# Statistics with Mathematica

Academic Press, 1999 - Mathematics - 632 pages
Mathematica's diverse capabilities make it particularly well suited to perform the many calculations encountered in statistics. This book introduces Mathematica for various types of statistical computations. It covers a broad range of topics, and should appeal to both students and professional statisticians.

Key Features
* Comprehensive: Covers the use of Mathematica for applications ranging from descriptive statistics, through multiple regression and nonparametric methods; uses virtually all of Mathematica's built-in statistical commands, as well as those contained in various Mathematica packages; Additionally, the authors have written numerous procedures to extend Mathematica's capabilities, which are also included on the CD-ROM
* Easy to read: Uses "by example" approach authors have used in several other books about Mathematica: works for beginners and experts alike
* Applied: Examples from diverse disciplines, including biostatistics, business, statistics, econometrics, engineering, and psychology
* Up-to-date: Compatible with Mathematica Version 3
* Includes CD-ROM: with all Mathematica inputs from text and also numerous procedures to extend Mathematica's built-in, statistical capabilities

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### Contents

 Data and Data File Manipulation with Mathematica 1 Mathematica Version 3 2 Preview 8 A Word of Caution 10 14 Getting Help from Mathematica 11 Mathematica Help 16 15 Data Manipulation 21 Entering Data into Mathematica 22
 75 Randomization 311 76 Random Data Generation 314 One and Two Sample Inferential Procedures 319 81 Confidence Intervals 320 Population Variance Unknown 322 Confidence Interval for the Variance of a Normal Population 327 Population Variances Known 330 Population Variances Unknown but Assumed Equal 332

 Selecting Rows 24 Selecting Columns 25 The Hominoid Molar Data Set 27 Selecting Records 36 Output from Mathematica 50 Univariate Methods for Describing Data 57 21 Measures of Location 58 Reporting Location Statistics 65 22 Measures of Dispersion 75 23 Measures of Shape 84 24 Coding 89 25 Expected Value Function 91 Multivariate Methods for Describing Data 95 31 Extension of Univariate Methods 96 Measures of Location 97 Measures of Dispersion 99 Measures of Shape 101 32 Bivariate Measures of Association 102 Rank Correlation 107 33 Multivariate Methods with No Univariate Analogues 112 Multivariate Dispersion Measures 117 Multivariate Shape Measures 123 34 Multivariate Measures of Association 125 35 Multivariate Data Transformations 127 Tabular and Graphical Methods for Presenting Data 131 Bar Graphs for Descriptive Measures 138 Frequency Tables and Histograms 141 Polygons 155 BoxandWhiskers Plots 161 StemandLeaf Charts 168 42 Bivariate Procedures 175 Contingency Tables Cross Tabulations 180 43 A Multivariate Procedure 186 Data Smoothing and Time Series An Introduction 189 52 Univariate Smoothing Procedures 192 Moving Average Smoothing 193 Moving Median Smoothing 196 Linear Filter Smoothing 198 Exponential Smoothing 201 53 Multivariate Extension 205 Probability and Probability Distributions 207 62 Discrete Random Variables and Distributions 212 Bernoulli Distribution 213 Binomial Distribution 215 Discrete Uniform Distribution 216 Geometric Distribution 219 Hypergeometric Distribution 222 Logarithmic Series Distribution 224 Negative Binomial Distribution Pascal Distribution 226 Poisson Distribution 229 63 Continuous Random Variables and Distributions 231 Beta Distribution 233 Cauchy Distribution 235 Chi Distribution 237 ChiSquare Distribution 239 Noncentral Chi Square Distribution 240 Exponential Distribution 243 Extreme Value Distribution 244 F Variance Ratio Distribution 247 Noncentral F Variance Ratio Distribution 249 Gamma Distribution 250 Normal Gaussian Distribution 253 HalfNormal Distribution 254 Laplace Distribution 256 LogNormal Distributions 258 Logistic Distribution 261 Pareto Distribution 263 Rayleigh Distribution 265 Students tDistribution 267 Noncentral Students tDistribution 269 Uniform Distribution 270 Weibull Distribution 272 64 The Multivariate Normal Distribution and Related Distributions 274 Multivariate Normal Multinormal Distribution 276 Multivariate tDistribution 281 Wishart Distribution 283 Hotellings T2Distribution 284 Quadratic Form Distribution 286 Random Number Generation and Simulation 287 71 Simulating Simple Experiments 288 72 Simulation to Illustrate Concepts 290 The Central Limit Theorem 293 73 Simulation in Problem Solving Monte Carlo Method 299 74 Random Sampling 308
 Population Variances Unknown and Assumed Unequal 333 Confidence Interval for the Ratio of Variances of Two Normal Populations 336 82 Hypothesis Tests 337 Population Variance Known 340 Population Variance Unknown 342 Hypothesis Test for the Variance of a Normal Population 344 Population Variances Known 346 Population Variances Unknown but Assumed Equal 348 Population Variances Unknown and Assumed Unequal 349 Hypothesis Test for the Ratio of Variances of Two Normal Populations 353 83 Investigating Confidence Level and Significance Level with Simulation 355 Significance Level 357 Analysis of Variance and Multiple Comparisons of Means 359 91 SingleFactor Analysis of Variance 360 92 Multiple Comparison Methods 371 Cautions 372 SingleStep Procedures for Pairwise Comparisons 374 mcmBonferroniPairs 375 mcmScheffePairs 376 SingleStep Procedures for Contrasts 380 mcmScheffeContrasts 381 mcmBonferroniContrasts 382 mcmTukeyContrasts 383 SingleStep Procedures for ManytoOne Comparisons 386 StepDown Procedures 389 mcmMultipleF 390 mcmPeritzQ 391 93 TwoFactor Analysis of Variance 393 Diagnostic Procedures and Transformations 409 102 Diagnostic Procedures 410 Outliers 411 Random Sampling 416 Normality 423 103 Transformations 434 Outliers 435 Normality 449 BoxCox Transformations 450 Regression and Correlation 455 Correlation 456 112 Simple Linear Regression 457 Inferences in Regression Analysis 462 Confidence Intervals and Hypothesis Tests for the Regression Coefficients 463 Confidence Interval for the Mean of the Distribution of ys 464 Prediction Interval for a New Observation Corresponding to xi 465 113 Polynomial Regression 468 114 Multiple Regression 471 Statistical Inference 473 115 Diagnostic Procedures 480 Outliers 485 Influential Cases 487 Random Sampling 491 LinearityAdditivity 492 Equality of Variance 495 Normality 497 116 Remedial Methods 500 Outliers and Influential Cases 501 Random Sampling and Independence 510 Equality of Variance 513 Normality 528 118 Correlation 539 Assumptions 540 Inference for Two Correlation Coefficients 543 Inference for More Than Two Correlation Coefficients 545 Rank Correlation 547 Nonparametric Methods 551 122 Methods for Single Samples 552 Population Proportion 559 Randomness 563 123 Methods for Two Independent Samples 566 Confidence Interval for the Difference between Two Medians Based on the MannWhitney Test 567 Comparing Variability 570 Comparing Proportions 576 ChiSquare Test for 2x2 Contingency Tables 580 LogLikelihood Ratio Test for 2x2 Contingency Tables 583 Based on a Normal Approximation 585 124 Methods for Two Related Samples 588 125 Methods for Three or More Independent Samples 595 Contingency Tables 602 Measures of Association 606 Tests for Heterogeneity Tests of Homogeneity 614 Comparing Population Proportions Related Samples 617 Selected References 621 Index 625 Copyright