Statistical Analysis And Data Display

by Heiberger, Richard M.; Holland, Burt

• ISBN13: 9780387402703
• ISBN10: 0387402705
• Format: Hardcover
• Copyright: 2004-08-30
• Publisher: Springer Verlag

Summary

This contemporary presentation of statistical methods features extensive use of graphical displays for exploring data and for displaying the analysis. The authors demonstrate how to analyze data''‚¬"showing code, graphics, and accompanying computer listings''‚¬"for all the methods they cover. They emphasize how to construct and interpret graphs, discuss principles of graphical design, and show how accompanying traditional tabular results are used to confirm the visual impressions derived directly from the graphs. Many of the graphical formats are novel and appear here for the first time in print. All chapters have exercises.This book can serve as a standalone text for statistics majors at the master's level and for other quantitatively oriented disciplines at the doctoral level, and as a reference book for researchers. In-depth discussions of regression analysis, analysis of variance, and design of experiments are followed by introductions to analysis of discrete bivariate data, nonparametrics, logistic regression, and ARIMA time series modeling. The authors illustrate classical concepts and techniques with a variety of case studies using both newer graphical tools and traditional tabular displays.The authors provide and discuss S-Plus, R, and SAS executable functions and macros for all new graphical display formats. All graphs and tabular output in the book were constructed using these programs. Complete transcripts for all examples and figures are provided for readers to use as models for their own analyses.Richard M. Heiberger and Burt Holland are both Professors in the Department of Statistics at Temple University and elected Fellows of the American Statistical Association. Richard M. Heiberger participated in the design of the S-Plus linear model and analysis of variance commands while on research leave at Bell Labs in 1987''‚¬"88 and has been closely involved as a beta tester and user of S-Plus. Burt Holland has made many research contributions to linear modeling and simultaneous statistical inference, and frequently serves as a consultant to medical investigators. Both teach the Temple University course sequence that inspired them to write this text.

Author Biography

Burt Holland is Professor in the Department of Statistics at Temple University and elected Fellow of the American Statistical Association.

Table of Contents

Preface	vii
Audience	vii
Structure	viii
Data and Programs	ix
Software	x
Microsoft Windows	xi
Unix	xi
Exercises	xi
Introduction and Motivation	1	(10)
Statistics in Context	3	(1)
Examples of Uses of Statistics	4	(3)
Investigation of Salary Discrimination	4	(1)
Measuring Body Fat	5	(1)
Minimizing Film Thickness	5	(1)
Surveys	6	(1)
Bringing Pharmaceutical Products to Market	6	(1)
The Rest of the Book	7	(4)
Fundamentals	7	(1)
Linear Models	7	(2)
Other Techniques	9	(1)
New Graphical Display Techniques	9	(2)
Data and Statistics	11	(10)
Types of Data	11	(1)
Data Display and Calculation	12	(2)
Presentation	13	(1)
Rounding	13	(1)
Importing Data	14	(2)
S-Plus	14	(1)
SAS	15	(1)
Data Rearrangement	15	(1)
Analysis with Missing Data	16	(1)
Missing Data in S-Plus	16	(1)
Missing Data in SAS	17	(1)
Tables and Graphs	17	(1)
Files for Statistical Analysis and Data Display (HH)	18	(3)
Datasets	18	(1)
Code, Transcripts, and Figures	18	(1)
Functions and Macros	19	(1)
Software	19	(2)
Statistics Concepts	21	(42)
A Brief Introduction to Probability	21	(1)
Random Variables and Probability Distributions	22	(5)
Discrete Versus Continuous Probability Distributions	23	(1)
Displaying Probability Distributions	24	(3)
Concepts That Are Used When Discussing Distributions	27	(10)
Expectation and Variance of Random Variables	27	(1)
Median of Random Variables	28	(1)
Symmetric and Skewed Distributions	28	(2)
Displays of Univariate Data	30	(4)
Multivariate Distributions---Covariance and Correlation	34	(3)
Three Probability Distributions	37	(3)
The Binomial Distribution	37	(1)
The Normal Distribution	38	(1)
The (Student's) t Distribution	39	(1)
Sampling Distributions	40	(1)
Estimation	41	(4)
Statistical Models	41	(1)
Point and Interval Estimators	42	(1)
Criteria for Point Estimators	42	(1)
Confidence Interval Estimation	43	(1)
Example---Confidence Interval on the Mean μ of a Population Having Known Standard Deviation	44	(1)
Example---One-Sided Confidence Intervals	44	(1)
Hypothesis Testing	45	(2)
Examples of Statistical Tests	47	(2)
Power and Operating Characteristic (O.C.) Curves	49	(3)
Sampling	52	(5)
Simple Random Sampling	53	(1)
Stratified Random Sampling	53	(1)
Cluster Random Sampling	54	(1)
Systematic Random Sampling	55	(1)
Standard Errors of Sample Means	56	(1)
Sources of Bias in Samples	56	(1)
Exercises	57	(6)
Graphs	63	(28)
Definition	64	(1)
Example---Ecological Correlation	64	(1)
Scatterplots	65	(2)
Scatterplot Matrix	67	(4)
Example---Life Expectancy	71	(3)
Scatterplot Matrices---Continued	74	(4)
Data Transformations	78	(4)
Life Expectancy Example---Continued	82	(3)
SAS Graphics	85	(2)
Exercises	87	(4)
Introductory Inference	91	(32)
Normal (z) Intervals and Tests	91	(4)
Test of a Hypothesis Concerning the Mean of a Population Having Known Standard Deviation	92	(1)
Confidence Intervals for Unknown Population Proportion p	93	(1)
Tests on an Unknown Population Proportion p	94	(1)
Example---One-Sided Hypothesis Test Concerning a Population Proportion	94	(1)
t-intervals and Tests for the Mean of a Population Having Unknown Standard Deviation	95	(1)
Confidence Interval on the Variance or Standard Deviation of a Normal Population	96	(1)
Comparisons of Two Populations Based on Independent Samples	97	(4)
Confidence Intervals on the Difference Between Two Population Proportions	98	(1)
Confidence Interval on the Difference of Between Two Means	98	(1)
Tests Comparing Two Population Means When the Samples Are Independent	99	(1)
Comparing the Variances of Two Normal Populations	100	(1)
Paired Data	101	(4)
Sample Size Determination	105	(1)
Sample Size for Estimation	105	(1)
Sample Size for Hypothesis Testing	106	(1)
Goodness of Fit	106	(4)
Chi-square Goodness-of-Fit Test	107	(1)
Example---Test of Goodness-of-Fit to a Discrete Uniform Distribution	108	(1)
Example---Test of Goodness-of-Fit to a Binomial Distribution	108	(2)
Normal Probability Plots and Quantile Plots	110	(4)
Normal Probability Plots	112	(1)
Example---Comparing t-Distributions	113	(1)
Kolmogorov-Smirnov Goodness-of-Fit Tests	114	(3)
Maximum Likelihood	117	(2)
Maximum Likelihood Estimation	118	(1)
Likelihood Ratio Tests	119	(1)
Exercises	119	(4)
One-Way Analysis of Variance	123	(32)
Example---Catalyst Data	123	(4)
Fixed Effects	127	(3)
Multiple Comparisons---Tukey Procedure for Comparing All Pairs of Means	130	(5)
Random Effects	135	(1)
Expected Mean Squares (EMS)	135	(1)
Example---Catalyst Data---Continued	136	(1)
Example---Batch Data	137	(1)
Example---Turkey Data	137	(7)
Analysis	139	(4)
Interpretation	143	(1)
Specification of Analysis	143	(1)
Contrasts	144	(3)
Mathematics of Contrasts	144	(2)
Scaling	146	(1)
Tests of Homogeneity of Variance	147	(1)
Exercises	148	(5)
Appendix: Computation for the Analysis of Variance	153	(2)
Computing Notes	153	(1)
Computation	153	(2)
Multiple Comparisons	155	(32)
Multiple Comparison Procedures	156	(12)
Bonferroni Method	156	(1)
Tukey Procedure for All Pairwise Comparisons	157	(1)
The Dunnett Procedure for Comparing One Mean with All Others	157	(5)
Simultaneously Comparing All Possible Contrasts---Scheffe and Extended Tukey	162	(6)
The Mean--Mean Multiple Comparisons Display (MMC Plot)	168	(16)
Difficulties with Standard Displays	168	(5)
Hsu and Peruggia's Mean-Mean Scatterplot	173	(5)
Extensions of the Mean-Mean Display to Arbitrary Contrasts	178	(2)
Display of an Orthogonal Basis Set of Contrasts	180	(2)
Hsu and Peruggia's Pulmonary Example	182	(2)
Exercises	184	(3)
Linear Regression by Least Squares	187	(28)
Introduction	187	(1)
Example---Body Fat Data	188	(2)
Simple Linear Regression	190	(15)
Algebra	190	(2)
Normal Distribution Theory	192	(1)
Calculations	193	(6)
Residual Mean Square in Regression Printout	199	(1)
New Observations	199	(6)
Diagnostics	205	(4)
Graphics	209	(1)
Exercises	210	(3)
Appendix: Computation for Regression Analysis	213	(2)
S-Plus Functions	213	(1)
SAS Macros and Procs	213	(2)
Multiple Regression---More Than One Predictor	215	(52)
Regression with Two Predictors---Least-Squares Geometry	215	(2)
Multiple Regression---Algebra	217	(4)
The Hat Matrix and Leverage	220	(1)
Multiple Regression---Two-X Analysis	221	(2)
Geometry of Multiple Regression	223	(1)
Programming	223	(2)
Model Specification	223	(1)
Printout Idiosyncrasies	224	(1)
Example---Albuquerque Home Price Data	225	(3)
Partial F-Tests	228	(2)
Polynomial Models	230	(3)
Models Without a Constant Term	233	(2)
Prediction	235	(1)
Example---Longley Data	236	(5)
Collinearity	241	(2)
Variable Selection	243	(11)
Manual Use of the Stepwise Philosophy	244	(3)
Automated Stepwise Regression	247	(3)
Automated Stepwise Modeling of the Longley Data	250	(4)
Residual Plots	254	(5)
Partial Residuals	254	(2)
Partial Residual Plots	256	(1)
Partial Correlation	256	(1)
Added Variable Plots	256	(1)
Interpretation of Residual Plots	257	(2)
Example U.S. Air Pollution Data	259	(5)
Exercises	264	(3)
Multiple Regression---Dummy Variables and Contrasts	267	(30)
Dummy (Indicator) Variables	267	(1)
Example---Height and Weight	268	(7)
Equivalence of Linear Independent X-Variables for Regression	275	(2)
Polynomial Contrasts and Orthogonal Polynomials	277	(6)
Specification and Interpretation of Interaction Terms	282	(1)
Analysis Using a Concomitant Variable (Analysis of Covariance)	283	(1)
Example---Hot Dog Data	284	(10)
One-Way ANOVA	284	(2)
Concomitant Explanatory Variable	286	(6)
Tests of Equality of Regression Lines	292	(2)
ancova Function	294	(1)
Exercises	294	(3)
Multiple Regression---Regression Diagnostics	297	(32)
Example---Rent Data	297	(12)
Rent Levels	298	(5)
Alfalfa Rent Relative to Other Rent	303	(6)
Checks on Model Assumptions	309	(3)
Scatterplot Matrix	309	(1)
Residual Plots	309	(3)
Case Statistics	312	(12)
Leverage	315	(1)
Deleted Standard Deviation	316	(1)
Standardized and Studentized Deleted Residuals	317	(2)
Cook's Distance	319	(2)
Dffits	321	(1)
Dfbetas	322	(1)
Calculation of Regression Diagnostics	323	(1)
Exercises	324	(5)
Two-Way Analysis of Variance	329	(52)
Example---Display Panel Data	329	(7)
Statistical Model	336	(1)
Main Effects and Interactions	336	(2)
Two-Way Interaction Plot	338	(1)
Sums of Squares in the Two-Way ANOVA Table	339	(1)
Treatment and Blocking Factors	339	(2)
Fixed and Random Effects	341	(1)
Randomized Complete Block Designs	342	(2)
Example---The Blood Plasma Data	344	(2)
Random Effects Models and Mixed Models	346	(1)
Introduction to Nesting	347	(2)
Example---Workstation Data	347	(2)
Example---Display Panel Data---Continued	349	(4)
Example---The Rhizobium Data	353	(18)
First Rhizobium Experiment: Alfalfa Plants	354	(1)
Second Rhizobium Experiment: Clover Plants	354	(1)
Initial Plots	355	(2)
Alfalfa Analysis	357	(5)
Clover Analysis	362	(9)
Models Without Interaction	371	(1)
Example---Animal Feed Data	372	(2)
Exercises	374	(5)
Appendix: Computation for the Analysis of Variance	379	(2)
Design of Experiments---Factorial Designs	381	(48)
A Three-Way ANOVA---Muscle Data	381	(8)
Latin Square Designs	389	(7)
Example---Latin Square	390	(6)
Simple Effects for Interaction Analyses	396	(5)
Example---The filmcoat Data	397	(4)
Nested Factorial Experiment	401	(12)
Example---Gunload Data	401	(9)
Example---Turkey Data (continued)	410	(3)
Specification of Model Formulas	413	(4)
Squential and Conditional Tests	417	(4)
SAS Types of Sums of Squares	418	(1)
Example---Application to Body Fat Data	419	(2)
Exercises	421	(6)
Appendix: Orientation for Boxplots	427	(2)
Design of Experiments---Complex Designs	429	(58)
Confounding	429	(2)
Split Plot Designs	431	(1)
Example---Yates Oat Data	432	(10)
Alternate Specification	439	(1)
Polynomial Effects for Nitrogen	440	(2)
Introduction to Fractional Factorial Designs	442	(6)
Example---28-2 Design	442	(2)
Example---25-1 Design	444	(4)
Introduction to Crossover Designs	448	(4)
Example---Apple Tree Data	452	(14)
Models in Table 14.17	453	(5)
Multiple Comparisons	458	(2)
Models in Figure 14.5	460	(6)
Example---testscore.dat	466	(6)
The Tukey One Degree of Freedom for Nonadditivity	472	(11)
Example---Crash Data	472	(9)
Theory	481	(2)
Exercises	483	(4)
Bivariate Statistics---Discrete Data	487	(24)
Two-Dimensional Contingency Tables---Chi-Square Analysis	487	(5)
Example---Drunkenness Data	487	(3)
Chi-Square Analysis	490	(2)
Two-Dimensional Contingency Tables---Fisher's Exact Test	492	(3)
Example---Do Juvenile Delinquents Eschew Wearing Eyeglasses?	493	(2)
Simpson's Paradox	495	(3)
Relative Risk and Odds Ratios	498	(5)
Glasses (Again)	499	(1)
Large Sample Approximations	500	(1)
Example---Treating Cardiac Arrest with Therapeutic Hypothermia	500	(3)
Retrospective and Prospective Studies	503	(1)
Mantel-Haenszel Test	504	(2)
Example---Salk Polio Vaccine	506	(2)
Exercises	508	(3)
Nonparametrics	511	(16)
Introduction	511	(1)
Sign Test for the Location of a Single Population	512	(2)
Comparing the Locations of Paired Populations	514	(6)
Sign Test	514	(2)
Wilcoxon Signed-Ranks Test	516	(4)
Mann-Whitney Test for Two Independent Samples	520	(3)
Kruskal-Wallis Test for Comparing the Locations of at Least Three Populations	523	(3)
Exercises	526	(1)
Logistic Regression	527	(38)
Example---The Space Shuttle Challenger Disaster	529	(8)
Graphical Display	530	(3)
Numerical Display	533	(4)
Estimation	537	(3)
Example---Budworm Data	540	(2)
Example---Lymph Nodes	542	(11)
Data	542	(1)
Data Analysis	543	(3)
Additional Techniques	546	(7)
Diagnostics	553	(1)
Numerical Printout	553	(1)
Graphics	553	(3)
Conditioned Scatterplots	553	(1)
Scatterplot Matrix	554	(1)
Common Scaling in Comparable Plots	554	(1)
Functions of Predicted Values	555	(1)
Model Specification	556	(1)
S-Plus	556	(1)
SAS	557	(1)
Fitting Models When the Response Is a Sample Proportion	557	(1)
LogXact	558	(1)
Exercises	558	(7)
Time Series Analysis	565	(58)
Introduction	565	(2)
The ARIMA Approach to Time Series Modeling	567	(3)
Autocorrelation	570	(1)
Autocorrelation Function (ACF)	570	(1)
Partial Autocorrelation Function (PACF)	570	(1)
Analysis Steps	571	(2)
Some Algebraic Development, Including Forecasting	573	(2)
The General ARIMA Model	573	(1)
Special case---The AR(1) model	574	(1)
Special Case---The MA(1) Model	575	(1)
Graphical Displays for Time Series Analysis	575	(5)
Models with Seasonal Components	580	(2)
Multiplicative Seasonal ARIMA Models	580	(1)
Example---co2 ARIMA(0, 1 ,1) x (0, 1, 1)12 Model	581	(1)
Determining the Seasonal AR and MA Parameters	581	(1)
Example of a Seasonal Model---The Monthly co2 Data	582	(7)
Identification of the Model	582	(2)
Parameter Estimation and Diagnostic Checking	584	(5)
Forecasting	589	(1)
Exercises	589	(29)
Appendix: Graphical Displays for Time Series Analysis	618	(5)
Characteristics of This Presentation of the Time Series Plot	619	(1)
Characteristics of This Presentation of the Sample ACF and PACF Plots	619	(1)
Construction of Graphical Displays	620	(1)
User Functions Written for S-Plus	620	(3)
A Software	623	(8)
Statistical Software	623	(1)
Text Editing Software	624	(1)
Emacs	624	(1)
Microsoft Word	625	(1)
Word Processing Software	625	(1)
LaTeX	626	(1)
Microsoft Word	626	(1)
Graphics Display Software	626	(1)
Operating Systems	627	(1)
Mathematical Fonts	627	(1)
Directory Structure	627	(4)
Home Directory	627	(2)
HH Book Online Files	629	(2)
B S-Plus and R	631	(18)
Create Your Working Directory and Make the HH Library Available	632	(5)
Windows---Both S-Plus and R	632	(1)
Windows and S-Plus	633	(1)
Windows and R	634	(1)
Unix---Both S-Plus and R	635	(1)
Unix and S-Plus	636	(1)
Unix and R	636	(1)
Using S-Plus and R with HH	637	(1)
S-Plus for Windows---Recommended Options	638	(2)
HH Library Functions	640	(1)
Learning the S Language	640	(3)
S Language Style	643	(2)
S-Plus Inexplicable Error Messages	645	(2)
Using S-Plus with Emacs and ESS	647	(1)
Constructing the HH Library with S-Plus and R	647	(2)
C SAS	649	(8)
Make the HH Library Available	649	(3)
Windows	649	(1)
Unix	650	(2)
Using SAS with HH	652	(3)
Reading HH Datasets	652	(1)
Any Other Data Files	653	(1)
ASCII Data Files with Tab Characters	653	(1)
Windows and Unix EOL (End-of-Line) Conventions	654	(1)
Macros	655	(1)
Learning the SAS Language	655	(1)
SAS Coding Conventions	656	(1)
D Probability Distributions	657	(6)
Common Probability Distributions with S-Plus and SAS Commands	657	(4)
An Example Involving Calculations with the Binomial Distribution	661	(1)
Noncentral Probability Distributions	661	(2)
E Editors	663	(20)
Working Style	664	(1)
Typography	665	(2)
Emacs and ESS	667	(6)
ESS	670	(1)
Mouse and Keyboard	671	(1)
Learning Emacs	672	(1)
Requirements	672	(1)
Microsoft Word	673	(1)
Learning Word	673	(1)
Requirements	673	(1)
Microsoft Excel	674	(3)
Database Management	674	(1)
Organizing Calculations	674	(1)
Excel as a Statistical Calculator	674	(3)
Exhortations, Some of Which Are Writing Style	677	(6)
Writing Style	677	(1)
Programming Style and Common Errors	678	(1)
Presentation of Results	679	(4)
F Mathematics Preliminaries	683	(20)
Algebra Review	683	(2)
Elementary Differential Calculus	685	(1)
An Application of Differential Calculus	686	(1)
Topics in Matrix Algebra	687	(13)
Elementary Operations	688	(2)
Linear Independence	690	(1)
Rank	691	(1)
Quadratic Forms	692	(1)
Orthogonal Transformations	692	(1)
Orthogonal Basis	693	(1)
Matrix Factorization---QR	693	(2)
Matrix Factorization---Cholesky	695	(1)
Orthogonal Polynomials	695	(1)
Projection Matrices	695	(1)
Geometry of Matrices	695	(1)
Eigenvalues and Eigenvectors	696	(2)
Singular Value Decomposition	698	(1)
Generalized Inverse	698	(1)
Solving Linear Equations	699	(1)
Combinations and Permutations	700	(1)
Factorial	700	(1)
Permutations	700	(1)
Combinations	700	(1)
Exercises	701	(2)
G Graphs Based on Cartesian Products	703	(6)
Structured Sets of Graphs	704	(1)
Cartesian Products	704	(1)
Trellis Paradigm	704	(1)
Scatterplot Matrices: splom and xysplom	705	(1)
Cartesian Products of Sets of Functions	706	(1)
Graphs Requiring Multiple Calls to xysplom	706	(1)
Asymmetric Roles for the Row and Column Sets	707	(1)
Rotated Plots	707	(1)
Squared Residual Plots	708	(1)
Alternate Presentations	708	(1)
References	709	(12)
List of Datasets	721	(2)
Index	723