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CHAPTER 16 Analysis of Categorical Data LEARNING OBJECTIVES The overall objective of this chapter is to give you an understanding of two statistical techniques used to analyze categorical data, thereby enabling you to: 1. Use the chi-square goodness-of-fit test to analyze probabilities of multinomial distribution trials along a single dimension and test a population proportion 2. Use the chi-square test of independence to perform contingency analysis Andrew Douglas/Masterfile
Selecting Suppliers in the Electronics Industry What criteria are used in the electronics industry to select a supplier? In years past, price has been the dominant criterion of suppliers in many industries, and the supplier with the low bid often got the job. In more recent years, companies have been forced by global competition and a marked increase in quality to examine other aspects of potential suppliers. Pearson and Ellram investigated the techniques used by firms in the electronics industry to select suppliers, and they wanted to determine if there is a difference between small and large firms in supplier selection. They sent out a survey instrument with questions about criteria used to select and evaluate suppliers, the participation of various functional areas in the selection process, and the formality of methods used in the selection. Of the 210 survey responses received, 87 were from small companies and 123 from large companies. The average sales were $33 million for the small companies and $583 million for the large companies. Survey questions were stated in such a way as to generate frequencies. The respondents were given a series of supplier selection and evaluation criteria such as quality, cost, current technology, design capabilities, speed to market, manufacturing process, location, and so on. They were asked to check off the criteria used in supplier selection and evaluation and to rank the criteria that they checked. As part of the analysis, the researchers recorded how many of each of the small and large company respondents ranked a criterion first, how many ranked it second, and how many ranked it third. The results are shown in the following table of raw numbers for the criteria of quality, cost, and current technology. In addition, companies in the study sometimes involved departments such as research/development or engineering in the supplier search process. For example, 41.38% of the small companies in the study included research/development in the supplier search process versus 48.78% of the large companies. Quality Company Size Small Large 1 48 70 2 17 27 3 7 6 Current Technology Cost Managerial and Statistical Questions Company Size Small Large 1 8 14 2 29 36 3 26 37 Company Size Small Large 1 5 13 2 8 11 3 5 12 1. Is there a difference between small and large companies in the ranking of criteria for the evaluation and selection of suppliers in the electronics industry? 2. The authors of the study used frequencies to measure the relative rankings of criteria. What is the appropriate statistical technique to analyze these data? 3. In comparing the participation of company employees in the process of selection and evaluation of suppliers by function and by company size, the researchers reported percentages. Are the differences in percentages merely chance differences from samples or is there a significant difference between small and large companies in the extent to which they involve people from various functional areas in the supplier selection and evaluation process? What statistical technique is appropriate for analyzing these data? Source: Adapted from John N. Pearson and Lisa M. Ellram.“Supplier Selection and Evaluation in Small Versus Large Electronics Firms,” Journal of Small Business Management, vol. 33, no. 4 (October 1995), pp. 53–65. In this chapter, we explore techniques for analyzing categorical data. Categorical data are nonnumerical data that are frequency counts of categories from one or more variables. For example, it is determined that of the 790 people attending a convention, 240 are engineers, 160 are managers, 310 are sales reps, and 80 are information technologists. The variable is “position in company” with four categories: engineers, managers, sales reps, and information technologists. The data are not ratings or sales figures but rather 645
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With WileyPLUS: This online teachin
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6 TH EDITION Business Statistics Fo
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Vice President & Publisher George H
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BRIEF CONTENTS UNIT I UNIT II UNIT
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x Contents 3.5 Descriptive Statisti
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xii Contents Statistical Hypotheses
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xiv Contents Forward Selection 572
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PREFACE The sixth edition of Busine
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Preface xix all of the inferential
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Preface xxi very limited access to
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Preface xxiii Interpreting the Outp
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Preface xxv ACKNOWLEDGMENTS John Wi
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UNIT I INTRODUCTION The study of bu
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Statistics Describe the State of Bu
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1.2 Basic Statistical Concepts 5 In
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1.3 Data Measurement 7 FIGURE 1.1 P
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1.3 Data Measurement 9 In addition,
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1.3 Data Measurement 11 Statistical
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Analyzing the Databases 13 1.3 Give
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Case 15 ASSIGNMENT Use the database
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Energy Consumption Around the World
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2.1 Frequency Distributions 19 TABL
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2.2 Quantitative Data Graphs 21 cla
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2.2 Quantitative Data Graphs 23 FIG
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2.2 Quantitative Data Graphs 25 FIG
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2.3 Qualitative Data Graphs 27 2.9
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2.3 Qualitative Data Graphs 29 FIGU
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2.3 Qualitative Data Graphs 31 STAT
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2.4 Graphical Depiction of Two-Vari
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Problems 35 Pie Charts for World Oi
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Supplementary Problems 37 2.19 Cons
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Supplementary Problems 39 include t
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Using the Computer 41 In 1983, the
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Using the Computer 43 ■ ■ ■ t
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CHAPTER 3 Descriptive Statistics LE
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48 Chapter 3 Descriptive Statistics
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ƒ ƒ 58 Chapter 3 Descriptive Stat
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CHAPTER 4 Probability LEARNING OBJE
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94 Chapter 4 Probability FIGURE 4.1
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96 Chapter 4 Probability Subjective
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98 Chapter 4 Probability FIGURE 4.3
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100 Chapter 4 Probability THE mn CO
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102 Chapter 4 Probability FIGURE 4.
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104 Chapter 4 Probability TABLE 4.2
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106 Chapter 4 Probability By the ge
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108 Chapter 4 Probability P (neithe
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110 Chapter 4 Probability 4.10 Use
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ƒ ƒ 112 Chapter 4 Probability ran
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114 Chapter 4 Probability DEMONSTRA
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116 Chapter 4 Probability 4.21 A st
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ƒ 118 Chapter 4 Probability The se
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ƒ 120 Chapter 4 Probability STATIS
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122 Chapter 4 Probability the South
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124 Chapter 4 Probability TABLE 4.8
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126 Chapter 4 Probability Event Pri
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128 Chapter 4 Probability ETHICAL C
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130 Chapter 4 Probability TESTING Y
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132 Chapter 4 Probability 4.49 In a
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UNIT II DISTRIBUTIONS AND SAMPLING
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Life with a Cell Phone As early as
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5.2 Describing a Discrete Distribut
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5.2 Describing a Discrete Distribut
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5.3 Binomial Distribution 143 5.3 T
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5.3 Binomial Distribution 145 selec
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5.3 Binomial Distribution 147 DEMON
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ƒ 5.3 Binomial Distribution 149 TA
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5.3 Binomial Distribution 151 FIGUR
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Problems 153 5.8 Use the probabilit
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5.4 Poisson Distribution 155 time i
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5.4 Poisson Distribution 157 Soluti
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5.4 Poisson Distribution 159 FIGURE
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5.4 Poisson Distribution 161 The Po
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Problems 163 data set as a basis fo
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5.5 Hypergeometric Distribution 165
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Problems 167 5.5 PROBLEMS 5.27 Comp
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Key Terms 169 problem, but it can b
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Supplementary Problems 171 5.36 Use
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Supplementary Problems 173 Suppose
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Case 175 ANALYZING THE DATABASES se
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Using the Computer 177 ■ in a col
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The Cost of Human Resources What is
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6.1 The Uniform Distribution 181 FI
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6.1 The Uniform Distribution 183 DE
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6.2 Normal Distribution 185 FIGURE
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6.2 Normal Distribution 187 TABLE 6
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6.2 Normal Distribution 189 This pr
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6.2 Normal Distribution 191 The pro
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6.2 Normal Distribution 193 DEMONST
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Problems 195 6.9 According to the I
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6.3 Using the Normal Curve to Appro
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6.3 Using the Normal Curve to Appro
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Problems 201 The answer obtained by
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6.4 Exponential Distribution 203 FI
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Problems 205 TABLE 6.6 Excel and Mi
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Summary 207 The area associated wit
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Supplementary Problems 209 6.36 Wor
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Supplementary Problems 211 availabi
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Using the Computer 213 that sales a
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CHAPTER 7 Sampling and Sampling Dis
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218 Chapter 7 Sampling and Sampling
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248 Making Inferences About Populat
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CHAPTER 8 Statistical Inference: Es
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252 Chapter 8 Statistical Inference
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Word-of-Mouth Business Referrals an
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9.1 Introduction to Hypothesis Test
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9.2 Testing Hypotheses About a Popu
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Problems 307 one-tailed hypothesis,
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Problems 313 Excel does not have a
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9.4 Testing Hypotheses About a Prop
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9.5 Testing Hypotheses About a Vari
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Problems 323 DEMONSTRATION PROBLEM
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9.6 Solving for Type II Errors 325
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Problems 333 9.40 The New York Stoc
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Supplementary Problems 335 with an
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Supplementary Problems 337 and she
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Case 339 CASE FRITO-LAY TARGETS THE
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Using the Computer 341 ■ To begin
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Online Shopping The use of online s
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Proportions 2-Samples Chapter 10 St
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10.1 Hypothesis Testing and Confide
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Problems 353 10.2 Use the following
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Problems 363 Test your conjecture,
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10.3 Statistical Inferences for Two
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Problems 373 Client Before After 1
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10.4 Statistical Inferences about T
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Problems 381 b. H 0 : p 1 - p 2 = 0
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10.5 Testing Hypotheses about Two P
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Problems 389 City 1 City 2 3.43 3.3
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Summary 391 SUMMARY Business resear
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Supplementary Problems 393 TESTING
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Supplementary Problems 395 machine
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Case 397 ANALYZING THE DATABASES 1.
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Using the Computer 399 ■ ■ add-
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CHAPTER 11 Analysis of Variance and
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404 Chapter 11 Analysis of Variance
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UNIT IV REGRESSION ANALYSIS AND FOR
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Predicting International Hourly Wag
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12.1 Correlation 467 FIGURE 12.1 Fi
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12.2 Introduction to Simple Regress
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12.3 Determining the Equation of th
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12.3 Determining the Equation of th
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Problems 475 Using these values, th
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12.4 Residual Analysis 477 Raw Stee
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12.4 Residual Analysis 479 FIGURE 1
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12.4 Residual Analysis 481 DEMONSTR
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Problems 483 Cost of Milk (per gall
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12.5 Standard Error of the Estimate
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12.6 Coefficient of Determination 4
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12.7 Hypothesis Tests for the Slope
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12.8 Estimation 495 result, yieldin
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12.8 Estimation 497 FIGURE 12.16 Mi
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12.9 Using Regression to Develop a
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12.9 Using Regression to Develop a
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Problems 503 Solution Shown here is
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12.10 Interpreting the Output 505 F
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12.10 Interpreting the Output 507 S
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Supplementary Problems 509 KEY TERM
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Supplementary Problems 511 publishe
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Case 513 Frequency 7 6 5 4 3 2 1 0
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Using the Computer 515 Cumulative H
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Are You Going to Hate Your New Job?
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13.1 The Multiple Regression Model
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13.1 The Multiple Regression Model
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Problems 523 Solution The following
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13.2 Significance Tests of the Regr
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13.2 Significance Tests of the Regr
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Problems 529 13.9 Using the data in
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13.3 Residuals, Standard Error of t
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13.3 Residuals, Standard Error of t
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13.4 Interpreting Multiple Regressi
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13.4 Interpreting Multiple Regressi
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Summary 539 SUMMARY OUTPUT Regressi
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Supplementary Problems 541 TESTING
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Case 543 ANALYZING THE DATABASES 1.
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CHAPTER 14 Building Multiple Regres
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548 Chapter 14 Building Multiple Re
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CHAPTER 15 Time-Series Forecasting
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590 Chapter 15 Time-Series Forecast
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592 Chapter 15 Time-Series Forecast
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694 Chapter 17 Nonparametric Statis
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Italy’s Piaggio Makes a Comeback
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18.1 Introduction to Quality Contro
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18.2 Process Analysis 733 18.2 PROC
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18.2 Process Analysis 735 FIGURE 18
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18.2 Process Analysis 737 FIGURE 18
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18.3 Control Charts 739 charts are
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18.3 Control Charts 741 UCL and LCL
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18.3 Control Charts 743 Using the s
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18.3 Control Charts 745 Compute R R
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18.3 Control Charts 747 Sample n Ou
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18.3 Control Charts 749 In computin
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18.3 Control Charts 751 below the c
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Problems 753 18.6 A machine operato
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Problems 755 a. 125 X bar Chart 3.0
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Formulas 757 identifying the effect
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Supplementary Problems 759 five con
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Analyzing the Databases 761 12.5 X
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Using the Computer 763 Sample Mean
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APPENDIX A Tables Table A.1: Random
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Appendix A Tables 767 TABLE A.2 Bin
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Appendix A Tables 775 TABLE A.3 Poi
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Appendix A Tables 777 TABLE A.3 Poi
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Appendix A Tables 779 TABLE A.4 The
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Appendix A Tables 781 TABLE A.6 Cri
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Appendix A Tables 783 TABLE A.7 Per
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Appendix A Tables 793 TABLE A.9 Cri
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Appendix A Tables 795 TABLE A.10 Cr
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Appendix A Tables 797 n 2 n 1 = .02
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Appendix A Tables 799 TABLE A.13 p-
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Appendix A Tables 801 TABLE A.13 p-
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Appendix A Tables 803 TABLE A.14 Cr
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APPENDIX B Answers to Selected Odd-
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Appendix B Answers to Selected Odd-
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GLOSSARY A a posteriori After the e
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Glossary 817 decision table A matri
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Glossary 819 the statistic below th
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Glossary 821 ratio level data Highe
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Glossary 823 W weighted aggregate p
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826 Index Centerline. See also Cont
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828 Index DMAIC (Define, Measure, A
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830 Index Law of improbable events,
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832 Index Populations accessing for
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834 Index Samples defined, 5 depend
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836 Index grouped data versus, 17-1
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Decision Making at the CEO Level CE
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19.1 The Decision Table and Decisio
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19.2 Decision Making Under Uncertai
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Problems C19-13 d. Compute an oppor
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19.3 Decision Making Under Risk C19
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Problems C19-21 Much information ha
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19.4 Revising Probabilities in Ligh
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Problems C19-29 The worth of the sa
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Problems C19-31 Decision Making at
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Supplementary Problems C19-33 for e
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Supplementary Problems C19-35 Decis
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Case C19-37 Following these initiat
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Critical Values from the t Distribu
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