## Statistics with MathematicaMathematica'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 |

621 | |

625 | |

### Common terms and phrases

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