Statistical Rules of Thumb E-Book

Gerald van Belle

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 470

Veröffentlichungsjahr: 2011

Beschreibung

Praise for the First Edition: "For a beginner [this book] is a treasure trove; for an experienced person it can provide new ideas on how better to pursue the subject of applied statistics." --Journal of Quality Technology Sensibly organized for quick reference, Statistical Rules of Thumb, Second Edition compiles simple rules that are widely applicable, robust, and elegant, and each captures key statistical concepts. This unique guide to the use of statistics for designing, conducting, and analyzing research studies illustrates real-world statistical applications through examples from fields such as public health and environmental studies. Along with an insightful discussion of the reasoning behind every technique, this easy-to-use handbook also conveys the various possibilities statisticians must think of when designing and conducting a study or analyzing its data. Each chapter presents clearly defined rules related to inference, covariation, experimental design, consultation, and data representation, and each rule is organized and discussed under five succinct headings: introduction; statement and illustration of the rule; the derivation of the rule; a concluding discussion; and exploration of the concept's extensions. The author also introduces new rules of thumb for topics such as sample size for ratio analysis, absolute and relative risk, ANCOVA cautions, and dichotomization of continuous variables. Additional features of the Second Edition include: * Additional rules on Bayesian topics * New chapters on observational studies and Evidence-Based Medicine (EBM) * Additional emphasis on variation and causation * Updated material with new references, examples, and sources A related Web site provides a rich learning environment and contains additional rules, presentations by the author, and a message board where readers can share their own strategies and discoveries. Statistical Rules of Thumb, Second Edition is an ideal supplementary book for courses in experimental design and survey research methods at the upper-undergraduate and graduate levels. It also serves as an indispensable reference for statisticians, researchers, consultants, and scientists who would like to develop an understanding of the statistical foundations of their research efforts. A related website www.vanbelle.org provides additional rules, author presentations and more.

Leseprobe

Contents

Preface to the Second Edition

Preface to the First Edition

Acronyms

1. The Basics

1.1 FOUR BASIC QUESTIONS

1.2 OBSERVATION IS SELECTION

1.3 REPLICATE TO CHARACTERIZE VARIABILITY

1.4 VARIABILITY OCCURS AT MULTIPLE LEVELS

1.5 INVALID SELECTION IS THE PRIMARY THREAT TO VALID INFERENCE

1.6 THERE IS VARIATION IN STRENGTH OF INFERENCE

1.7 DISTINGUISH BETWEEN RANDOMIZED AND OBSERVATIONAL STUDIES

1.8 BEWARE OF LINEAR MODELS

1.9 KEEP MODELS AS SIMPLE AS POSSIBLE, BUT NOT MORE SIMPLE

1.10 UNDERSTAND OMNIBUS QUANTITIES

1.11 DO NOT MULTIPLY PROBABILITIES MORE THAN NECESSARY

1.12 USE TWO-SIDED/J-VALUES

1.13 USEP-VALUES TO DETERMINE SAMPLE SIZE, CONFIDENCE INTERVALS TO REPORT RESULTS

1.14 USE AT LEAST TWELVE OBSERVATIONS IN CONSTRUCTING A CONFIDENCE INTERVAL

1.15 ESTIMATE ± TWO STANDARD ERRORS IS REMARKABLY ROBUST

1.16 KNOW THE UNIT OF THE VARIABLE

1.17 BE FLEXIBLE ABOUT SCALE OF MEASUREMENT DETERMINING ANALYSIS

1.18 BE ECLECTIC AND ECUMENICAL IN INFERENCE

2. Sample Size

2.1 BEGIN WITH A BASIC FORMULA FOR SAMPLE SIZE-LEHR’S EQUATION

2.2 CALCULATING SAMPLE SIZE USING THE COEFFICIENT OF VARIATION

2.3 IGNORE THE FINITE POPULATION CORRECTION IN CALCULATING SAMPLE SIZE FOR A SURVEY

2.4 THE RANGE OF THE OBSERVATIONS PROVIDES BOUNDS FOR THE STANDARD DEVIATION

2.5 DO NOT FORMULATE A STUDY SOLELY IN TERMS OF EFFECT SIZE

2.6 OVERLAPPING CONFIDENCE INTERVALS DO NOT IMPLY NONSIGNIFICANCE

2.7 SAMPLE SIZE CALCULATION FOR THE POISSON DISTRIBUTION

2.8 SAMPLE SIZE CALCULATION FOR POISSON DISTRIBUTION WITH BACKGROUND RATE

2.9 SAMPLE SIZE CALCULATION FOR THE BINOMIAL DISTRIBUTION

2.10 WHEN UNEQUAL SAMPLE SIZES MATTER; WHEN THEY DON’T

2.11 DETERMINING SAMPLE SIZE WHEN THERE ARE DIFFERENT COSTS ASSOCIATED WITH THE TWO SAMPLES

2.12 USE THE RULE OF THREES TO CALCULATE 95% UPPER BOUNDS WHEN THERE HAVE BEEN NO EVENTS

2.13 SAMPLE SIZE CALCULATIONS SHOULD BE BASED ON THE WAY THE DATA WILL BE ANALYZED

3. bservational Studies

3.1 THE MODEL FOR AN OBSERVATIONAL STUDY IS THE SAMPLE SURVEY

3.2 LARGE SAMPLE SIZE DOES NOT GUARANTEE VALIDITY

3.3 GOOD OBSERVATIONAL STUDIES ARE DESIGNED

3.4 TO ESTABLISH CAUSE EFFECT REQUIRES LONGITUDINAL DATA

3.5 MAKE THEORIES ELABORATE TO ESTABLISH CAUSE AND EFFECT

3.6 THE HILL GUIDELINES ARE A USEFUL GUIDE TO SHOW CAUSE EFFECT

3.7 SENSITIVITY ANALYSES ASSESS MODEL UNCERTAINTY AND MISSING DATA

4. Covariation

4.1 ASSESSING AND DESCRIBING COVARIATION

4.2 DON’T SUMMARIZE REGRESSION SAMPLING SCHEMES WITH CORRELATION

4.3 DO NOT CORRELATE RATES OR RATIOS INDISCRIMINATELY

4.4 DETERMINING SAMPLE SIZE TO ESTIMATE A CORRELATION

4.5 PAIRING DATA IS NOT ALWAYS GOOD

4.6 GO BEYOND CORRELATION IN DRAWING CONCLUSIONS

4.7 ASSESS AGREEMENT IN TERMS OF ACCURACY, SCALE DIFFERENTIAL, AND PRECISION

4.8 ASSESS TEST RELIABILITY BY MEANS OF AGREEMENT

4.9 THE RANGE OF THE PREDICTOR VARIABLE DETERMINES THE PRECISION OF REGRESSION

4.10 IN MEASURING CHANGE, WIDTH IS MORE IMPORTANT THAN NUMBER OF OBSERVATIONS

5. Environmental Studies

5.1 BEGIN WITH THE LOGNORMAL DISTRIBUTION IN ENVIRONMENTAL STUDIES

5.2 DIFFERENCES ARE MORE SYMMETRICAL

5.3 KNOW THE SAMPLE SPACE FOR STATEMENTS OF RISK

5.4 BEWARE OF PSEUDOREPLICATION

5.5 THINK BEYOND SIMPLE RANDOM SAMPLING

5.6 CONSIDER THE SIZE OF THE POPULATION AFFECTED BY SMALL EFFECTS

5.7 STATISTICAL MODELS OF SMALL EFFECTS ARE VERY SENSITIVE TO ASSUMPTIONS

5.8 DISTINGUISH BETWEEN VARIABILITY AND UNCERTAINTY

5.9 DESCRIPTION OF THE DATABASE IS AS IMPORTANT AS ITS DATA

5.10 ALWAYS ASSESS THE STATISTICAL BASIS FOR AN ENVIRONMENTAL STANDARD

5.11 HOW A STANDARD IS MEASURED AFFECTS POLICY, ENFORCEMENT, AND RESPONSE

5.12 PARAMETRIC ANALYSES MAKE MAXIMUM USE OF THE DATA

5.13 DISTINGUISH BETWEEN CONFIDENCE, PREDICTION, AND TOLERANCE INTERVALS

5.14 STATISTICS PLAYS A KEY ROLE IN RISK ASSESSMENT, LESS IN RISK MANAGEMENT

5.15 EXPOSURE ASSESSMENT IS THE WEAK LINK IN ASSESSING HEALTH EFFECTS OF POLLUTANTS

5.16 ASSESS THE ERRORS IN CALIBRATION DUE TO INVERSE REGRESSION

6. Epidemiology

6.1 START WITH THE POISSON TO MODEL INCIDENCE OR PREVALENCE

6.2 THE ODDS RATIO APPROXIMATES THE RELATIVE RISK ASSUMING THE DISEASE IS RARE

6.3 THE NUMBER OF EVENTS IS CRUCIAL IN ESTIMATING SAMPLE SIZES

6.4 USE A LOGARITHMIC FORMULATION TO CALCULATE SAMPLE SIZE

6.5 TAKE NO MORE THAN FOUR OR FIVE CONTROLS PER CASE

6.6 OBTAIN AT LEAST TEN SUBJECTS FOR EVERY VARIABLE INVESTIGATED

6.7 BEGIN WITH THE EXPONENTIAL DISTRIBUTION TO MODEL TIME TO EVENT

6.8 BEGIN WITH TWO EXPONENTIALS FOR COMPARING SURVIVAL TIMES

6.9 BE WARY OF SURROGATES

6.10 PREVALENCE DOMINATES IN SCREENING RARE DISEASES

6.11 DO NOT DICHOTOMIZE UNLESS ABSOLUTELY NECESSARY

6.12 SELECT AN ADDITIVE OR MULTIPLICATIVE MODEL ON THE BASIS OF MECHANISM OF ACTION

7. Evidence-Based Medicine

7.1 STRENGTH OF EVIDENCE

7.2 RELEVANCE OF INFORMATION: POEM VS. DOE

7.3 BEGIN WITH ABSOLUTE RISK REDUCTION, THEN FOLLOW WITH RELATIVE RISK

7.4 THE NUMBER NEEDED TO TREAT (NNT) IS CLINICALLY USEFUL

7.5 VARIABILITY IN RESPONSE TO TREATMENT NEEDS TO BE CONSIDERED

7.6 SAFETY IS THE WEAK COMPONENT OF EBM

7.7 INTENT TO TREAT IS THE DEFAULT ANALYSIS

7.8 USE PRIOR INFORMATION BUT NOT PRIORS

7.9 THE FOUR KEY QUESTIONS FOR META-ANALYSTS

8. Design, Conduct, and analysis

8.1 RANDOMIZATION PUTS SYSTEMATIC EFFECTS INTO THE ERROR TERM

8.2 BLOCKING IS THE KEY TO REDUCING VARIABILITY

8.3 FACTORIAL DESIGNS SHOULD BE USED TO ASSESS JOINT EFFECTS OF VARIABLES

8.4 HIGH-ORDER INTERACTIONS OCCUR RARELY

8.5 BALANCED DESIGNS ALLOW EASY ASSESSMENT OF JOINT EFFECTS

8.6 ANALYSIS FOLLOWS DESIGN

8.7 ASSESS INDEPENDENCE, EQUAL VARIANCE, AND NORMALITY-IN THAT ORDER

8.8 PLAN TO GRAPH THE RESULTS OF AN ANALYSIS

8.9 DISTINGUISH BETWEEN DESIGN STRUCTURE AND TREATMENT STRUCTURE

8.10 MAKE HIERARCHICAL ANALYSES THE DEFAULT ANALYSIS

8.11 DISTINGUISH BETWEEN NESTED AND CROSSED DESIGNS-NOT ALWAYS EASY

8.12 PLAN FOR MISSING DATA

8.13 ADDRESS MULTIPLE COMPARISONS BEFORE STARTING THE STUDY

8.14 KNOW PROPERTIES PRESERVED WHEN TRANSFORMING UNITS

8.15 CONSIDER BOOTSTRAPPING FOR COMPLEX RELATIONSHIPS

9. Words, Tables, and Graphs

9.1 USE TEXT FOR A FEW NUMBERS, TABLES FOR MANY NUMBERS, GRAPHS FOR COMPLEX RELATIONSHIPS

9.2 ARRANGE INFORMATION IN A TABLE TO DRIVE HOME THE MESSAGE

9.3 ALWAYS GRAPH THE DATA

9.4 ALWAYS GRAPH RESULTS OF AN ANALYSIS OF VARIANCE

9.5 NEVER USE A PIE CHART

9.6 BAR GRAPHS WASTE INK; THEY DON’T ILLUMINATE COMPLEX RELATIONSHIPS

9.7 STACKED BAR GRAPHS ARE WORSE THAN BAR GRAPHS

9.8 THREE-DIMENSIONAL BAR GRAPHS CONSTITUTE MISDIRECTED ARTISTRY

9.9 IDENTIFY CROSS-SECTIONAL AND LONGITUDINAL PATTERNS IN LONGITUDINAL DATA

9.10 USE RENDERING, MANIPULATION, AND LINKING IN HIGH-DIMENSIONAL DATA

10. Consulting

10.1 STRUCTURE A CONSULTATION SESSION TO HAVE A BEGINNING, A MIDDLE, AND AN END

10.2 ASK QUESTIONS

10.3 MAKE DISTINCTIONS

10.4 KNOW YOURSELF, KNOW THE INVESTIGATOR

10.5 TAILOR ADVICE TO THE LEVEL OF THE INVESTIGATOR

10.6 USE UNITS THE INVESTIGATOR IS COMFORTABLE WITH

10.7 AGREE ON ASSIGNMENT OF RESPONSIBILITIES

10.8 ANY BASIC STATISTICAL COMPUTING PACKAGE WILL DO

10.9 ETHICS PRECEDES, GUIDES, AND FOLLOWS CONSULTATION

10.10 BE PROACTIVE IN STATISTICAL CONSULTING

10,11 USE THE WEB FOR REFERENCE, RESOURCE, AND EDUCATION

10.12 LISTEN TO, AND HEED THE ADVICE OF EXPERTS IN THE FIELD

Epilogue

References

Author Index

Topic Index

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†ABRAHAM and LEDOLTER • Statistical Methods for ForecastingAGRESTI • Analysis of Ordinal Categorical DataAGRESTI • An Introduction to Categorical Data Analysis, Second EditionAGRESTI • Categorical Data Analysis, Second EditionALTMAN, GILL, and McDONALD • Numerical Issues in Statistical Computing for the Social ScientistAMARATUNGA and CABRERA • Exploration and Analysis of DNA Microarray and Protein Array DataANDĚL • Mathematics of ChanceANDERSON • An Introduction to Multivariate Statistical Analysis, Third Edition*ANDERSON • The Statistical Analysis of Time SeriesANDERSON, AUQUIER, HAUCK, OAKES, VANDAELE, and WEISBERG • Statistical Methods for Comparative StudiesANDERSON and LOYNES • The Teaching of Practical StatisticsARMITAGE and DAVID (editors) • Advances in BiometryARNOLD, BALAKRISHNAN, andNAGARAJA • Records*ARTHANARI and DODGE • Mathematical Programming in Statistics*BAILEY • The Elements of Stochastic Processes with Applications to the Natural SciencesBALAKRISHNAN and KOUTRAS • Runs and Scans with ApplicationsBALAKRISHNAN and NG • Precedence-Type Tests and ApplicationsBARNETT • Comparative Statistical Inference, Third EditionBARNETT • Environmental StatisticsBARNETT and LEWIS • Outliers in Statistical Data, Third EditionBARTOSZYNSKI and NIEWIADOMSKA-BUGAJ • Probability and Statistical Inference BASILEVSKY • Statistical Factor Analysis and Related Methods: Theory and ApplicationsBASU and RIGDON • Statistical Methods for the Reliability of Repairable SystemsBATES and WATTS • Nonlinear Regression Analysis and Its ApplicationsBECHHOFER, SANTNER, and GOLDSMAN • Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple ComparisonsBELSLEY • Conditioning Diagnostics: Collinearity and Weak Data in Regression†BELSLEY, KUH, and WELSCH • Regression Diagnostics: Identifying Influential Data and Sources of CollinearityBENDAT and PIERSOL • Random Data: Analysis and Measurement Procedures, Third EditionBERRY, CHALONER, and GEWEKE • Bayesian Analysis in Statistics and Econometrics: Essays in Honor of Arnold ZellnerBERNARDO and SMITH • Bayesian TheoryBHAT and MILLER • Elements of Applied Stochastic Processes, Third EditionBHATTACHARYA and WAYMIRE • Stochastic Processes with ApplicationsBILLINGSLEY • Convergence of Probability Measures, second EditionBILLINGSLEY • Probability and Measure, Third EditionBIRKES and DODGE • Alternative Methods of RegressionBISWAS, DATTA, FINE, and SEGAL • Statistical Advances in the Biomedical Sciences: Clinical Trials, Epidemiology, Survival Analysis, and BioinformaticsBLISCHKE AND MURTHY (editors) • Case Studies in Reliability and MaintenanceBLISCHKE AND MURTHY • Reliability: Modeling, Prediction, and OptimizationBLOOMFIELD • Fourier Analysis of Time Series: An Introduction, second EditionBOLLEN • Structural Equations with Latent VariablesBOLLEN and CURRAN • Latent Curve Models: A Structural Equation PerspectiveBOROVKOV • Ergodicity and Stability of Stochastic ProcessesBOULEAU • Numerical Methods for Stochastic ProcessesBOX • Bayesian Inference in Statistical AnalysisBOX • R. 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Library of Congress Cataloging-in-Publication Data:

van Belle, Gerald.

Statistical rules of thumb / Gerald van Belle. — 2nd ed.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-14448-0 (pbk.)

1. Mathematical statistics. I. Title.

QA276.12.V36 2008

519.5—dc22

2008004431