchers compared four groups in one study, which allowed them to discover that a conversation on a hands-free mobile phone was more dangerous than a conversation with a real passenger seated next to us, a conversation with a remote passenger using a videophone, or when driving alone. The main reason we use ANOVA is to compare three or more groups in a single study.

For researchers, a four-group ANOVA is a bargain: multiple experiments for the price of one! In this chapter, we will learn about (a) the distributions used with ANOVA (the F distributions); (b) how to conduct an ANOVA when we have a between-groups design; (c) the effect-size statistic used with between-groups ANOVA; (d) how to conduct a post hoc (or follow-up) test to determine exactly which groups are different from one another; and (e) how to apply those same skills to a within-groups ANOVA, the test we would use for the within-groups talking-while-driving study.