Applied Statistics Using SPSS, STATISTICA, MATLAB and R

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390 10 Directional Data * 2 z = ( 1−1 /( 2 n)) z + z /( 10 n) , 10.19 it can be proven that the distribution of z * is asymptotically 2 χ 3 with an error decreasing as 1/n (Mardia KV, Jupp PE, 2000). The Rayleigh test is implemented in MATLAB and R function rayleigh (see Commands 10.5) Example 10.11 Q: Apply the Rayleigh test to the wind direction WDF data of the Weather dataset and to the measurement data M1 of the Soil Pollution dataset. A: Denoting by wdf and m1 the matrices for the datasets, the probability values under the null hypothesis are obtained in MATLAB as follows: » p=rayleigh(wdf) p = 0.1906 » p=rayleigh(m1) p = 0 Thus, we accept the null hypothesis of uniformity at the 5% level for the WDF data, and reject it for the soil pollution M1 data (see Figure 10.9). X Figure 10.9. Measurement set M1 (negative gradient of Pb-tetraethyl concentration in the soil) of the Soil Pollution dataset. Z Y
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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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Page 766: 1. The Log-Rank Test. 9.3 Comparing
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Page 786: 10 Directional Data The analysis an
Page 790: 10.1 Representing Directional Data
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Page 798: 10.2 Descriptive Statistics 381 com
Page 802: 10.3 The von Mises Distributions 38
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Page 820: 392 10 Directional Data 10.4.3 The
Page 824: 394 10 Directional Data Example 10.
Page 828: 396 10 Directional Data 10.5.2 Mean
Page 832: 398 10 Directional Data Similar res
Page 836: 400 10 Directional Data Exercises 1
Page 840: Appendix A - Short Survey on Probab
Page 844: A.1 Basic Notions 405 corresponding
Page 848: A.2 Conditional Probability and Ind
Page 852: A. 4 Bayes ’ Theorem 409 The firs
Page 856: A.5 Random Variables and Distributi
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n [ X ] = ∑ i= 1 A.6 Expectation,
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A.7 The Binomial and Normal Distrib
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A.7 The Binomial and Normal Distrib
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The following results are worth men
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A.8.2 Moments A.8 Multivariate Dist
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For the d-variate case, this genera
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0.25 0.2 0.15 0.1 0.05 p(x) A.8 Mul
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432 Appendix B - Distributions A: T
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436 Appendix B - Distributions For
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440 Appendix B - Distributions Dist
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442 Appendix B - Distributions 0.45
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444 Appendix B - Distributions B.2.
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448 Appendix B - Distributions B.2.
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450 Appendix B - Distributions Dist
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452 Appendix B - Distributions 1 0.
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456 Appendix C - Point Estimation T
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458 Appendix C - Point Estimation
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460 Appendix D - Tables p n k 0.05
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466 Appendix D - Tables D.3 Student
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468 Appendix D - Tables D.5 Critica
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470 Appendix E - Datasets The varia
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472 Appendix E - Datasets E.6 CTG T
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474 Appendix E - Datasets E.9 FHR T
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476 Appendix E - Datasets E.14 Fore
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478 Appendix E - Datasets DATE_REOP
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480 Appendix E - Datasets CG: Conic
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482 Appendix E - Datasets E.26 Soil
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484 Appendix E - Datasets E.29 VCG
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Appendix F - Tools F.1 MATLAB Funct
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Appendix F - Tools 489 r
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References Chapters 1 and 2 Anderso
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References 493 Gardner MJ, Altman D
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References 495 Raudys S, Pikelis V
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References 497 Mardia KV, Jupp PE (
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500 Index 5.9 (two paired samples t
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502 Index H hazard function, 353 ha
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504 Index S sample, 5 mean, 416 siz
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Applied Statistics Using SPSS, STATISTICA, MATLAB and R

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