One-Way Analysis of Variance
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CHAPTER OUTLINE
- 14.1 One-Way Analysis of Variance
- 14.2 Comparing Group Means
- 14.3 The Power of the ANOVA Test
Introduction
Many of the most effective statistical studies are comparative. We may wish to compare customer satisfaction of men and women who use an online fantasy football site or compare perceptions of sales careers between business students in the United States, Canada, and China. Companies use comparative studies to develop better products and to determine how best to reach their target audience. Here are some examples.
- A lithium-air battery is a next-generation battery with a high specific energy. Toyota investigates the capacity of four lithium-air battery cell designs to better understand their potential in high-performance electric vehicles.
- Razors, especially multi-blade cartridges, are expensive. Are there ways to make the blades last longer? Gillette researchers compare different methods to increase blade life. These include storing the cartridge in rubbing alcohol, olive oil, or water in between shaves. They also look at drying it off with a towel and doing nothing (control).
- IKEA studies customers’ reactions to three advertisements concerning their new kitchen furnishings line. This information will be used to help determine which advertisement to use on TV.
With a quantitative response, we display these comparisons with back-to-back stemplots or side-by-side boxplots and histograms, and we measure them with five-number summaries or with means and standard deviations.
When only two groups are compared, Chapter 7 provides the tools we need to answer the question, “Is the difference between groups statistically significant?” Two-sample procedures compare the means of the two populations and are sufficiently robust to be widely useful. In this chapter, we compare any number of means by techniques that generalize the two-sample methods and share its robustness and usefulness.
Reminder
comparing two means, p. 378