Daniel W.W. Biostatistics: A Foundation for Analysis in the Health Sciences

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I-1

Accuracy, 14

Addition rule, 73–74

Analysis of variance, 305–308

assumptions, 307

completely randomized design, 308–334

one-way, 308–334

procedure, 307–308

randomized complete block design, 334–346

repeated measures design, 346–353

two-way, 334–346

Arithmetic mean, 38

Average hazard rate, 655

Backward selection, 560

Bayes’s theorem, 68, 81–83

Bernoulli process, 100–101

␤

, conﬁdence interval, 434

hypothesis test, 431–434

Binomial distribution, 100–109

parameters, 106–108

table, A-3–A-31

Use of table, 104–106

Biostatistics, 3

Birth rate, crude, 773

Bivariate normal distribution, 441

Bonferroni’s method, 324, 327

Box-and-whisker plot, 50–52

Case-fatality ratio, 776

Cause-of-death ratio, 770

Censored data, 649

Central limit theorem, 140–141

Central tendency, measures, 38–43

Chi-square distribution, 195–197, 593–629

mathematical properties, 594–595

table, A-41

use in goodness-of-ﬁt tests, 597–612

small expected frequencies, 597

use in tests of homogeneity, 623–629

small expected frequencies, 626

use in tests of independence, 612–623

small expected frequencies, 618

2  2 table, 618–620

Class interval, 22

Coefﬁcient of determination, 423–428

Coefﬁcient of multiple determination, 497–499

Coefﬁcient of variation, 45–46

Combination, 102

Completely randomized design, 308–334

ANOVA table, 317

assumptions, 311

Compound symmetry, 348

Computers:

and analysis of variance, 308, 321–323, 325–327,

341–343, 349–351, 362, 364

and biostatistical analysis, 15–16

and chi-square, 608, 616-617, 625

and descriptive statistics, 21, 25–27, 29–30, 46–47

and hypothesis testing, 230–231, 244–245, 255

and interval estimation, 170–171

and logistic regression, 573

and multiple correlation analysis, 508–509, 511–515

and multiple regression analysis, 490–492, 508

and random numbers, 16

and simple linear regression and correlation analysis,

416–418, 437, 446–447

and stepwise regression, 556–559

Conﬁdence coefﬁcient, 168

Conﬁdence interval:

for ␤

, 434

multiple regression, 502

for difference between two

population means, 178–185

nonnormal populations, 179–180

for difference between two

population proportions, 187–189

for mean of Y, given X, 437–438

INDEX

Numbers preceded by A refer to Appendix pages.

Conﬁdence interval (Continued)

for ␮

y|1

…

, 504–505

for population mean, 166–178

nonnormal populations, 169–171

for population proportion, 185–187

practical interpretation, 168

for predicted Y, 437–438, 504–505

probabilistic interpretation, 169

for ratio of two variances, 199–203

for ␳, 450–451

for variance, 194–198

Confusion matrix, 220

Contingency table, 612

Correction for continuity, 153

Correlation coefﬁcient:

multiple, 506–509

simple, 442–451

Correlation model:

multiple, 508–509

simple, 441–442

Cox regression model, 659–660

Critical region, 225

Critical value, 225–226

Cumulative frequencies, 25

Cumulative relative frequencies, 25

Data, 2

grouped, 22–37

raw, 20

sources, 3

Death rate:

crude, 765

fetal, 769

speciﬁc, 765

standardized, 766

Death rates and ratios, 765–772

Death ratio, fetal, 778

Decision rule, 219

Degrees of freedom, 41–42

Density function, 116

Descriptive statistics, 2, 19–64

Dispersion, measures, 43–49

Distribution-free procedures, 684

Dummy variable, 540–555

Epidemiology, 764

Estimation, 102–214

in simple linear regression analysis, 434,

437–438

Estimator, 164

robust, 171

Events:

complementary, 75

independent, 74–75

mutually exclusive, 69

EXCEL:

and binomial distribution, 107

Exclusive or, 73

Experiments, 10

designing, 14–15

Exploratory data analysis, 52

Extrapolation, 438, 455–456

Factorial, 102

Factorial experiment, 353–368

ANOVA table, 359

assumptions, 357

False negative, 79

False positive, 79

Family-wise error rates, 502

F distribution, 199–200

table of, A-42–A-51

Fecundity, 772

Fertility, 772

measures, 772–776

Fertility rate:

age-speciﬁc, 774

cumulative, 774

general, 773

standardized, 774

total, 774

Finite population correction, 142

Fisher exact test, 629–634

table for, A-55–A-85

Fisher’s z, 449–451

table, A-54

Fixed effects model, 311

F-max test, 199

Forward selection, 559

Frequency distribution, 24–27

Frequency polygon, 27–28

Friedman test, 725–731

table for, A-102–A-103

F test, 316–317

Goodness-of-ﬁt tests, 597–612,

711–717

Grouped data, 22–37

I-2 INDEX

Histogram, 25–27

Hypothesis, 216

alternative, 217

formulating, 14

null, 217

research, 216

statistical, 217

Hypothesis tests, 215–304

by means of conﬁdence interval, 226–227

difference between means, 237–250

nonnormal populations, 243–244

population variances known, 237–239

population variances unknown, 239–243

for ␤

, multiple regression, 499–503

for ␤

, simple linear regression, 428–433

one-sided, 227–228

purpose, 216, 221

single population mean, 223–237

nonnormal population, 231–233

population variance known, 223–229

population variance unknown, 229–231

single population proportion, 258–261

single population variance, 265–268

steps in, 217–221

two population proportions, 262–265

two population variances, 268–273

two-sided, 227

Immaturity ratio, 776

Incidence rate, 776

Inclusive or, 73

Inferential statistics, 2, 163

Interaction, 354–356, 546

Interpolation, 438

Interquartile range, 48

Interval estimate, 164

Interval scale, 6

Joint distribution, 441

Kaplan-Meier procedure, 650–659

Kolmogrov–Smirnov test, 711–717

and StatXact computer analysis, 715

table for, A-99

Kruskal–Wallis test, 717–725

table for, A-l00–A-101

Kurtosis, 48–49

Least squares, method, 416

Least-squares line, 416–418

Levene’s test, 202, 271

Location parameters, 47

Log rank test, 656–658

Logistic regression, 565–575

Loss to followup, 648

Mann–Whitney test, 703–710

table for, A-95–A-98

Mantel–Haenszel statistic, 641–646

Margin of error, 169

Mean, 38–40

properties, 40

Measurement, 6

Measurement scales, 5–6, 685

Median, 40

properties, 41

Median test, 699–703

MINITAB:

and binomial distribution, 107–108

and box-and-whisker plots, 51–52

and chi-square, 608–616, 625

and conﬁdence intervals for a mean, 170–171

and descriptive measures, 46–47

and dummy variables, 542–543, 547, 551

and factorial experiment, 362–363

and frequency distributions, 25–26

and Friedman test, 729

and histograms, 26–27

and hypothesis testing, 230–231, 244–245, 255–260

and Kruskal–Wallis test, 721–722

and Mann–Whitney test, 708–709

and median test, 702

and multiple correlation, 503–509, 511–513

and multiple regression, 491–492, 505

and normal distribution, 127–1278

and one-way ANOVA, 321–327

and ordered array, 21

and Poisson distribution, 112–113

and repeated measures ANOVA, 349–350

and sign test, 693

and simple linear regression, 416–418, 437,

446–447

and Spearman rank correlation, 737

and stem-and-leaf displays, 29–30

and stepwise regression, 556–559

and two-way ANOVA, 341–342

and Wilcoxon test, 698

INDEX I-3

Mode, 41

Morbidity, 776

measures, 776–777

Mortality rate:

infant, 769

maternal, 768

neonatal, 769

perinatal, 770

Multicollinearity, 538

Multiple comparison, 322–327

Multiple correlation coefﬁcient, 506–509

Multiple correlation model, 506–509

Multiplication rule, 71–72

Multivariate distribution, 506

Multivariate normal distribution, 506

NCSS:

and box and whisker plots, 51

Nominal scale, 6

Nonparametric statistics, 683–762

advantages, 684

disadvantages, 685

Nonrejection region, 219

Normal distribution, 117–129

applications, 123–129

characteristics, 117–118

standard, 119–123

table, A-38–A-39

Observation, 14

Observational study, 635–636

Odds, 639

Odds ratio, 638–641

Ogive, 97

Operating characteristic curve, 278

Ordered array, 20–21

Ordinal scale, 6

Outliers, 51–171

Paired comparisons, 250–255

Parameter, 38

Partial correlation, 508–515

Partial regression coefﬁcients, 488

Percentile, 47

Point estimate, 164

Poisson distribution, 109–114

table of, A-32–A-37

Poisson process, 110

Population, 5

ﬁnite, 5

inﬁnite, 5

sampled, 165

target, 165

Power, 273–280

Precision, 14, 169

Predictive value negative, 81

Predictive value positive, 80

Prospective study, 635

Prediction interval, multiple regression, 504–505

simple linear regression, 437–438

Prevalence rate, 776

Probability, 65–86

posterior, 68

prior, 68

classical, 66

conditional, 70–72

joint, 71

marginal, 70, 75

objective, 66–67

personalistic, 67

properties, 68–69

relative frequency, 67

subjective, 67–68

Probability distributions, 93–134

of continuous variables, 114–129

of discrete variables, 94–115

cumulative, 97–99

properties, 96

Product-limit method, see

Kaplan–Meier procedure

Proportional hazards model, see

Cox regression model

Proportional mortality ratio, 770

p values, 221

Qualitative variables, 4, 539–555

Quartile, 47–48

Random digits, table, A-2

use, 9–10

Randomized complete block design, 334–346

ANOVA table, 338

assumptions, 337

Range, 43–44

Rank transformation, 685

I-4 INDEX

Rate, 764–765

Ratio, 765

Ratio scale, 6

Regression:

logistic, 565–575

multiple, 485–506

assumptions, 487

equation, 487–492

model, 486–488

nonparametric, 740–743

resistant line, 438–440

simple linear, 409–440

assumptions, 411–412

equation, 413–422

model, 410–412

stepwise, 556–565

Rejection region, 219

Relative frequencies, 24–25

Relative risk, 634–638

Reliability, 14

Reliability coefﬁcient, 168

Repeated measures design, 346–353

assumptions, 347–348

deﬁnition, 347

Research study, 10

Residual, 425

Resistant line, 438–440

Retrospective study, 636

Risk factor, 635

Sample, 5

convenience, 166

nonrandom, 165–166

random, 165–166

simple random, 7–10

size for controlling Type II errors, 278–280

size for estimating means, 189–192

size for estimating proportions, 192–193

stratiﬁed proportional to size, 13

stratiﬁed random, 12

stratiﬁed systematic, 12

systematic, 11

Sampling distribution, 135–161

characteristics, 137

construction of, 136

deﬁnition, 136

of difference between sample means, 146–151

nonnormal populations, 149

of difference between sample proportions, 155–157

of sample mean, 137–146

nonnormal populations, 140–142

of sample proportion, 151–155

SAS:

and chi-square analysis, 616–617

and descriptive measures, 47

and factorial experiment, 362, 364

and hypothesis testing, 234, 244–245

and logistic regression, 568–571

and multiple regression, 492

and one-way ANOVA, 322

and repeated measures ANOVA, 350–351

and simple linear regression and correlation,

438–439, 446–447

and Tukey’s HSD test, 326

and two-way ANOVA, 341–343

Scatter diagram, 415–416

Scientiﬁc methods, 13–15

Secondary attack rate, 776

Sensitivity, 80

Signiﬁcance level, 219–220

Sign test, 636–694

Simple random sampling,

7–11

without replacement, 7–8

with replacement, 7–8

Skewness, 41–42

Slope, 411

Spearman rank correlation coefﬁcient, 731–740

table for, A-104

Speciﬁcity, 80

Sphericity, 348

SPSS:

and Fisher exact test, 633

and frequency distribution, 25–26

and kurtosis, 49

and logistic regression, 573

and Mann-Whitney test, 708–709

and Mantel-Haenzcel test, 645–646

and multiple regression, 490

and odds ratio, 641

and partial correlation, 512, 514–515

and repeated measures ANOVA, 350–351

and skewness, 43

and survival analysis, 658–659

and Turkey’s HSD test, 326

Standard deviation, 45

Standard error of mean, 140

Standard normal distribution, 119–123

table of, A-38–A-39

INDEX I-5

Statistic, 38

Statistical inference, 7, 163

Statistics, 2

Stem-and-leaf-display, 28–30

Stepwise regression, 556–565

Studentized range, 324

table of, A-52–A-54

Student’s distribution, 172–177

table of, A-40

Sturges’ rule, 22

Survival analysis, 648–633

t distribution, 172–177

and difference between means, 180–183

population variances equal, 180–181

population variances not equal, 181–183

properties, 173

table of, A-40

Test statistic, 218–219

Trimmed mean, 171

Tukey’s HSD test, 323–324

Tukey’s line, 438–439

Type I error, 220

Type II error, 220, 273–280

Unbiasedness, 164

Uniform distribution, 607–609

Unit of association, 455

Variable, 3

continuous random, 4

dependent, 411

discrete random, 4

dummy, 540–555

explanatory, 486

extraneous, 307

independent, 411

predictor, 413, 486

qualitative, 4, 539–555

quantitative, 4

random, 4

response, 307, 413

treatment, 307

Variable selection procedures, 556–565

Variance, 44–45

interval estimation, 195–198

Variance ratio, 316

Variance ratio test, 199, 269–273

Vital statistics, 763–782

Wilcoxon test, 694–697

table for, A-86–A-95

Yates’ correction, 620

y-intercept, 411

I-6 INDEX