Applied Statistics Using SPSS, STATISTICA, MATLAB and R

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296 7 Data Regression 7.2.5 ANOVA and Extra Sums of Squares The simple ANOVA test presented in 7.1.4, corresponding to the decomposition of the total sum of squares as expressed by formula 7.24, can be generalised in a straightforward way to the multiple regression model. Example 7.14 Q: Apply the simple ANOVA test to the foetal weight regression in Example 7.13. A: Table 7.2 lists the results of the simple ANOVA test, obtainable with SPSS STATISTICA, or R, for the foetal weight data, showing that the regression model is statistically significant ( p ≈ 0). Table 7.2. ANOVA test for Example 7.13. Sum of Squares df Mean Squares F p SSR 128252147 3 42750716 501.9254 0.00 SSE 34921110 410 85173 SST 163173257 It is also possible to apply the ANOVA test for lack of fit in the same way as was done in 7.1.4. However, when there are several predictor values playing their influence in the regression model, it is useful to assess their contribution by means of the so-called extra sums of squares. An extra sum of squares measures the marginal reduction in the error sum of squares when one or several predictor variables are added to the model. We now illustrate this concept using the foetal weight data. Table 7.3 shows the regression lines, SSE and SSR for models with one, two or three predictors. Notice how the model with (BPD,CP) has a decreased error sum of squares, SSE, when compared with either the model with BPD or CP alone, and has an increased regression sum of squares. The same happens to the other models. As one adds more predictors one expects the linear fit to improve. As a consequence, SSE and SSR are monotonic decreasing and increasing functions, respectively, with the number of variables in the model. Moreover, what SSE decreases is reflected by an equal increase of SSR. We now define the following extra sum of squares, SSR(X2|X1), which measures the improvement obtained by adding a second variable X2 to a model that has already X1: SSR(X2 | X1) = SSE(X1) − SSE(X1, X2) = SSR(X1, X2) − SSR(X1).
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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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322 7 Data Regression VIF and Mean
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324 7 Data Regression Taking the na
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326 7 Data Regression Example 7.22
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328 7 Data Regression possible to p
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330 8 Data Structure Analysis In Fi
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332 8 Data Structure Analysis of th
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334 8 Data Structure Analysis 2 −
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336 8 Data Structure Analysis using
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338 8 Data Structure Analysis ∑
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340 8 Data Structure Analysis We se
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342 8 Data Structure Analysis p = 0
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344 8 Data Structure Analysis In or
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346 8 Data Structure Analysis A: On
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348 8 Data Structure Analysis ⎡0.
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350 8 Data Structure Analysis 1 0 -
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352 8 Data Structure Analysis 8.9 C
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354 9 Survival Analysis P( t ≤ T
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356 9 Survival Analysis Example 9.2
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358 9 Survival Analysis the Fatigue
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360 9 Survival Analysis “death”
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362 9 Survival Analysis A: The Hear
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364 9 Survival Analysis From Figure
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366 9 Survival Analysis denominator
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368 9 Survival Analysis The exponen
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370 9 Survival Analysis γ This is
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372 9 Survival Analysis the proport
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374 9 Survival Analysis 9.5 Compute
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376 10 Directional Data Example 10.
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380 10 Directional Data The MATLAB
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382 10 Directional Data A: We use t
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384 10 Directional Data For p = 2,
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386 10 Directional Data Thus, the r
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388 10 Directional Data from a unif
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390 10 Directional Data * 2 z = ( 1
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392 10 Directional Data 10.4.3 The
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396 10 Directional Data 10.5.2 Mean
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398 10 Directional Data Similar res
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400 10 Directional Data Exercises 1
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Appendix A - Short Survey on Probab
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A.1 Basic Notions 405 corresponding
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A.2 Conditional Probability and Ind
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A. 4 Bayes ’ Theorem 409 The firs
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A.5 Random Variables and Distributi
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a 0.5 0.4 0.3 0.2 0.1 0 f (x ) a a+
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Example A. 12 A.6 Expectation, Vari
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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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