Chapter 11 Analysis of Variance

Back to List | Introduction | Heart Rates and Gender | What is in your Food? | Football | Exercises

Introduction

In Chapter 8 we saw how to test for equality of two means, but the Analysis of Variance (ANOVA) technique allows us to test for equality of three or more means. In this project you will compare the two methods as well as take advantage of this important difference. First we locate the necessary data.

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Heart Rates and Gender

There are many differences between men and women, but do you think the two sexes differ in such basic physical measurements as body temperature? A body temperature of 98.6º F is considered normal at least historically. Maybe the genders deviate from this norm. Let's see what we can learn from one set of sample data.

In the project on correlation coefficients and regression (Chapter 9) you found a data set consisting of heart rate and body temperature for a group of men and women. As a reminder you can return to that project to find information on how to locate this data. Separate it into two sets of data, one for males and one for females. The exercises will guide you in the appropriate test.

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What is in your Food?

There are many brands of hot dogs in your local supermarket. Hot dogs differ in size, and most importantly ingredients. A hot dog is typically made of beef, pork, turkey, or chicken, along with assorted spices and byproducts. Fortunately consumer-labeling laws prevent anything mysterious from being in there. The question does arise of which types of wieners are better for you.

Consumer Reports conducted a study of a number of brands of hot dogs focusing on the number of calories per dog and the sodium content. These data can be found by searching the Data and Story Library at http://lib.stat.cmu.edu/DASL/.

Locate the data set and read the accompanying description to understand the organization of the data. You will find hot dogs classified in three categories as to their primary meat ingredient: beef, poultry and meat. Here the word "meat" is used to refer to a combination of beef and pork with some poultry. The exercises will have you compare the characteristics of these three groups.

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Comparing Conferences and Divisions in Football

The National Football League (NFL) is divided into two conferences, the AFC (American Football Conference) and the NFC (National Football Conference.) Each conference is then broken into three divisions (East, Central and West) according (roughly) to geographic location.

The chart below summarizes this arrangement and gives the total number of points scored by each team over the 16 regular season games in the 1999-2000 season. Such data are readily available at sites such as http://www.nfl.com.

AFC		NFC
East		East
Team	Points Scored	Team	Points Scored
Indianapolis Colts	423	Washington Redskins	443
Buffalo Bills	320	Dallas Cowboys	352
Miami Dolphins	326	NY Giants	299
NY Jets	308	Arizona Cardinals	245
New England Patriots	299	Philadelphia Eagles	272
Central		Central
Team	Points Scored	Team	Points Scored
Jacksonville Jaguars	396	Tampa Bay Buccaneers	270
Tennessee Titans	392	Minnesota Vikings	399
Baltimore Ravens	324	Detroit Lions	322
Pittsburgh Steelers	317	Green Bay Packers	357
Cincinnati Bengals	283	Chicago Bears	272
Cleveland Browns	217
West		West
Team	Points Scored	Team	Points Scored
Seattle Seahawks	338	St. Louis Rams	526
Kansas City Chiefs	390	Carolina Panthers	421
San Diego Chargers	269	Atlanta Falcons	285
Oakland Raiders	390	San Francisco 49ers	295
Denver Broncos	314	New Orleans Saints	260

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Exercises

In the following exercises you will be asked to compare the scoring performances of the divisions.

In all exercises use ANOVA Tables where appropriate unless otherwise specified. Use a significance level of 0.05 in all cases.

When you've completed each exercise, click "Submit for Grade" in order to submit your answers to your professor.

© 2000 by Addison Wesley Longman A division of Pearson Education