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362 CHAPTER 8 ANALYSIS OF VARIANCE respectively. The subscript i runs from 1 to a and j runs from 1 to b. The total number of observations is nab. To show that Table 8.5.3 represents data from a completely randomized design, we consider that each combination of factor levels is a treatment and that we have n observations for each treatment. An alternative arrangement of the data would be obtained by listing the observations of each treatment in a separate column. Table 8.5.3 may also be used to display data from a two-factor randomized block design if we consider the first observation in each cell as belonging to block 1, the second observation in each cell as belonging to block 2, and so on to the nth observation in each cell, which may be considered as belonging to block n. Note the similarity of the data display for the factorial experiment as shown in Table 8.5.3 to the randomized complete block data display of Table 8.3.1. The factorial experiment, in order that the experimenter may test for interaction, requires at least two observations per cell, whereas the randomized complete block design requires only one observation per cell. We use two-way analysis of variance to analyze the data from a factorial experiment of the type presented here. 2. Assumptions. We assume a fixed-effects model and a two-factor completely randomized design. For a discussion of other designs, consult the references at the end of this chapter. The Model The fixed-effects model for the two-factor completely randomized design may be written as x ijk ¼ m þ a i þ b j þ ðabÞ ij þ e ijk i ¼ 1; 2; ...; a; j ¼ 1; 2; ...; b; k ¼ 1; 2; ...; n (8.5.1) where x ijk is a typical observation, m is a constant, a i represents an effect due to factor A, b j represents an effect due to factor B, ðabÞ ij represents an effect due to the interaction of factors A and B, and e ijk represents the experimental error. Assumptions of the Model a. The observations in each of the ab cells constitute a random independent sample of size n drawn from the population defined by the particular combination of the levels of the two factors. b. Each of the ab populations is normally distributed. c. The populations all have the same variance. 3. Hypotheses. The following hypotheses may be tested: a. H 0 : a i ¼ 0 i ¼ 1; 2; ...; a H A : notall a i ¼ 0 b. H 0 : b j ¼ 0 j ¼ 1; 2; ...; b H A : not all b j ¼ 0 c. H 0 : ðabÞ ij ¼ 0 i ¼ 1; 2; ...; a; j ¼ 1; 2; ...; b H A : not all ðabÞ ij ¼ 0
8.5 THE FACTORIAL EXPERIMENT 363 Before collecting data, the researchers may decide to test only one of the possible hypotheses. In this case they select the hypothesis they wish to test, choose a significance level a, and proceed in the familiar, straightforward fashion. This procedure is free of the complications that arise if the researchers wish to test all three hypotheses. When all three hypotheses are tested, the situation is complicated by the fact that the three tests are not independent in the probabilistic sense. If we let a be the significance level associated with the test as a whole, and a 0 ; a 00 ; and a 000 the significance levels associated with hypotheses 1, 2, and 3, respectively, we find a < 1 ð1 a 0 Þð1 a 00 Þð1 a 000 Þ (8.5.2) If a 0 ¼ a 00 ¼ a 000 ¼ :05, then a < 1 ð:95Þ 3 , or a
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TENTH EDITION BIOSTATISTICS A Found
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VP & EXECUTIVE PUBLISHER: ACQUISITI
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PREFACE This 10th edition of Biosta
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PREFACE ix SUPPLEMENTS Instructor
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BRIEF CONTENTS 1 INTRODUCTION TO BI
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xiv CONTENTS 6.3 The t Distribution
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CHAPTER1 INTRODUCTION TO BIOSTATIST
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1.2 SOME BASIC CONCEPTS 3 Sources o
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1.3 MEASUREMENT AND MEASUREMENT SCA
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1.4 SAMPLING AND STATISTICAL INFERE
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1.5 THE SCIENTIFIC METHOD AND THE D
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1.6 COMPUTERS AND BIOSTATISTICAL AN
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REVIEW QUESTIONS AND EXERCISES 17 a
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CHAPTER2 DESCRIPTIVE STATISTICS CHA
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2.2 THE ORDERED ARRAY 21 TABLE 2.2.
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2.3 GROUPED DATA: THE FREQUENCY DIS
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EXERCISES 31 3 ¼ an abundance of s
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EXERCISES 33 25.21 30.49 27.38 36.4
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EXERCISES 35 2.3.7 In a study of ph
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EXERCISES 37 0.6870 0.6900 0.6910 0
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2.4 DESCRIPTIVE STATISTICS: MEASURE
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EXERCISES 53 2.5.1 Porcellini et al
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SUMMARY OF FORMULAS FOR CHAPTER 2 5
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REVIEW QUESTIONS AND EXERCISES 57 R
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REVIEW QUESTIONS AND EXERCISES 59 1
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REFERENCES 63 DRINK TOUNCES TGRAMS
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CHAPTER3 SOME BASIC PROBABILITY CON
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3.2 TWO VIEWS OF PROBABILITY: OBJEC
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3.4 CALCULATING THE PROBABILITY OF
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EXERCISES 77 (d) If we pick a subje
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3.5 BAYES’ THEOREM, SCREENING TES
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3.5 BAYES’ THEOREM, SCREENING TES
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EXERCISES 83 EXERCISES 3.5.1 A medi
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REVIEW QUESTIONS AND EXERCISES 87 (
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REVIEW QUESTIONS AND EXERCISES 89 i
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REFERENCES 91 Applications Referenc
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4.2 PROBABILITY DISTRIBUTIONS OF DI
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4.3 THE BINOMIAL DISTRIBUTION 99 TA
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4.3 THE BINOMIAL DISTRIBUTION 101 E
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4.3 THE BINOMIAL DISTRIBUTION 103 f
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EXAMPLE 4.3.4 According to a June 2
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EXERCISES 107 Data: C1: 0 1 2 3 4 5
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4.4 THE POISSON DISTRIBUTION 109 pr
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4.4 THE POISSON DISTRIBUTION 111 or
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4.5 CONTINUOUS PROBABILITY DISTRIBU
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4.5 CONTINUOUS PROBABILITY DISTRIBU
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4.6 THE NORMAL DISTRIBUTION 117 .68
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4.6 THE NORMAL DISTRIBUTION 119 σ
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4.6 THE NORMAL DISTRIBUTION 121 _ 2
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4.7 NORMAL DISTRIBUTION APPLICATION
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TableD,wefindthattheareatotheleftof
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EXERCISES 127 Data: C1:-3-2-10123 D
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SUMMARY OF FORMULAS FOR CHAPTER 4 S
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REVIEW QUESTIONS AND EXERCISES 131
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REFERENCES 133 REFERENCES Methodolo
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5.2 SAMPLING DISTRIBUTIONS 135 voca
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5.3 DISTRIBUTION OF THE SAMPLE MEAN
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5.4 DISTRIBUTION OF THE DIFFERENCE
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EXERCISES 149 FIGURE 5.4.2 Sampling
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5.5 DISTRIBUTION OF THE SAMPLE PROP
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EXERCISES 153 51 percent had adequa
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CHAPTER6 ESTIMATION CHAPTER OVERVIE
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6.1 INTRODUCTION 163 We will find t
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6.2 CONFIDENCE INTERVAL FOR A POPUL
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6.3 THE t DISTRIBUTION 171 someone
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6.3 THE t DISTRIBUTION 173 Normal d
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EXERCISES 175 Yes Population normal
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6.4 CONFIDENCE INTERVAL FOR THE DIF
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EXERCISES 183 EXERCISES R Code: > t
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6.7 DETERMINATION OF SAMPLE SIZE FO
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6.8 DETERMINATION OF SAMPLE SIZE FO
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6.9 CONFIDENCE INTERVAL FOR THE VAR
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6.9 CONFIDENCE INTERVAL FOR THE VAR
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EXERCISES 197 x 2 1 ða=2Þ ¼ 14:4
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6.10 CONFIDENCE INTERVAL FOR THE RA
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6.10 CONFIDENCE INTERVAL FOR THE RA
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REFERENCES 211 3. W. V. BEHRENS,
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REFERENCES 213 A-30. ELENI KOUSTA,
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7.1 INTRODUCTION 215 7.1 INTRODUCTI
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7.1 INTRODUCTION 217 question: Can
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7.1 INTRODUCTION 219 DEFINITION The
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7.1 INTRODUCTION 221 Evaluate data
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7.2 HYPOTHESIS TESTING: A SINGLE PO
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EXERCISES 233 Dialog box: Session c
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EXERCISES 235 7.2.10 Following a we
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7.3 HYPOTHESIS TESTING: THE DIFFERE
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EXAMPLE 7.3.2 The purpose of a stud
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EXERCISES 245 The SAS System The TT
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EXERCISES 247 Primary Hypertensive
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7.4 PAIRED COMPARISONS 249 7.3.10 R
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7.4 PAIRED COMPARISONS 251 where d
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7.4 PAIRED COMPARISONS 253 a = .05
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EXERCISES 255 7.4.1 Ellen Davis Jon
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EXERCISES 263 MINITAB Output Test a
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7.8 HYPOTHESIS TESTING: THE RATIO O
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7.8 HYPOTHESIS TESTING: THE RATIO O
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EXERCISES 271 EXERCISES In the foll
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7.9 THE TYPE II ERROR AND THE POWER
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7.9 THE TYPE II ERROR AND THE POWER
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7.10 DETERMINING SAMPLE SIZE TO CON
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EXERCISES 279 We set the right-hand
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REFERENCES 301 A-17. JOHN S. MORLEY
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REFERENCES 303 A-56. LUIGI BENINI,
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8.1 INTRODUCTION 305 8.1 INTRODUCTI
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8.1 INTRODUCTION 307 who received d
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8.2 THE COMPLETELY RANDOMIZED DESIG
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CHAPTER9 SIMPLE LINEAR REGRESSION A
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9.2 THE REGRESSION MODEL 415 some e
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9.3 THE SAMPLE REGRESSION EQUATION
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EXERCISES EXERCISES 423 The Least-S
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EXERCISES 425 CoaguChek Hospital Co
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9.4 EVALUATING THE REGRESSION EQUAT
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9.5 USING THE REGRESSION EQUATION I
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9.5 USING THE REGRESSION EQUATION 4
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9.6 THE CORRELATION MODEL 445 9.6 T
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9.7 THE CORRELATION COEFFICIENT 447
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EXERCISES 455 is employed. We first
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EXERCISES 457 9.7.3 In the study by
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9.8 SOME PRECAUTIONS 459 X Y X Y 5.
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9.9 SUMMARY 461 variance, which tes
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9.7.3 t statistic for correlation c
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REFERENCES 487 A-4. ROBERT B. PARKE
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CHAPTER10 MULTIPLE REGRESSION AND C
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Assumptions follows. 10.2 THE MULTI
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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 497 EXERCISES Obtain the
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EXERCISES 499 10.3.3 In a study of
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10.4 EVALUATING THE MULTIPLE REGRES
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10.5 USING THE MULTIPLE REGRESSION
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EXERCISES 509 and has an education
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10.6 THE MULTIPLE CORRELATION MODEL
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This equation may be used for estim
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EXERCISES 521 HIV DNA Blood (Y) HIV
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SUMMARY OF FORMULAS FOR CHAPTER 10
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10.6.7 t statistic for testing hypo
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REFERENCES 537 4. Refer to the data
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CHAPTER11 REGRESSION ANALYSIS: SOME
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11.1 INTRODUCTION 541 TABLE 11.1.1
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11.2 QUALITATIVE INDEPENDENT VARIAB
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EXERCISES 557 11.2.1 For subjects u
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EXERCISES 559 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 565 CGAGE CGINCOME CGDUR
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EXERCISES 567 11.3.2 Machiel Naeije
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11.4 LOGISTIC REGRESSION 569 REACTI
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11.4 LOGISTIC REGRESSION 571 betwee
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11.4 LOGISTIC REGRESSION 573 The LO
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11.4 LOGISTIC REGRESSION 575 Standa
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11.4 LOGISTIC REGRESSION 577 Parame
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11.4 LOGISTIC REGRESSION 579 Model
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EXERCISES EXERCISES 581 Further Rea
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REFERENCES 597 KNOW ¼ Knowledge. S
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REFERENCES 599 A-26. EITHNE MULLOYa
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12.1 INTRODUCTION 12.2 THE MATHEMAT
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12.2 THE MATHEMATICAL PROPERTIES OF
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12.3 TESTS OF GOODNESS-OF-FIT 605 W
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12.3 TESTS OF GOODNESS-OF-FIT 607 x
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12.3 TESTS OF GOODNESS-OF-FIT 609 9
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that the first expected frequency i
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12.3 TESTS OF GOODNESS-OF-FIT 613 T
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12.3 TESTS OF GOODNESS-OF-FIT 615 V
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EXERCISES 617 EXERCISES 12.3.1 The
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12.4 TESTS OF INDEPENDENCE 619 12.3
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Observed Versus Expected Frequencie
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12.4 TESTS OF INDEPENDENCE 623 Comp
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12.4 TESTS OF INDEPENDENCE 625 Note
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12.4 TESTS OF INDEPENDENCE 627 9. C
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EXERCISES 629 Performed Baseline Te
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12.5 TESTS OF HOMOGENEITY 631 TABLE
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12.5 TESTS OF HOMOGENEITY 633 8. St
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EXERCISES 635 12.5.2 Coughlin et al
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Hypotheses alternatives. 12.6 THE F
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12.6 THE FISHER EXACT TEST 639 TABL
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12.7 RELATIVE RISK, ODDS RATIO, AND
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EXERCISES 653 Smoking_status * Obse
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12.8 SUMMARY 655 collected data on
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REFERENCES 667 12. R. LATSCHA, “T
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REFERENCES 669 A-35. CRAIG R. COHEN
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13.1 INTRODUCTION 671 2. be able to
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13.3 THE SIGN TEST 673 13.3 THE SIG
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13.3 THE SIGN TEST 675 TABLE 13.3.2
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13.3 THE SIGN TEST 677 EXAMPLE 13.3
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13.3 THE SIGN TEST 679 one sample i
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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 687 TABLE 13.5
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EXAMPLE 13.6.1 A researcher designe
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13.6 THE MANN-WHITNEY TEST 693 to t
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13.6 THE MANN-WHITNEY TEST 695 Dial
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EXERCISES 697 deficit in Sprague-Da
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13.7 THE KOLMOGOROV-SMIRNOV GOODNES
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EXERCISES 703 1.0 .9 Cumulative rel
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13.8 THE KRUSKAL-WALLIS ONE-WAY ANA
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13.8 THE KRUSKAL-WALLIS ONE-WAY ANA
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EXERCISES 709 Data: C1: 12.22 28.44
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EXERCISES 711 Improvement (Control)
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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 717 Subject Area Student
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13.10 THE SPEARMAN RANK CORRELATION
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EXERCISES 725 Rank by Rank by Area
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13.11 NONPARAMETRIC REGRESSION ANAL
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13.11 NONPARAMETRIC REGRESSION ANAL
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REFERENCES 747 cardiac operations.
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REFERENCES 749 A-14. WENDY GANTT an
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14.2 TIME-TO-EVENT DATA AND CENSORI
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14.3 THE KAPLAN-MEIER PROCEDURE 757
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14.3 THE KAPLAN-MEIER PROCEDURE 759
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EXERCISES 761 1.0 .8 73% Low-grade
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14.4 COMPARING SURVIVAL CURVES 763
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14.4 COMPARING SURVIVAL CURVES 765
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EXERCISES 767 EXERCISES 14.4.1 If a
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14.5 COX REGRESSION: THE PROPORTION
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14.5 COX REGRESSION: THE PROPORTION
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REFERENCES 777 REFERENCES Methodolo
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A-2 APPENDIX STATISTICAL TABLES
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ANSWERS TO ODD-NUMBERED EXERCISES C
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ANSWERS TO ODD-NUMBERED EXERCISES A
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I-2 INDEX Confidence coefficient, 1
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I-4 INDEX Median test, 686-689 MINI
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I-6 INDEX SAS: and chi-square analy
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