Elsevier S & T

Advanced Statistics from an Elementary Point of View

Panik, Michael J

In stock

No reviews

47.750 KD inc. VAT

License

perpetual

Table of contents

Table of contentsvii
Prefacexv
Chapter 1. Introduction1
1.1 Statistics Defined1
1.2 Types of Statistics1
1.3 Levels of Discourse: Sample vs. Population2
1.4 Levels of Discourse: Target vs. Sampled Population4
1.5 Measurement Scales5
1.6 Sampling and Sampling Errors7
1.7 Exercises7
Chapter 2. Elementary Descriptive Statistical Techniques9
2.1 Summarizing Sets of Data Measured on a Ratio or Interval Scale9
2.2 Tabular Methods11
2.3 Quantitative Summary Characteristics16
2.4 Correlation between Variables X and Y38
2.5 Rank Correlation between Variables X and Y42
2.6 Exercises46
Chapter 3. Probability Theory53
3.1 Mathematical Foundations: Sets, Set Relations, and Functions53
3.2 The Random Experiment, Events, Sample Space, and the Random Variable59
3.3 Axiomatic Development of Probability Theory62
3.4 The Occurrence and Probability of an Event64
3.5 General Addition Rule for Probabilities65
3.6 Joint, Marginal, and Conditional Probability66
3.7 Classification of Events72
3.8 Sources of Probabilities77
3.9 Bayes’ Rule79
3.10 Exercises82
Chapter 4. Random Variables and Probability Distributions93
4.1 Random Variables93
4.2 Discrete Probability Distributions94
4.3 Continuous Probability Distributions101
4.4 Mean and Variance of a Random Variable106
4.5 Chebyshev’s Theorem for Random Variables111
4.6 Moments of a Random Variable113
4.7 Quantiles of a Probability Distribution117
4.8 Moment-Generating Function119
4.9 Probability-Generating Function127
4.10 Exercises132
Chapter 5. Bivariate Probability Distributions147
5.1 Bivariate Random Variables147
5.2 Discrete Bivariate Probability Distributions147
5.3 Continuous Bivariate Probability Distributions154
5.4 Expectations and Moments of Bivariate Probability Distributions162
5.5 Chebyshev’s Theorem for Bivariate Probability Distributions169
5.6 Joint Moment–Generating Function169
5.7 Exercises174
Chapter 6. Discrete Parametric Probability Distributions187
6.1 Introduction187
6.2 Counting Rules188
6.3 Discrete Uniform Distribution194
6.4 The Bernoulli Distribution195
6.5 The Binomial Distribution197
6.6 The Multinomial Distribution203
6.7 The Geometric Distribution206
6.8 The Negative Binomial Distribution208
6.9 The Poisson Distribution212
6.10 The Hypergeometric Distribution218
6.11 The Generalized Hypergeometric Distribution225
6.12 Exercises226
Chapter 7. Continuous Parametric Probability Distributions235
7.1 Introduction235
7.2 The Uniform Distribution236
7.3 The Normal Distribution238
7.4 The Normal Approximation to Binomial Probabilities253
7.5 The Normal Approximation to Poisson Probabilities257
7.6 The Exponential Distribution258
7.7 Gamma and Beta Functions264
7.8 The Gamma Distribution266
7.9 The Beta Distribution270
7.10 Other Useful Continuous Distributions276
7.11 Exercises285
Chapter 8. Sampling and the Sampling Distribution of a Statistic293
8.1 The Purpose of Random Sampling293
8.2 Sampling Scenarios294
8.3 The Arithmetic of Random Sampling301
8.4 The Sampling Distribution of a Statistic306
8.5 The Sampling Distribution of the Mean308
8.6 A Weak Law of Large Numbers316
8.7 Convergence Concepts319
8.8 A Central Limit Theorem322
8.9 The Sampling Distribution of a Proportion326
8.10 The Sampling Distribution of the Variance333
8.11 A Note on Sample Moments338
8.12 Exercises342
Chapter 9. The Chi-Square, Student’s t, and Snedecor’s F Distributions349
9.1 Derived Continuous Parametric Distributions349
9.2 The Chi-Square Distribution350
9.3 The Sampling Distribution of the Variance When Sampling from a Normal Population354
9.4 Student’s t Distribution357
9.5 Snedecor’s F Distribution362
9.6 Exercises368
Chapter 10. Point Estimation and Properties of Point Estimators373
10.1 Statistics as Point Estimators373
10.2 Desirable Properties of Estimators as Statistical Properties375
10.3 Small Sample Properties of Point Estimators376
10.4 Large Sample Properties of Point Estimators408
10.5 Techniques for Finding Good Point Estimators419
10.6 Exercises431
Chapter 11. Interval Estimation and Confidence Interval Estimates439
11.1 Interval Estimators439
11.2 Central Confidence Intervals441
11.3 The Pivotal Quantity Method442
11.4 A Confidence Interval for µ Under Random Sampling from a Normal Population with Known Variance443
11.5 A Confidence Interval for µ Under Random Sampling from a Normal Population with Unknown Varian446
11.6 A Confidence Interval for s2 Under Random Sampling from a Normal Population with Unknown Mean447
11.7 A Confidence Interval for p Under Random Sampling from a Binomial Population451
11.8 Joint Estimation of a Family of Population Parameters455
11.9 Confidence Intervals for the Difference of Means When Sampling from Two Independent Normal Popu458
11.10 Confidence Intervals for the Difference of Means When Sampling from Two Dependent Populations:464
11.11 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Bino470
11.12 Confidence Interval for the Ratio of Two Variances When Sampling from Two Independent Normal P471
11.13 Exercises473
Chapter 12. Tests of Parametric Statistical Hypotheses483
12.1 Statistical Inference Revisited483
12.2 Fundamental Concepts for Testing Statistical Hypotheses484
12.3 What Is the Research Question?486
12.4 Decision Outcomes487
12.5 Devising a Test for a Statistical Hypothesis488
12.6 The Classical Approach to Statistical Hypothesis Testing491
12.7 Types of Tests or Critical Regions493
12.8 The Essentials of Conducting a Hypothesis Test495
12.9 Hypothesis Test for µ Under Random Sampling from a Normal Population with Known Variance496
12.10 Reporting Hypothesis Test Results501
12.11 Determining the Probability of a Type II Error β504
12.12 Hypothesis Tests for µ Under Random Sampling from a Normal Population with Unknown Variance510
12.13 Hypothesis Tests for p Under Random Sampling from a Binomial Population512
12.14 Hypothesis Tests for σ2 Under Random Sampling from a Normal Population516
12.15 The Operating Characteristic and Power Functions of a Test519
12.16 Determining the Best Test for a Statistical Hypothesis528
12.17 Generalized Likelihood Ratio Tests537
12.18 Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populat546
12.19 Hypothesis Tests for the Difference of Means When Sampling from Two Dependent Populations: Pai553
12.20 Hypothesis Tests for the Difference of Proportions When Sampling from Two Independent Binomial555
12.21 Hypothesis Tests for the Difference of Variances When Sampling from Two Independent Normal Pop557
12.22 Hypothesis Tests for Spearman’s Rank Correlation Coefficient .S559
12.23 Exercises561
Chapter 13. Nonparametric Statistical Techniques569
13.1 Parametric vs. Nonparametric Methods569
13.2 Tests for the Randomness of a Single Sample572
13.3 Single-Sample Sign Test Under Random Sampling580
13.4 Wilcoxon Signed Rank Test of a Median583
13.5 Runs Test for Two Independent Samples587
13.6 Mann-Whitney (Rank-Sum) Test for Two Independent Samples590
13.7 The Sign Test When Sampling from Two Dependent Populations: Paired Comparisons597
13.8 Wilcoxon Signed Rank Test When Sampling from Two Dependent Populations: Paired Comparisons599
13.9 Exercises603
Chapter 14. Testing Goodness of Fit609
14.1 Distributional Hypotheses609
14.2 The Multinomial Chi-Square Statistic: Complete Specification of H0609
14.3 The Multinomial Chi-Square Statistic: Incomplete Specification of H0616
14.4 The Kolmogorov-Smirnov Test for Goodness of Fit621
14.5 The Lilliefors Goodness-of-Fit Test for Normality630
14.6 The Shapiro-Wilk Goodness-of-Fit Test for Normality631
14.7 The Kolmogorov-Smirnov Test for Goodness of Fit: Two Independent Samples632
14.8 Assessing Normality via Sample Moments634
14.9 Exercises638
Chapter 15. Testing Goodness of Fit: Contingency Tables643
15.1 An Extension of the Multinomial Chi-Square Statistic643
15.2 Testing Independence643
15.3 Testing k Proportions649
15.4 Testing for Homogeneity651
15.5 Measuring Strength of Association in Contingency Tables655
15.6 Testing Goodness of Fit with Nominal-Scale Data: Paired Samples661
15.7 Exercises664
Chapter 16. Bivariate Linear Regression and Correlation669
16.1 The Regression Model669
16.2 The Strong Classical Linear Regression Model670
16.3 Estimating the Slope and Intercept of the Population Regression Line673
16.4 Mean, Variance, and Sampling Distribution of the Least Squares Estimators . β0 and . β1676
16.5 Precision of the Least Squares Estimators . β0, . β1: Confidence Intervals679
16.6 Testing Hypotheses Concerning β0, β1680
16.7 The Precision of the Entire Least Squares Regression Equation: A Confidence Band684
16.8 The Prediction of a Particular Value of Y Given X687
16.9 Decomposition of the Sample Variation of Y691
16.10 The Correlation Model695
16.11 Estimating the Population Correlation Coefficient .697
16.12 Inferences about the Population Correlation Coefficient .698
16.13 Exercises705
Appendix A717
Solutions to Selected Exercises767
References and Suggested Reading785
Index789

Book details

Vendor Elsevier S & T
SKU 9780120884940
ISBN-13 9780080559322
Author Panik, Michael J
Category Mathematics
Subject General

Do you have questions about this book?

Ask an expert!

The highly readable text captures the flavor of a course in mathematical statistics without imposing too much rigor; students can concentrate on the statistical strategies without getting lost in the theory.
Students who use this book will be well on their way to thinking like a statistician. Practicing statisticians will find this book useful in that it is replete with statistical test procedures (both parametric and non-parametric) as well as numerous detailed examples.

· Comprehensive coverage of descriptive statistics
· More detailed treatment of univariate and
bivariate probability distributions
· Thorough coverage of probability theory with
numerous event classifications

Instant delivery by email
Your access email arrives within minutes of checkout, with a sign-in link for each book — no shipping, no waiting.

Read on any device
Books open in VitalSource Bookshelf on your phone, tablet, or computer, online or offline. Your library is always available at aafaq.vitalsource.com — just log in with the email you used at checkout.

Lost the email?
Resend it to yourself in seconds from My eBook orders, or email cs@aafaqeducation.com and we'll help.