Book cover for Stats Data and Models

Stats Data and Models

Richard D. De Veaux, Paul F. Velleman, David E. Bock

ISBN #9780321986498

4th Edition

1,406 Questions

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16,980 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

Chapters 12 and 13 cover the design and analysis of experiments and observational studies, emphasizing the distinction between causal experiments and associative observational studies. The principles of experimental design—control, randomization, replication, and blocking—are essential for minimizing bias and confounding. In addition, the introduction to random phenomena sets the stage for understanding probability as a tool for predicting the long-term behavior of random events. Together, these concepts form the foundation for rigorous data collection and analysis in statistics.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Analysis of Variance (ANOVA)

A collection of statistical techniques used to compare the means of three or more groups by partitioning total variability into components due to differences among groups (between-group) and within groups.

Example Problems

Example 1

The 1990 s and early 2000 s could be considered the steroids era in Major League Baseball, as many players have admitted to using the drug to increase performance on the field. If a sports writer wanted to compare home run totals from the steroids era to an earlier decade, say the $1960 \mathrm{~s}$, explain why this would be an observational study. Could the writer conclude that it was the steroids that caused the increase in home runs? Why or why not?

Example 2

A business student conjectures that the Internet caused companies to become more profitable, since many transactions previously handled "face-to-face" could now be completed online. The student compares earnings from a sample of companies from the $1980 \mathrm{~s}$ to a sample from the 2000 s. Explain why this is an observational study. If indeed profitability increased, can she conclude the Internet was the cause? Why or why not?

Example 3

A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips. After 40 deliveries, he will compare the average tip percentage between the customers he called and those he did not. What are the experimental units and how did he randomize treatments?

Example 4

You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the experimental units? What is the response variable?

Example 5

For the experiment described in Exercise 3 , list the factor, the levels, and the response variable.

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Step-by-Step Explanations

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Common Mistakes

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