Applied Statistics Using SPSS, STATISTICA, MATLAB and R

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466 Appendix D - Tables D.3 Student´s t Distribution The following table lists the values of (see B.1.2): P ( t df ≤ x) = 1− ∫ t −∞ df ( t) dt. x 1 3 5 7 9 11 13 15 17 19 21 23 25 0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.532 0.537 0.538 0.538 0.539 0.539 0.539 0.539 0.539 0.539 0.539 0.539 0.539 0.2 0.563 0.573 0.575 0.576 0.577 0.577 0.578 0.578 0.578 0.578 0.578 0.578 0.578 0.3 0.593 0.608 0.612 0.614 0.615 0.615 0.616 0.616 0.616 0.616 0.616 0.617 0.617 0.4 0.621 0.642 0.647 0.649 0.651 0.652 0.652 0.653 0.653 0.653 0.653 0.654 0.654 0.5 0.648 0.674 0.681 0.684 0.685 0.687 0.687 0.688 0.688 0.689 0.689 0.689 0.689 0.6 0.672 0.705 0.713 0.716 0.718 0.72 0.721 0.721 0.722 0.722 0.723 0.723 0.723 0.7 0.694 0.733 0.742 0.747 0.749 0.751 0.752 0.753 0.753 0.754 0.754 0.755 0.755 0.8 0.715 0.759 0.77 0.775 0.778 0.78 0.781 0.782 0.783 0.783 0.784 0.784 0.784 0.9 0.733 0.783 0.795 0.801 0.804 0.806 0.808 0.809 0.81 0.81 0.811 0.811 0.812 1 0.75 0.804 0.818 0.825 0.828 0.831 0.832 0.833 0.834 0.835 0.836 0.836 0.837 1.1 0.765 0.824 0.839 0.846 0.85 0.853 0.854 0.856 0.857 0.857 0.858 0.859 0.859 1.2 0.779 0.842 0.858 0.865 0.87 0.872 0.874 0.876 0.877 0.878 0.878 0.879 0.879 1.3 0.791 0.858 0.875 0.883 0.887 0.89 0.892 0.893 0.895 0.895 0.896 0.897 0.897 1.4 0.803 0.872 0.89 0.898 0.902 0.905 0.908 0.909 0.91 0.911 0.912 0.913 0.913 1.5 0.813 0.885 0.903 0.911 0.916 0.919 0.921 0.923 0.924 0.925 0.926 0.926 0.927 1.6 0.822 0.896 0.915 0.923 0.928 0.931 0.933 0.935 0.936 0.937 0.938 0.938 0.939 1.7 0.831 0.906 0.925 0.934 0.938 0.941 0.944 0.945 0.946 0.947 0.948 0.949 0.949 1.8 0.839 0.915 0.934 0.943 0.947 0.95 0.952 0.954 0.955 0.956 0.957 0.958 0.958 1.9 0.846 0.923 0.942 0.95 0.955 0.958 0.96 0.962 0.963 0.964 0.964 0.965 0.965 2 0.852 0.93 0.949 0.957 0.962 0.965 0.967 0.968 0.969 0.97 0.971 0.971 0.972 2.1 0.859 0.937 0.955 0.963 0.967 0.97 0.972 0.973 0.975 0.975 0.976 0.977 0.977 2.2 0.864 0.942 0.96 0.968 0.972 0.975 0.977 0.978 0.979 0.98 0.98 0.981 0.981 2.3 0.869 0.948 0.965 0.973 0.977 0.979 0.981 0.982 0.983 0.984 0.984 0.985 0.985 2.4 0.874 0.952 0.969 0.976 0.98 0.982 0.984 0.985 0.986 0.987 0.987 0.988 0.988 2.5 0.879 0.956 0.973 0.98 0.983 0.985 0.987 0.988 0.989 0.989 0.99 0.99 0.99 2.6 0.883 0.96 0.976 0.982 0.986 0.988 0.989 0.99 0.991 0.991 0.992 0.992 0.992 2.7 0.887 0.963 0.979 0.985 0.988 0.99 0.991 0.992 0.992 0.993 0.993 0.994 0.994 2.8 0.891 0.966 0.981 0.987 0.99 0.991 0.992 0.993 0.994 0.994 0.995 0.995 0.995 2.9 0.894 0.969 0.983 0.989 0.991 0.993 0.994 0.995 0.995 0.995 0.996 0.996 0.996 3 0.898 0.971 0.985 0.99 0.993 0.994 0.995 0.996 0.996 0.996 0.997 0.997 0.997 3.1 0.901 0.973 0.987 0.991 0.994 0.995 0.996 0.996 0.997 0.997 0.997 0.997 0.998 3.2 0.904 0.975 0.988 0.992 0.995 0.996 0.997 0.997 0.997 0.998 0.998 0.998 0.998 3.3 0.906 0.977 0.989 0.993 0.995 0.996 0.997 0.998 0.998 0.998 0.998 0.998 0.999 3.4 0.909 0.979 0.99 0.994 0.996 0.997 0.998 0.998 0.998 0.998 0.999 0.999 0.999 3.5 0.911 0.98 0.991 0.995 0.997 0.998 0.998 0.998 0.999 0.999 0.999 0.999 0.999 df x
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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
Page 914: B.2.2 Normal Distribution B.2 Conti
Page 918: Distribution function: ∫ − = =
Page 922: Properties: 1. w1,1/λ(x) ≡ ελ(
Page 926: Properties: 1. β1,1(x) ≡ u(x). 2
Page 930: B.2 Continuous Distributions 449 Pr
Page 934: B.2.9 F Distribution B.2 Continuous
Page 938: B.2 Continuous Distributions 453 ci
Page 942: Appendix C - Point Estimation In Ap
Page 946: dL( n−1 n−2 p) = q dp − ( n
Page 950: Appendix D - Tables D.1 Binomial Di
Page 954: Appendix D - Tables 461 p n k 0.05
Page 958: Appendix D - Tables 463 p n k 0.05
Page 962: D.2 Normal Distribution The followi
Page 968: 468 Appendix D - Tables D.5 Critica
Page 972: 470 Appendix E - Datasets The varia
Page 976: 472 Appendix E - Datasets E.6 CTG T
Page 980: 474 Appendix E - Datasets E.9 FHR T
Page 984: 476 Appendix E - Datasets E.14 Fore
Page 988: 478 Appendix E - Datasets DATE_REOP
Page 992: 480 Appendix E - Datasets CG: Conic
Page 996: 482 Appendix E - Datasets E.26 Soil
Page 1000: 484 Appendix E - Datasets E.29 VCG
Page 1004: Appendix F - Tools F.1 MATLAB Funct
Page 1008: Appendix F - Tools 489 r
Page 1012: 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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