Statistics with JMP : graphs, descriptive statistics and probability

목차 (Table of Contents)

• CONTENTS
• Preface = xiii
• Acknowledgments = xvii
• 1 What is statistics? = 1
• 1.1 Why statistics? = 1
• 1.2 Definition of statistics = 3
• 1.3 Examples = 4
• 1.4 The subject of statistics = 5
• 1.5 Probability = 6
• 1.6 Software = 7
• 2 Data and its representation = 8
• 2.1 Types of data and measurement scales = 8
• 2.1.1 Categorical or qualitative variables = 8
• 2.1.2 Quantitative variables = 9
• 2.1.3 Hierarchy of scales = 10
• 2.1.4 Measurement scales in JMP = 10
• 2.2 The data matrix = 11
• 2.3 Representing univariate qualitative variables = 12
• 2.4 Representing univariate quantitative variables = 16
• 2.4.1 Stem and leaf diagram = 16
• 2.4.2 Needle charts for univariate discrete quantitative variables = 17
• 2.4.3 Histograms and frequency polygons for continuous variables = 22
• 2.4.4 Empirical cumulative distribution functions = 27
• 2.5 Representing bivariate data = 30
• 2.5.1 Qualitative variables = 30
• 2.5.2 Quantitative variables = 34
• 2.6 Representing time series = 38
• 2.7 The use of maps = 39
• 2.8 More graphical capabilities = 47
• 3 Descriptive statistics of sample data = 54
• 3.1 Measures of central tendency or location = 55
• 3.1.1 Median = 56
• 3.1.2 Mode = 57
• 3.1.3 Arithmetic mean = 58
• 3.1.4 Geometric mean = 61
• 3.2 Measures of relative location = 63
• 3.2.1 Order statistics, quantiles, percentiles, deciles = 63
• 3.2.2 Quartiles = 64
• 3.3 Measures of variation or spread = 64
• 3.3.1 Range = 64
• 3.3.2 Interquartile range = 65
• 3.3.3 Mean absolute deviation = 65
• 3.3.4 Variance = 65
• 3.3.5 Standard deviation = 68
• 3.3.6 Coefficient of variation = 69
• 3.3.7 Dispersion indices for nominal and ordinal variables = 70
• 3.4 Measures of skewness = 76
• 3.5 Kurtosis = 78
• 3.6 Transformation and standardization of data = 78
• 3.7 Box plots = 79
• 3.8 Variability charts = 84
• 3.9 Bivariate data = 88
• 3.9.1 Covariance = 89
• 3.9.2 Correlation = 92
• 3.9.3 Rank correlation = 94
• 3.10 Complementarity of statistics and graphics = 98
• 3.11 Descriptive statistics using JMP = 100
• 4 Probability = 106
• 4.1 Random experiments = 108
• 4.2 Definition of probability = 110
• 4.3 Calculation rules = 113
• 4.4 Conditional probability = 114
• 4.5 Independent and dependent events = 119
• 4.6 Total probability and Bayes' rule = 122
• 4.7 Simulating random experiments = 127
• 5 Additional aspects of probability theory = 129
• 5.1 Combinatorics = 129
• 5.1.1 Addition rule = 129
• 5.1.2 Multiplication principle = 130
• 5.1.3 Permutations = 130
• 5.1.4 Combinations = 131
• 5.2 Number of possible orders = 132
• 5.2.1 Two different objects = 133
• 5.2.2 More than two different objects = 133
• 5.3 Applications of probability theory = 134
• 5.3.1 Sequences of independent random experiments = 134
• 5.3.2 Euromillions = 135
• 6 Univariate random variables = 138
• 6.1 Random variables and distribution functions = 138
• 6.2 Discrete random variables and probability distributions = 140
• 6.3 Continuous random variables and probability densities = 143
• 6.4 Functions of random variables = 151
• 6.4.1 Functions of one discrete random variable = 151
• 6.4.2 Functions of one continuous random variable = 152
• 6.5 Families of probability distributions and probability densities = 154
• 6.6 Simulation of random variables = 155
• 7 Statistics of populations and processes = 159
• 7.1 Expected value of a random variable = 159
• 7.2 Expected value of a function of a random variable = 161
• 7.3 Special cases = 162
• 7.4 Variance and standard deviation of a random variable = 163
• 7.5 Other statistics = 166
• 7.6 Moment generating functions = 169
• 8 Important discrete probability distributions = 173
• 8.1 The uniform distribution = 173
• 8.2 The Bernoulli distribution = 175
• 8.3 The binomial distribution = 176
• 8.3.1 Probability distribution = 176
• 8.3.2 Expected value and variance = 183
• 8.4 The hypergeometric distribution = 184
• 8.5 The Poisson distribution = 188
• 8.6 The geometric distribution = 194
• 8.7 The negative binomial distribution = 197
• 8.8 Probability distributions in JMP = 200
• 8.8.1 Tables with probability distributions and cumulative distribution functions = 200
• 8.8.2 Graphical representations = 204
• 8.9 The simulation of discrete random variables with JMP = 209
• 9 Important continuous probability densities = 212
• 9.1 The continuous uniform density = 213
• 9.2 The exponential density = 215
• 9.2.1 Definition and statistics = 215
• 9.2.2 Some interesting properties = 216
• 9.3 The gamma density = 220
• 9.4 The Weibull density = 221
• 9.5 The beta density = 223
• 9.6 Other densities = 224
• 9.7 Graphical representations and probability calculations in JMP = 226
• 9.8 Simulating continuous random variables in JMP = 230
• 10 The normal distribution = 232
• 10.1 The normal density = 233
• 10.2 Calculation of probabilities for normally distributed variables = 237
• 10.2.1 The standard normal distribution = 237
• 10.2.2 General normally distributed variables = 238
• 10.2.3 JMP = 240
• 10.2.4 Examples = 241
• 10.3 Lognormal probability density = 247
• 11 Multivariate random variables = 252
• 11.1 Introductory notions = 252
• 11.2 Joint (discrete) probability distributions = 254
• 11.3 Marginal or unconditional (discrete) probability distribution = 256
• 11.4 Conditional (discrete) probability distribution = 257
• 11.5 Examples of discrete bivariate random variables = 258
• 11.6 The multinomial probability distribution = 266
• 11.7 Joint (continuous) probability density = 268
• 11.8 Marginal or unconditional (continuous) probability density = 276
• 11.9 Conditional (continuous) probability density = 279
• 12 Functions of several random variables = 282
• 12.1 Functions of several random variables = 282
• 12.2 Expected value of functions of several random variables = 283
• 12.3 Conditional expected values = 288
• 12.4 Probability distributions of functions of random variables = 289
• 12.4.1 Discrete random variables = 289
• 12.4.2 Continuous random variables = 290
• 12.5 Functions of independent Poisson, normally, and lognormally distributed random variables = 295
• 13 Covariance, correlation, and variance of linear functions = 300
• 13.1 Covariance and correlation = 300
• 13.2 Variance of linear functions of two random variables = 305
• 13.3 Variance of linear functions of several random variables = 306
• 13.4 Variance of linear functions of independent random variables = 307
• 13.4.1 Two independent random variables = 307
• 13.4.2 Several pairwise independent random variables = 308
• 13.5 Linear functions of normally distributed random variables = 308
• 13.6 Bivariate and multivariate normal density = 310
• 13.6.1 Bivariate normal probability density = 310
• 13.6.2 Graphical representations = 310
• 13.6.3 Independence, marginal, and conditional densities = 314
• 13.6.4 General multivariate normal density = 318
• 14 The central limit theorem = 319
• 14.1 Probability density of the sample mean from a normally distributed population = 319
• 14.2 Probability distribution and density of the sample mean from a non-normally distributed population = 320
• 14.2.1 Central limit theorem = 320
• 14.2.2 Illustration of the central limit theorem = 322
• 14.3 Applications = 326
• 14.4 Normal approximation of the binomial distribution = 328
• Appendix A : The Greek alphabet = 330
• Appendix B : Binomial distribution = 331
• Appendix C : Poisson distribution = 336
• Appendix D : Exponential distribution = 339
• Appendix E : Standard normal distribution = 341
• Index = 343