Applied Statistics Using SPSS, STATISTICA, MATLAB and R

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De Moivre’s Theorem, 420 decile, 60 decision function, 223 region, 223 rule, 223, 261 threshold, 112 tree, 259 declination, 375 degrees of freedom, 63, 96, 448, 451 deleted residuals, 307 density function, 13, 412 dependent samples, 133 dimensional reduction, 330, 337 dimensionality ratio, 243 discordant pair, 71 discrete random variable, 411 distribution Bernoulli, 431 Beta, 446 binomial, 12, 93, 419, 435 chi-square, 96, 180, 448 circular normal, 452 exponential, 353, 367, 442 F, 97, 129, 146, 451 function, 11, 13, 411 Gamma, 445 Gauss, 13, 420, 441 geometric, 433 hypergeometric, 365, 434 multimodal, 60 multinomial, 179, 436 normal, 13, 420, 441 Poisson, 438 Rayleigh, 445 Student’s t, 86, 118, 122, 449 uniform, 413, 432, 439 von Mises, 383, 452 von Mises-Fisher, 383, 453 Weibull, 353, 369, 444 dynamic search, 254 E effects, 132, 142 additive, 157 interaction, 159 eigenvalue, 331, 393 eigenvector, 331, 393 elevation, 375 empirical distribution, 183 equality of variance, 143 ergodic process, 8 error, 272 bias, 256 experimental, 143, 157, 159 function, 421 mean square, 144 probability, 242 proportional reduction of, 75 root mean square, 63 standard deviation, 244 sum of squares, 143, 275 test set, 243 training set, 230, 243 type I, 113 type II, 115 variance, 256 expectation, 414 explanatory variable, 371 exponential regression, 301 exposed group, 364 extra sums of squares, 296 F factor (R), 150 factor loadings, 339, 347 factorial experiment, 158 factors, 132, 142, 156 failure rate, 353 feature selection, 253 Fisher coefficients, 230 fixed factors, 142 forward search, 253, 304 frequency, 7 absolute, 11, 40, 59, 403 relative, 11, 40, 403 table, 48 full model, 287, 299 G Index 501 gamma function, 445 gamma statistic, 198 Gauss’ approximation formulae, 417 Gaussian distribution, 420 generalised variance, 332 Gini index, 263 Goodman and Kruskal lambda, 199 goodness of fit, 179, 183, 187 grand total, 160 Greenwood’s formula, 362 group variable, 132 Guttman-Kaiser criterion, 337
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Applied Statistics Using SPSS, STAT
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E d itors Prof. Dr. Joaquim P. Marq
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Contents Preface to the Second Edit
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Contents ix 5.2.3 The Chi-Square Te
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Contents xi Appendix A - Short Surv
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Contents xiii E.26 Soil Pollution .
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Preface to the First Edition This b
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Symbols and Abbreviations Sample Se
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|A| determinant of matrix A tr(A) t
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Σ covariance matrix x arithmetic m
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1 Introduction 1.1 Deterministic Da
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18 h 16 14 12 10 8 6 4 2 0 1.1 Dete
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1.2 Population, Sample and Statisti
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Table 1.3 1.2 Population, Sample an
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Table 1.4 1.3 Random Variables 9 Da
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1.4 Probabilities and Distributions
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1.5 Beyond a Reasonable Doubt... 13
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1.5 Beyond a Reasonable Doubt... 15
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1.6 Statistical Significance and Ot
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1.8 Software Tools 19 book we will
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1.8 Software Tools 21 In the follow
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1.8 Software Tools 23 illustrates t
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1.8 Software Tools 25 On-line help
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1.8 Software Tools 27 Figure 1.12.
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2 Presenting and Summarising the Da
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2.1 Preliminaries 31 The data can t
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» meteo=[ 181 143 36 39 37 % Pasti
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2.1 Preliminaries 35 are interested
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2.1 Preliminaries 37 Besides the in
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2.2 Presenting the Data 39 Sorting
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2.2 Presenting the Data 41 In Table
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2.2 Presenting the Data 43 With SPS
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2.2 Presenting the Data 45 Figure 2
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2.2 Presenting the Data 47 Figure 2
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2.2 Presenting the Data 49 Let X de
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2.2 Presenting the Data 51 Commands
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2.2 Presenting the Data 53 A: The c
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2.2 Presenting the Data 55 The s, c
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2.2 Presenting the Data 57 histogra
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2.3 Summarising the Data 59 type da
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2.3 Summarising the Data 61 delimit
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2.3 Summarising the Data 63 The sam
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Note that: 2.3 Summarising the Data
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where sXY, the sample covariance of
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2.3 Summarising the Data 69 STATIST
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2.3 Summarising the Data 71 A: The
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2.3.6 Measures of Association for N
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2.3 Summarising the Data 75 with th
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Exercises 77 A: We use the N, S and
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Exercises 79 2.13 Determine the box
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3 Estimating Data Parameters Making
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3.1 Point Estimation and Interval E
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3.2 Estimating a Mean 85 In Chapter
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3.2 Estimating a Mean 87 There are
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3.2 Estimating a Mean 89 A: Using M
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3.2 Estimating a Mean 91 Figure 3.5
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3.3 Estimating a Proportion 93 esti
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3.4 Estimating a Variance 95 is to
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3.5 Estimating a Variance Ratio 97
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3.6 Bootstrap Estimation 99 i. F df
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3.6 Bootstrap Estimation 101 about
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3.6 Bootstrap Estimation 103 The bi
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3.6 Bootstrap Estimation 105 In the
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Exercises 107 In order to obtain bo
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Exercises 109 3.14 Consider the CTG
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112 4 Parametric Tests of Hypothese
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5 Non-Parametric Tests of Hypothese
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5.1 Inference on One Population 173
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s = npq = 224× 0. 75× 0. 25 = 6.4
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5.1.3 The Chi-Square Goodness of Fi
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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 F
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5.1.5 The Lilliefors Test for Norma
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5.2 Contingency Tables 189 fewer mi
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2 1 5.2 Contingency Tables 191 degr
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5.2 Contingency Tables 193 An alter
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5.2 Contingency Tables 195 male and
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5.2 Contingency Tables 197 first ca
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5.2 Contingency Tables 199 very low
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5.3.1 Tests for Two Independent Sam
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5.3 Inference on Two Populations 20
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Example 5.19 5.3 Inference on Two P
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3 ( N − N ) 5.4 Inference on More
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5.4 Inference on More Than Two Popu
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5.4 Inference on More Than Two Popu
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Exercises 219 5.7 Several previous
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Exercises 221 5.23 Run the non-para
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6 Statistical Classification Statis
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x 2 o o o o o o o o oo o o o o o o
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6.2 Linear Discriminants 227 Figure
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6.2 Linear Discriminants 229 Figure
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6.2 Linear Discriminants 231 Let us
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Table 6.5. Summary of minimum dista
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6.3 Bayesian Classification 235 Not
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6.3 Bayesian Classification 237 Fig
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6.3 Bayesian Classification 239 Let
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6.3 Bayesian Classification 241 Not
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0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15
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6.3 Bayesian Classification 245 For
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Reality A N Decision A N a b c d 6.
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6.4 The ROC Curve 249 Figure 6.17.
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6.4 The ROC Curve 251 In order to o
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6.5 Feature Selection 253 A: The RO
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6.5 Feature Selection 255 comfortab
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6.6 Classifier Evaluation 257 Resub
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259 A: Table 6.12 shows the leave-o
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6.7 Tree Classifiers 261 Figure 6.2
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6.7 Tree Classifiers 263 or not a g
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6.7 Tree Classifiers 265 The classi
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6.7 Tree Classifiers 267 The classi
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Exercises 269 6.2 Repeat the previo
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7 Data Regression An important obje
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7.1.2 Estimating the Regression Fun
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7.1 Simple Linear Regression 275 Fi
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2 2 2 7.1 Simple Linear Regression
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7.1 Simple Linear Regression 279 Co
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Example 7.3 7.1 Simple Linear Regre
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7.1 Simple Linear Regression 283 Th
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7.1 Simple Linear Regression 285 Fi
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7.1 Simple Linear Regression 287 Le
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7.2 Multiple Regression 7.2.1 Gener
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7.2 Multiple Regression 291 For the
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YYˆ = ∑ ∑ ( y ( y − y)( yˆ
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7.2 Multiple Regression 295 Figure
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7.2 Multiple Regression 297 Table 7
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7.2.5.1 Tests for Regression Coeffi
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The Yi can also be linearly modelle
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3000 2000 1000 0 -1000 -2000 Raw Re
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7.3 Building and Evaluating the Reg
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There are other ways to detect outl
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a 4 3 2 1 0 -1 -2 -3 Expected Norma
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Example 7.19 7.4 Regression Through
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6 y 4 2 0 -2 -4 -6 -8 -10 x 7.5 Rid
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7.5 Ridge Regression 319 The b vect
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Example 7.20 7.5 Ridge Regression 3
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7.5 Logit and Probit Models 323 Let
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7.5 Logit and Probit Models 325 sec
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Exercises 327 Commands 7.7. SPSS an
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8 Data Structure Analysis In the pr
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8.1 Principal Components 331 where
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8.1 Principal Components 333 » % E
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8.1 Principal Components 335 A: The
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8.2 Dimensional Reduction 8.2 Dimen
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12000 10000 8000 6000 4000 2000 eig
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0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 U2 8.
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8.3 Principal Components of Correla
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8.3 Principal Components of Correla
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8.4 Factor Analysis 8.4 Factor Anal
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8.4 Factor Analysis 349 The main be
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Exercises 351 c) The scatter plot o
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9 Survival Analysis In medical stud
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9.2 Non-Parametric Analysis of Surv
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1. The Log-Rank Test. 9.3 Comparing
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9.4 Models for Survival Data 367 Th
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9.4 Models for Survival Data 369 ST
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9.4 Models for Survival Data 371 Ex
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1.0 0.9 0.8 0.7 0.6 0.5 0.4 Cumulat
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10 Directional Data The analysis an
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10.1 Representing Directional Data
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10.1 Representing Directional Data
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10.2 Descriptive Statistics 381 com
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10.3 The von Mises Distributions 38
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10.3 The von Mises Distributions 38
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10.4 Assessing the Distribution of
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Example 10.10 10.4 Assessing the Di
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10.5 Tests on von Mises Distributio
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10.6 Non-Parametric Tests 10.6 Non-
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10.6 Non-Parametric Tests 399 Examp
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Exercises 401 10.8 Compare the two
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404 Appendix A - Short Survey on Pr
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Appendix B - Distributions B.1 Disc
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51 50 52 − ( k −1) 1 1 p ( k) =
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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 h 100
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B.1 Discrete Distributions 437 Prob
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2. b n, p 0.4 0.35 0.3 0.25 0.2 0.1
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B.2.2 Normal Distribution B.2 Conti
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Distribution function: ∫ − = =
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Properties: 1. w1,1/λ(x) ≡ ελ(
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Properties: 1. β1,1(x) ≡ u(x). 2
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B.2 Continuous Distributions 449 Pr
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B.2.9 F Distribution B.2 Continuous
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B.2 Continuous Distributions 453 ci
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Appendix C - Point Estimation In Ap
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dL( n−1 n−2 p) = q dp − ( n
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Appendix D - Tables D.1 Binomial Di
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Appendix D - Tables 461 p n k 0.05
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Appendix D - Tables 463 p n k 0.05
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D.2 Normal Distribution The followi
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D.4 Chi-Square Distribution Appendi
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Appendix E - Datasets Datasets incl
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Appendix E - Datasets 471 Age: Geol
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Page 994: E.24 Rocks Appendix E - Datasets 48
Page 998: Appendix E - Datasets 483 Source: W
Page 1002: Appendix E - Datasets 485 Data 2: W
Page 1006: 488 Appendix F - Tools t=scattermx(
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Page 1014: 492 References Nie NH, Hull CH, Jen
Page 1018: 494 References Chapter 6 Argentiero
Page 1022: 496 References Loehlin JC (1987), L
Page 1026: Index A accuracy, 82 actuarial tabl
Page 1032: 502 Index H hazard function, 353 ha
Page 1036: 504 Index S sample, 5 mean, 416 siz
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