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282 CHAPTER 7 HYPOTHESIS TESTING 7.9.1, 7.9.2 Upper and lower critical values for x x U ¼ m 0 þ z p s ffiffi n x L ¼ m 0 z p s ffiffi n 7.10.1, 7.10.2 Critical value for determining sample size to control type II errors s s C ¼ m 0 z 0 p ffiffi ¼ m n 1 þ z 1 p ffiffi n 7.10.3 Sample size to control type II errors n ¼ z ð 0 þ z 1 Þs 2 ðm 0 m 1 Þ Symbol Key a ¼ type 1 error rate C ¼ critical value x 2 ¼ chi-square distribution d ¼ average difference m ¼ mean of population m 0 ¼ hypothesized mean n ¼ sample size p ¼ proportion for population p ¼ average proportion q ¼ ð1 pÞ ^p ¼ estimated proportion for sample s 2 ¼ population variance s ¼ population standard deviation sd ¼ standard error of difference s x ¼ standard error s ¼ standard deviation of sample sd ¼ standard deviation of the difference s p ¼ pooled standard deviation t ¼ Student’s t-transformation t 0 ¼ Cochran’s correction to t x ¼ mean of sample x L ¼ lower limit of critical value for x x U ¼ upper limit of critical value for x z ¼ standard normal transformation REVIEW QUESTIONS AND EXERCISES 1. What is the purpose of hypothesis testing? 2. What is a hypothesis? 3. List and explain each step in the ten-step hypothesis testing procedure.
REVIEW QUESTIONS AND EXERCISES 283 4. Define: (a) Type I error (c) The power of a test (e) Power curve (b) Type II error (d) Power function (f) Operating characteristic curve 5. Explain the difference between the power curves for one-sided tests and two-sided tests. 6. Explain how one decides what statement goes into the null hypothesis and what statement goes into the alternative hypothesis. 7. What are the assumptions underlying the use of the t statistic in testing hypotheses about a single mean? The difference between two means? 8. When may the z statistic be used in testing hypotheses about (a) a single population mean? (b) the difference between two population means? (c) a single population proportion? (d) the difference between two population proportions? 9. In testing a hypothesis about the difference between two population means, what is the rationale behind pooling the sample variances? 10. Explain the rationale behind the use of the paired comparisons test. 11. Give an example from your field of interest where a paired comparisons test would be appropriate. Use real or realistic data and perform an appropriate hypothesis test. 12. Give an example from your field of interest where it would be appropriate to test a hypothesis about the difference between two population means. Use real or realistic data and carry out the ten-step hypothesis testing procedure. 13. Do Exercise 12 for a single population mean. 14. Do Exercise 12 for a single population proportion. 15. Do Exercise 12 for the difference between two population proportions. 16. Do Exercise 12 for a population variance. 17. Do Exercise 12 for the ratio of two population variances. 18. Ochsenk€uhn et al. (A-33) studied birth as a result of in vitro fertilization (IVF) and birth from spontaneous conception. In the sample, there were 163 singleton births resulting from IVF with a mean birth weight of 3071 g and sample standard deviation of 761 g. Among the 321 singleton births resulting from spontaneous conception, the mean birth weight was 3172 g with a standard deviation of 702 g. Determine if these data provide sufficient evidence for us to conclude that the mean birth weight in grams of singleton births resulting from IVF is lower, in general, than the mean birth weight of singleton births resulting from spontaneous conception. Let a ¼ :10. 19. William Tindall (A-34) performed a retrospective study of the records of patients receiving care for hypercholesterolemia. The following table gives measurements of total cholesterol for patients before and 6 weeks after taking a statin drug. Is there sufficient evidence at the a ¼ :01 level of significance for us to conclude that the drug would result in reduction in total cholesterol in a population of similar hypercholesterolemia patients?
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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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Page 319 and 320: REFERENCES 301 A-17. JOHN S. MORLEY
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EXERCISES 333 Group 1 Group 2 Group
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Objective The objective in using th
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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 group were randomly a
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8.4 THE REPEATED MEASURES DESIGN 34
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EXERCISES 357 Is there sufficient e
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8.5 THE FACTORIAL EXPERIMENT 359 In
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8.5 THE FACTORIAL EXPERIMENT 361 In
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8.5 THE FACTORIAL EXPERIMENT 363 Be
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8.5 THE FACTORIAL EXPERIMENT 365 TA
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8.5 THE FACTORIAL EXPERIMENT 367 Ro
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EXERCISES 369 The SAS System Analys
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EXERCISES 371 Physical Psychiatric
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8.6 SUMMARY 373 Percent Change in C
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REFERENCES 409 Applications Referen
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REFERENCES 411 Postmenopausal Women
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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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EXERCISES 685 Dialog box: Session c
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13.5 THE MEDIAN TEST 687 TABLE 13.5
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EXERCISES 689 Dialog box: Session c
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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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Assumptions the following: 1. The s
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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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