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CHAPTER8 ANALYSIS OF VARIANCE CHAPTER OVERVIEW The topic of this chapter, analysis of variance, provides a methodology for partitioning the total variance computed from a data set into components, each of which represents the amount of the total variance that can be attributed to a specific source of variation. The results of this partitioning can then be used to estimate and test hypotheses about population variances and means. In this chapter we focus our attention on hypothesis testing of means. Specifically, we discuss the testing of differences among means when there is interest in more than two populations or two or more variables. The techniques discussed in this chapter are widely used in the health sciences. TOPICS 8.1 INTRODUCTION 8.2 THE COMPLETELY RANDOMIZED DESIGN 8.3 THE RANDOMIZED COMPLETE BLOCK DESIGN 8.4 THE REPEATED MEASURES DESIGN 8.5 THE FACTORIAL EXPERIMENT 8.6 SUMMARY LEARNING OUTCOMES After studying this chapter, the student will 1. understand how the total variation in a data set can be partitioned into different components. 2. be able to compare the means of more than two samples simultaneously. 3. understand multiple comparison tests and when their use is appropriate. 4. understand commonly used experimental designs. 305
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PUBLISHER ACQUISITIONS EDITOR ASSOC
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vi PREFACE Chapter 1 Introduction t
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viii PREFACE Edward Danial David El
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x CONTENTS 6.3 The t Distribution 1
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2 CHAPTER 1 INTRODUCTION TO BIOSTAT
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10 CHAPTER 1 INTRODUCTION TO BIOSTA
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20 CHAPTER 2 DESCRIPTIVE STATISTICS
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66 CHAPTER 3 SOME BASIC PROBABILITY
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94 CHAPTER 4 PROBABILITY DISTRIBUTI
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100 CHAPTER 4 PROBABILITY DISTRIBUT
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136 CHAPTER 5 SOME IMPORTANT SAMPLI
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CHAPTER6 ESTIMATION CHAPTER OVERVIE
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164 CHAPTER 6 ESTIMATION We will fi
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166 CHAPTER 6 ESTIMATION many insta
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168 CHAPTER 6 ESTIMATION Interval E
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170 CHAPTER 6 ESTIMATION Solution:
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172 CHAPTER 6 ESTIMATION someone wh
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174 CHAPTER 6 ESTIMATION Normal dis
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176 CHAPTER 6 ESTIMATION Yes Popula
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178 CHAPTER 6 ESTIMATION Construct
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180 CHAPTER 6 ESTIMATION By Equatio
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182 CHAPTER 6 ESTIMATION The proble
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184 CHAPTER 6 ESTIMATION error of t
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186 CHAPTER 6 ESTIMATION distributi
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188 CHAPTER 6 ESTIMATION EXAMPLE 6.
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190 CHAPTER 6 ESTIMATION since the
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192 CHAPTER 6 ESTIMATION age of per
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194 CHAPTER 6 ESTIMATION 6.9 CONFID
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196 CHAPTER 6 ESTIMATION FIGURE 6.9
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198 CHAPTER 6 ESTIMATION for s 2 ,
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200 CHAPTER 6 ESTIMATION f (x) 1.0
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202 CHAPTER 6 ESTIMATION the column
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204 CHAPTER 6 ESTIMATION SUMMARY OF
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206 CHAPTER 6 ESTIMATION • df de
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208 CHAPTER 6 ESTIMATION 22. Determ
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210 CHAPTER 6 ESTIMATION 29. The pu
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212 CHAPTER 6 ESTIMATION 7. Refer t
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214 CHAPTER 6 ESTIMATION A-26. MOHE
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216 CHAPTER 7 HYPOTHESIS TESTING 7.
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218 CHAPTER 7 HYPOTHESIS TESTING Ru
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220 CHAPTER 7 HYPOTHESIS TESTING st
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222 CHAPTER 7 HYPOTHESIS TESTING Ev
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224 CHAPTER 7 HYPOTHESIS TESTING th
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226 CHAPTER 7 HYPOTHESIS TESTING ca
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228 CHAPTER 7 HYPOTHESIS TESTING at
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230 CHAPTER 7 HYPOTHESIS TESTING So
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232 CHAPTER 7 HYPOTHESIS TESTING is
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234 CHAPTER 7 HYPOTHESIS TESTING Di
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238 CHAPTER 7 HYPOTHESIS TESTING wh
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240 CHAPTER 7 HYPOTHESIS TESTING EX
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242 CHAPTER 7 HYPOTHESIS TESTING to
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244 CHAPTER 7 HYPOTHESIS TESTING We
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246 CHAPTER 7 HYPOTHESIS TESTING Th
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248 CHAPTER 7 HYPOTHESIS TESTING To
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252 CHAPTER 7 HYPOTHESIS TESTING wh
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254 CHAPTER 7 HYPOTHESIS TESTING a
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256 CHAPTER 7 HYPOTHESIS TESTING Wh
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258 CHAPTER 7 HYPOTHESIS TESTING Af
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264 CHAPTER 7 HYPOTHESIS TESTING MI
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270 CHAPTER 7 HYPOTHESIS TESTING .0
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276 CHAPTER 7 HYPOTHESIS TESTING TA
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Page 640: 8.1 INTRODUCTION 307 is variability
Page 644: 8.2 THE COMPLETELY RANDOMIZED DESIG
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Page 684: EXERCISES 329 Elbow Angle (Degrees)
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EXERCISES 331 Age Groups (Years) Ag
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EXERCISES 333 Group 1 Group 2 Group
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8.3 THE RANDOMIZED COMPLETE BLOCK D
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x ij (a) Each that is observed cons
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9. Conclusion. If we reject H 0 , w
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8.3 THE RANDOMIZED COMPLETE BLOCK D
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EXERCISES 343 The SAS System Analys
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EXERCISES 345 8.3.3 A remotivation
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8.4 THE REPEATED MEASURES DESIGN 34
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8.4 THE REPEATED MEASURES DESIGN 34
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EXERCISES 351 The ANOVA Procedure D
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8.5 THE FACTORIAL EXPERIMENT 353 Su
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8.5 THE FACTORIAL EXPERIMENT 355 TA
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8.5 THE FACTORIAL EXPERIMENT 357 re
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8.5 THE FACTORIAL EXPERIMENT 359 TA
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8.5 THE FACTORIAL EXPERIMENT 361 5.
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8.5 THE FACTORIAL EXPERIMENT 363 Di
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EXERCISES 365 Percent Compared to T
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EXERCISES 367 Change in Change in F
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SUMMARY OF FORMULAS FOR CHAPTER 8 S
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REVIEW QUESTIONS AND EXERCISES 371
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REFERENCES 405 A-7. FARHAD ATASSI,
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REFERENCES 407 A-44. JIN-R. ZHOU, E
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CHAPTER9 SIMPLE LINEAR REGRESSION A
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9.2 THE REGRESSION MODEL 411 to be
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9.3 THE SAMPLE REGRESSION EQUATION
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EXERCISES 419 The Least-Squares Cri
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EXERCISES 421 CoaguChek Hospital Co
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9.4 EVALUATING THE REGRESSION EQUAT
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9.5 USING THE REGRESSION EQUATION 9
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9.5 USING THE REGRESSION EQUATION 4
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9.6 THE CORRELATION MODEL 441 9.6 T
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9.7 THE CORRELATION COEFFICIENT 443
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EXERCISES 451 is employed. We first
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9.7.3 In the study by Parker et al.
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9.8 SOME PRECAUTIONS 455 X Y X Y 5.
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SUMMARY OF FORMULAS FOR CHAPTER 9 4
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SUMMARY OF FORMULAS FOR CHAPTER 9 4
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REFERENCES 483 9. WILLIAM MENDENHAL
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CHAPTER10 MULTIPLE REGRESSION AND C
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10.2 THE MULTIPLE LINEAR REGRESSION
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10.3 OBTAINING THE MULTIPLE REGRESS
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10.3 OBTAINING THE MULTIPLE REGRESS
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EXERCISES 493 EXERCISES Obtain the
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EXERCISES 495 10.3.3 In a study of
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10.4 EVALUATING THE MULTIPLE REGRES
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R 2 R 2 1. and all b N i significan
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EXERCISES 505 of age and has an edu
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10.6 THE MULTIPLE CORRELATION MODEL
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EXERCISES 517 HIV DNA Blood HIV Co-
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SUMMARY OF FORMULAS FOR CHAPTER 10
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REFERENCES 533 4. Refer to the data
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CHAPTER11 REGRESSION ANALYSIS: SOME
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11.1 INTRODUCTION 537 TABLE 11.1.1
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11.2 QUALITATIVE INDEPENDENT VARIAB
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Note in these examples that when th
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EXERCISES 553 age of the subject (y
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EXERCISES 555 11.2.4 Refer to Exerc
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11.3 VARIABLE SELECTION PROCEDURES
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11.3 VARIABLE SELECTION PROCEDURES
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EXERCISES 561 CGAGE CGINCOME CGDUR
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EXERCISES 563 11.3.2 Machiel Naeije
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11.4 LOGISTIC REGRESSION 565 REACTI
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11.4 LOGISTIC REGRESSION 567 betwee
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11.4 LOGISTIC REGRESSION 569 The LO
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11.4 LOGISTIC REGRESSION 571 Standa
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11.4 LOGISTIC REGRESSION 573 Parame
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11.5 SUMMARY 575 Hospital Anxiety a
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REFERENCES 591 A-3. MANOJ PANDEY, L
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CHAPTER12 THE CHI-SQUARE DISTRIBUTI
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12.2 THE MATHEMATICAL PROPERTIES OF
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e equal to zero for each pair of ob
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12.3 TESTS OF GOODNESS-OF-FIT 599 3
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12.3 TESTS OF GOODNESS-OF-FIT 601 C
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12.3 TESTS OF GOODNESS-OF-FIT 603 W
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12.3 TESTS OF GOODNESS-OF-FIT 605 E
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12.3 TESTS OF GOODNESS-OF-FIT 607 E
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12.3 TESTS OF GOODNESS-OF-FIT 609 u
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EXERCISES 611 Test the goodness-of-
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a n 1. n ban .1 n b 12.4 TESTS OF I
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12.4 TESTS OF INDEPENDENCE 615 3. H
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12.4 TESTS OF INDEPENDENCE 617 The
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12.4 TESTS OF INDEPENDENCE 619 EXAM
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EXERCISES 621 EXERCISES In the exer
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12.5 TESTS OF HOMOGENEITY 623 Polic
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12.5 TESTS OF HOMOGENEITY 625 data,
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EXERCISES 627 If we wish to test th
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12.6 THE FISHER EXACT TEST 629 12.5
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, A - a, and B - b are all greater
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EXERCISES 633 Pl * Remained Cross-T
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12.7 RELATIVE RISK, ODDS RATIO, AND
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EXERCISES 647 12.7.2 The objective
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12.8 SURVIVAL ANALYSIS 649 (3) the
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12.8 SURVIVAL ANALYSIS 651 techniqu
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12.8 SURVIVAL ANALYSIS 653 TABLE 12
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cumulative proportion changes from
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12.8 SURVIVAL ANALYSIS 657 TABLE 12
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12.8 SURVIVAL ANALYSIS 659 Means an
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EXERCISES 661 EXERCISES 12.8.1 Fift
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EXERCISES 663 (c) Explain the meani
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SUMMARY OF FORMULAS FOR CHAPTER 12
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REFERENCES 679 19. WENDELL E. CARR,
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A-30. A-31. A-32. A-33. A-34. A-35.
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CHAPTER13 NONPARAMETRIC AND DISTRIB
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13.2 MEASUREMENT SCALES 685 measure
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13.3 THE SIGN TEST 687 TABLE 13.3.1
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13.3 THE SIGN TEST 689 7. Calculati
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13.3 THE SIGN TEST 691 TABLE 13.3.4
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EXERCISES 693 Data: C1: 4 5 8 8 9 6
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13.4 THE WILCOXON SIGNED-RANK TEST
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13.4 THE WILCOXON SIGNED-RANK TEST
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13.5 THE MEDIAN TEST 699 Subject 1
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13.5 THE MEDIAN TEST 701 TABLE 13.5
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13.6 THE MANN-WHITNEY TEST 703 Woul
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13.6 THE MANN-WHITNEY TEST 705 TABL
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13.6 THE MANN-WHITNEY TEST 707 FIGU
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EXERCISES 709 Mann-Whitney-Wilcoxon
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13.7 THE KOLMOGOROV-SMIRNOV GOODNES
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13.8 THE KRUSKAL-WALLIS ONE-WAY ANA
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EXERCISES 723 Young (19-50 Years) S
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13.9 THE FRIEDMAN TWO-WAY ANALYSIS
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13.9 THE FRIEDMAN TWO-WAY ANALYSIS
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EXERCISES 729 Dialog box: Stat ➤
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13.10 THE SPEARMAN RANK CORRELATION
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EXERCISES 737 Dialog box: Stat ➤
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EXERCISES 739 Duration of Follow-Up
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13.11 NONPARAMETRIC REGRESSION ANAL
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13.12 SUMMARY 743 36.4046 59.15 39.
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REFERENCES 761 8. W. H. KRUSKAL and
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CHAPTER14 VITAL STATISTICS CHAPTER
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2. Ratio. A ratio is a fraction of
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14.2 DEATH RATES AND RATIOS 767 TAB
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14.2 DEATH RATES AND RATIOS 769 Som
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EXERCISES 771 EXERCISES 14.2.1 The
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14.3 MEASURES OF FERTILITY 773 1. C
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EXERCISES 775 Age of Number of Birt
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14.5 SUMMARY 777 4. Immaturity rati
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REFERENCES 783 A-7. Georgia Divisio
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APPENDIX STATISTICAL TABLES List of
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APPENDIX STATISTICAL TABLES A-3 TAB
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TABLE B (continued ) APPENDIX STATI
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TABLE C (continued ) APPENDIX STATI
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TABLE D (continued ) APPENDIX STATI
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APPENDIX STATISTICAL TABLES A-41 TA
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TABLE G (continued ) APPENDIX STATI
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TABLE H (continued ) APPENDIX STATI
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TABLE J (continued ) APPENDIX STATI
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TABLE K (continued ) APPENDIX STATI
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TABLE L (continued ) APPENDIX STATI
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TABLE N (continued ) APPENDIX STATI
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APPENDIX STATISTICAL TABLES A-103 T
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APPENDIX STATISTICAL TABLES A-105 A
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ANSWERS TO ODD-NUMBERED EXERCISES A
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Family error rate = 0.0500 Individu
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The regression equation is WL = 0.7
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S 1.06 1.01 0.990 R-Sq 8.57 18.10 2
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INDEX Numbers preceded by A refer t
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INDEX I-3 H Histogram, 25-27 Hypoth
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INDEX I-5 Rate, 764-765 Ratio, 765
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