Applied Statistics : Using SPSS, STATISTICA, and MATLAB

by Marques De Sa, Joaquim P.; De Sa, J. P. Marques; Sa, J. P. Marques De

• ISBN13: 9783540011569
• ISBN10: 3540011560
• Format: Hardcover
• Copyright: 2003-08-01
• Publisher: Springer Verlag

Summary

Aimed at students, professionals and research workers who need to apply statistical analysis to a large variety of practical problems using SPSS, MATLAB and STATISTICA, this text provides a comprehensive coverage of the main statistical analysis topics important for practical applications such as data description, statistical inference, classification and regression, factor analysis, survival data and directional statistics. The relevant notions and methods are explained concisely, illustrated with practical examples using real data, presented with the distinct intention of clarifying sensible practical issues. The solutions presented in the examples are obtained with one of the software packages in a pedagogical way. It provides guidance on how to use SPSS, MATALB and STATISTICA in statistical analysis applications without having to delve in the manuals. The accompanying CD-Rom includes several specific software tools for the topics described in the book, including a set of MATLAB functions for directional statistics as well as the data sets used in the examples and exercises covering a broad spectrum of areas from engineering, medicine, biology, psychology, economy, geology, and astronomy.

Table of Contents

Preface	vii
Symbols and Abbreviations	xvii
1 Introduction	1	(20)
1.1 Deterministic Data and Random Data	1	(4)
1.2 Population, Sample and Statistics	5	(3)
1.3 Random Variables	8	(2)
1.4 Probabilities and Distributions	10	(3)
1.4.1 Discrete Variables	10	(2)
1.4.2 Continuous Variables	12	(1)
1.5 Beyond a Reasonable Doubt	13	(4)
1.6 STATISTICA, SPSS and MATLAB	17	(4)
2 Presenting and Summarising the Data	21	(46)
2.1 Preliminaries	21	(7)
2.1.1 Reading in the Data	21	(4)
2.1.2 Operating with the Data	25	(3)
2.2 Presenting the Data	28	(17)
2.2.1 Counts and Bar Graphs	28	(7)
2.2.2 Frequencies and Histograms	35	(4)
2.2.3 Multivariate Tables, Scatter Plots and 3D Plots	39	(4)
2.2.4 Categorised Plots	43	(2)
2.3 Summarising the Data	45	(18)
2.3.1 Measures of Location	45	(3)
2.3.2 Measures of Spread	48	(2)
2.3.3 Measures of Shape	50	(3)
2.3.4 Measures of Association for Continuous Variables	53	(2)
2.3.5 Measures of Association for Ordinal Variables	55	(4)
2.3.6 Measures of Association for Nominal Variables	59	(4)
Exercises	63	(4)
3 Estimating Data Parameters	67	(18)
3.1 Point Estimation and Interval Estimation	67	(4)
3.2 Estimating a Mean	71	(6)
3.3 Estimating a Proportion	77	(3)
3.4 Estimating a Variance	80	(1)
3.5 Estimating a Variance Ratio	81	(2)
Exercises	83	(2)
4 Parametric Tests of Hypotheses	85	(56)
4.1 Hypothesis Test Procedure	85	(4)
4.2 Test Errors and Test Power	89	(6)
4.3 Inference on One Population	95	(5)
4.3.1 Testing a Mean	95	(4)
4.3.2 Testing a Variance	99	(1)
4.4 Inference on Two Populations	100	(13)
4.4.1 Testing a Correlation	100	(2)
4.4.2 Comparing Two Variances	102	(3)
4.4.3 Comparing Two Means	105	(8)
4.5 Inference on More Than Two Populations	113	(24)
4.5.1 Introduction to the Analysis of Variance	113	(1)
4.5.2 One-Way ANOVA	114	(13)
4.5.3 Two-Way ANOVA	127	(10)
Exercises	137	(4)
5 Non-Parametric Tests of Hypotheses	141	(50)
5.1 Inference on One Population	142	(16)
5.1.1 The Runs Test	142	(2)
5.1.2 The Binomial Test	144	(4)
5.1.3 The Chi-Square Goodness of Fit Test	148	(4)
5.1.4 The Kolmogorov-Smirnov Goodness of Fit Test	152	(4)
5.1.5 The Lilliefors Test for Normality	156	(1)
5.1.6 The Shapiro-Wilk Test for Normality	156	(2)
5.2 Contingency Tables	158	(11)
5.2.1 The 2x2 Contingency Table	158	(4)
5.2.2 The rxc Contingency Table	162	(2)
5.2.3 The Chi-Square Test of Independence	164	(2)
5.2.4 Measures of Association Revisited	166	(3)
5.3 Inference on Two Populations	169	(11)
5.3.1 Tests for Two Independent Samples	169	(5)
5.3.2 Tests for Two Paired Samples	174	(6)
5.4 Inference on More Than Two Populations	180	(6)
5.4.1 The Kruskat-Wallis Test for Independent Samples	180	(3)
5.4.2 The Friedmann Test for Paired Samples	183	(2)
5.4.3 The Cochran Q test	185	(1)
Exercises	186	(5)
6 Statistical Classification	191	(46)
6.1 Decision Regions and Functions	191	(2)
6.2 Linear Discriminants	193	(9)
6.2.1 Minimum Euclidian Distance Discriminant	193	(3)
6.2.2 Minimum Mahalanobis Distance Discriminant	196	(6)
6.3 Bayesian Classification	202	(12)
6.3.1 Bayes Rule for Minimum Risk	202	(6)
6.3.2 Normal Bayesian Classification	208	(3)
6.3.3 Dimensionality Ratio and Error Estimation	211	(3)
6.4 The ROC Curve	214	(6)
6.5 Feature Selection	220	(4)
6.6 Classifier Evaluation	224	(3)
6.7 Tree Classifiers	227	(6)
Exercises	233	(4)
7 Data Regression	237	(46)
7.1 Simple Linear Regression	238	(14)
7.1.1 Simple Linear Regression Model	238	(1)
7.1.2 Estimating the Regression Function	238	(5)
7.1.3 Inferences in Regression Analysis	243	(5)
7.1.4 ANOVA Tests	248	(4)
7.2 Multiple Regression	252	(11)
7.2.1 General Linear Regression Model	252	(1)
7.2.2 General Linear Regression in Matrix Terms	253	(3)
7.2.3 Inferences on Regression Parameters	256	(1)
7.2.4 ANOVA and Extra Sums of Squares	257	(4)
7.2.5 Polynomial Regression and Other Models	261	(2)
7.3 Building and Evaluating the Regression Model	263	(10)
7.3.1 Building the Model	263	(2)
7.3.2 Evaluating the Model	265	(2)
7.3.3 Case Study	267	(6)
7.4 Regression Through the Origin	273	(1)
7.5 Ridge Regression	274	(2)
7.6 Logit and Probit Models	276	(5)
Exercises	281	(2)
8 Data Structure Analysis	283	(22)
8.1 Principal Components	283	(6)
8.2 Dimensional Reduction	289	(3)
8.3 Principal Components of Correlation Matrices	292	(7)
8.4 Factor Analysis	299	(3)
Exercises	302	(3)
9 Survival Analysis	305	(22)
9.1 Survivor Function and Hazard Function	305	(1)
9.2 Non-Parametric Analysis of Survival Data	306	(9)
9.2.1 The Life Table Analysis	306	(5)
9.2.2 The Kaplan-Meier Analysis	311	(2)
9.2.3 Statistics for Non-Parametric Analysis	313	(2)
9.3 Comparing Two Groups of Survival Data	315	(3)
9.4 Models for Survival Data	318	(6)
9.4.1 The Exponential Model	318	(2)
9.4.2 The Weibull Model	320	(2)
9.4.3 The Cox Regression Model	322	(2)
Exercises	324	(3)
10 Directional Data	327	(26)
10.1 Representing Directional Data	327	(4)
10.2 Descriptive Statistics	331	(3)
10.3 The von Mises Distributions	334	(4)
10.4 Assessing the Distribution of Directional Data	338	(8)
10.4.1 Graphical Assessment of Uniformity	338	(2)
10.4.2 The Rayleigh Test of Uniformity	340	(2)
10.4.3 The Watson Goodness of Fit Test	342	(2)
10.4.4 Assessing the von Misesness of Spherical Distributions	344	(2)
10.5 Tests on von Mises Distributions	346	(1)
10.5.1 One-Sample Mean Test	346	(1)
10.5.2 Mean Test for Two Independent Samples	346	(1)
10.6 Non-Parametric Tests	347	(3)
10.6.1 The Uniform Scores Test for Circular Data	347	(1)
10.6.2 The Watson Test for Spherical Data	348	(2)
10.6.3 Testing Two Paired Samples	350	(1)
Exercises	350	(3)
Appendix A - Short Survey on Probability Theory	353	(28)
A.1 Basic Notions	353	(3)
A.1.1 Events and Frequencies	353	(1)
A.1.2 Probability Axioms	354	(2)
A.2 Conditional Probability and Independence	356	(2)
A.2.1 Conditional Probability and Intersection Rule	356	(1)
A.2.2 Independent Events	356	(2)
A.3 Compound Experiments	358	(1)
A.4 Bayes' Theorem	359	(1)
A.5 Random Variables and Distributions	360	(4)
A.5.1 Definition of Random Variable	360	(1)
A.5.2 Distribution and Density Functions	361	(2)
A.5.3 Transformation of a Random Variable	363	(1)
A.6 Expectation, Variance and Moments	364	(4)
A.6.1 Definitions and Properties	364	(3)
A.6.2 Moment-Generating Function	367	(1)
A.6.3 Chebyshev Theorem	368	(1)
A.7 The Binomial and Normal Distributions	368	(4)
A.7.1 The Binomial Distribution	368	(1)
A.7.2 The Laws of Large Numbers	369	(1)
A.7.3 The Normal Distribution	370	(2)
A.8 Multivariate Distributions	372	(9)
A.8.1 Definitions	372	(2)
A.8.2 Moments	374	(1)
A.8.3 Conditional Densities and Independence	375	(2)
A.8.4 Sums of Random Variables	377	(1)
A.8.5 Central Limit Theorem	378	(3)
Appendix B - Distributions	381	(24)
B.1 Discrete Distributions	381	(8)
B.1.1 Bernoulli Distribution	381	(1)
B.1.2 Uniform Distribution	382	(1)
B.1.3 Geometric Distribution	383	(1)
B.1.4 Hypergeometris Distribution	384	(1)
B.1.5 Binomial Distribution	385	(1)
B.1.6 Multinomial Distribution	386	(2)
B.1.7 Poisson Distribution	388	(1)
B.2 Continuous Distributions	389	(16)
B.2.1 Uniform Distribution	389	(2)
B.2.2 Normal Distribution	391	(1)
B.2.3 Exponential Distribution	392	(2)
B.2.4 Weibull Distribution	394	(1)
B.2.5 Gamma Distribution	395	(1)
B.2.6 Beta Distribution	396	(2)
B.2.7 Chi-Square Distribution	398	(1)
B.2.8 Student's t Distribution	399	(2)
B.2.9 F Distribution	401	(1)
B.2.10 Von Mises Distributions	402	(3)
Appendix C - Point Estimation	405	(4)
C.1 Definitions	405	(1)
C.2 Estimation of Mean and Variance	406	(3)
Appendix D - Tables	409	(10)
D.1 Binomial Distribution	409	(6)
D.2 Normal Distribution	415	(1)
D.3 Student's t Distribution	416	(1)
D.4 Chi-Square Distribution	417	(1)
D.5 Critical Values for the F Distribution	418	(1)
Appendix E - Datasets	419	(18)
E.1 Breast Tissue	419	(1)
E.2 arSale	419	(1)
E.3 Cells	420	(1)
E.4 Clays	420	(1)
E.5 Cork Stoppers	421	(1)
E.6 CTG	422	(1)
E.7 Culture	423	(1)
E.8 Fatigue	423	(1)
E.9 FHR	424	(1)
E.10 FHR-Apgar	424	(1)
E.11 Firms	425	(1)
E.12 Flow Rate	425	(1)
E.13 Foetal Weight	425	(1)
E.14 Forest Fires	426	(1)
E.15 Freshmen	426	(1)
E.16 Heart Valve	427	(1)
E.17 Infarct	428	(1)
E.18 Joints	428	(1)
E.19 Metal Firms	429	(1)
E.20 Meteo	429	(1)
E.21 Moulds	429	(1)
E.22 Neonatal	430	(1)
E.23 Programming	430	(1)
E.24 Rocks	431	(1)
E.25 Signal & Noise	431	(1)
E.26 Soil Pollution	432	(1)
E.27 Stars	432	(1)
E.28 Stock Exchange	433	(1)
E.29 VCG	434	(1)
E.30 Wave	434	(1)
E.31 Weather	434	(1)
E.32 Wines	435	(2)
Appendix F - Tools	437	(2)
F.1 MATLAB Functions	437	(1)
F.2 Tools EXCEL File	438	(1)
F.3 SCSIZE Program	438	(1)
References	439