Statistics with Mathematica

Front Cover
Academic Press, 1999 - Mathematics - 632 pages
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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

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About the author (1999)

Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro where they have extensive experience in Mathematica-assisted instruction at both the undergraduate and graduate levels. In addition, they have given numerous presentations on Mathematica, throughout the United States and abroad. Other books by the authors include Differential Equations with Mathematica, Second Edition and Statistics with Mathematica. Martha became Dean of the College of Science and Mathematics at Georgia Southern University in 2014.

Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro. Martha recently received Georgia Southern's award for 'excellence in research and/or creative scholarly activity.' Both authors have extensive experience with using Mathematica as well as Mathematica-assisted instruction at both the undergraduate and graduate levels. In addition, they have given numerous presentations on Mathematica, throughout the United States and abroad. Other books by the authors include Differential Equations with Mathematica, Second Edition and Statistics with Mathematica. Martha Abell became Dean of the College of Science and Mathematics at Georgia Southern University, Statesboro, Georgia, in 2014.

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