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170 CHAPTER 6 ESTIMATION Solution: Since the sample size is fairly large (greater than 30), and since the population standard deviation is known, we draw on the central limit theorem and assume the sampling distribution of x to be approximately normally distributed. From Appendix Table D we find the reliability coefficient corresponding to a confidence coefficient of .90 to be about 1.645, if we interpolate. The standard error is s x = 8> 135 = 1.3522, so that our 90 percent confidence interval for m is 17.2 ; 1.64511.35222 17.2 ; 2.2 15.0, 19.4 ■ Frequently, when the sample is large enough for the application of the central limit theorem, the population variance is unknown. In that case we use the sample variance as a replacement for the unknown population variance in the formula for constructing a confidence interval for the population mean. Computer Analysis When confidence intervals are desired, a great deal of time can be saved if one uses a computer, which can be programmed to construct intervals from raw data. EXAMPLE 6.2.4 The following are the activity values (micromoles per minute per gram of tissue) of a certain enzyme measured in normal gastric tissue of 35 patients with gastric carcinoma. .360 1.189 .614 .788 .273 2.464 .571 1.827 .537 .374 .449 .262 .448 .971 .372 .898 .411 .348 1.925 .550 .622 .610 .319 .406 .413 .767 .385 .674 .521 .603 .533 .662 1.177 .307 1.499 We wish to use the MINITAB computer software package to construct a 95 percent confidence interval for the population mean. Suppose we know that the population variance is .36. It is not necessary to assume that the sampled population of values is normally distributed since the sample size is sufficiently large for application of the central limit theorem. Solution: We enter the data into Column 1 and proceed as shown in Figure 6.2.2. These instructions tell the computer that the reliability factor is z, that a 95 percent confidence interval is desired, that the population standard deviation is .6, and that the data are in Column 1. The output tells us that the sample mean is .718, the sample standard deviation is .511, and the standard error of the mean, s>1n is .6>135 = .101. ■ We are 95 percent confident that the population mean is somewhere between .519 and .917. Confidence intervals may be obtained through the use of many other software packages. Users of SAS ® , for example, may wish to use the output from PROC MEANS or PROC UNIVARIATE to construct confidence intervals.
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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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6.9 CONFIDENCE INTERVAL FOR THE VAR
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6.9 CONFIDENCE INTERVAL FOR THE VAR
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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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6.11 SUMMARY 203 populations of sim
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SUMMARY OF FORMULAS FOR CHAPTER 6 2
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REVIEW QUESTIONS AND EXERCISES 207
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REFERENCES 213 A-8. SILVIA IANNELO,
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CHAPTER7 HYPOTHESIS TESTING CHAPTER
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7.1 INTRODUCTION 217 determine whet
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7.1 INTRODUCTION 219 to reject or n
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7.1 INTRODUCTION 221 8. Statistical
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7.2 HYPOTHESIS TESTING: A SINGLE PO
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EXERCISES 235 WOMAC mean function s
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7.3 HYPOTHESIS TESTING: THE DIFFERE
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EXERCISES 247 in healthy postmenopa
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EXERCISES 249 the local health depa
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7.4 PAIRED COMPARISONS 251 use of r
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percents from the postop percents.
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Paired T-Test and CI: C2, C1 Paired
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EXERCISES 257 Baseline Follow-up Ba
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EXERCISES 261 EXERCISES For each of
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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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7.9 THE TYPE II ERROR AND THE POWER
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7.10 DETERMINING SAMPLE SIZE TO CON
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54. The objective of a study by Rei
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REFERENCES 301 REFERENCES Methodolo
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REFERENCES 303 Veins Due to Greater
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CHAPTER8 ANALYSIS OF VARIANCE CHAPT
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8.1 INTRODUCTION 307 is variability
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8.2 THE COMPLETELY RANDOMIZED DESIG
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Dependent Variable: Selenium Tukey
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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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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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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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