Statistics : Theory and Methods,9780534504793

Statistics : Theory and Methods

by
Edition: 2nd
ISBN13: 9780534504793
ISBN10: 0534504795
Format: Paperback
Pub. Date: 1995-10-23
Publisher(s): Duxbury Press
List Price: $136.95

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Summary

1. Probability 2. Discrete Random Variables 3. Averages 4. Bernoulli and Related Variables 5. Continuous Random Variables 6. Families of Continuous Distributions 7. Organizing and Describing Data 8. Samples, Statistics, and Sampling Distributions 9. Estimation 10. Significance Testing 11. Tests as Decision Rules 12. Comparing Two Populations 13. Goodness of Fit 14. Analysis of Variance 15. Regression

Table of Contents

Preface ix
Prologue 1(4)
Probability
5(36)
Sample Spaces and Events
5(2)
Event Algebra
7(7)
Probability for Experiments with Symmetries
14(4)
Composition of Experiments
18(8)
Sampling at Random
26(4)
Binomial and Multinomial Coefficients
30(2)
Discrete Probability Distributions
32(3)
Subjective Probability
35(6)
Chapter Perspective
40(1)
Discrete Random Variables
41(38)
Probability Functions
42(4)
Joint Distributions
46(6)
Conditional Probability
52(7)
Bayes' Theorem
59(7)
Independent Random Variables
66(5)
Exchangeable Random Variables
71(8)
Chapter Perspective
77(2)
Averages
79(36)
The Mean
80(5)
Expected Value of a Function of Random Variables
85(7)
Variability
92(5)
Convariance and Correlation
97(5)
Sums of Random Variables
102(5)
Probability Generating Functions
107(8)
Chapter Perspective
113(2)
Bernoulli and Related Variables
115(42)
Sampling Bernoulli Populations
115(4)
The Binomial Distribution
119(6)
Hypergeometric Distributions
125(4)
Inverse Sampling
129(6)
Approximating Binomial Probabilities
135(6)
Poisson Distributions
141(6)
Sample Proportions and the Law of Averages
147(2)
Multinomial Distributions
149(2)
Applying the Probability Generating Function
151(6)
Chapter Perspective
156(1)
Continuous Random Variables
157(71)
The Distribution Function
158(10)
Density and the Probability Element
168(12)
The Median and Other Percentiles
180(2)
Expected Value
182(4)
Expected Value of g(X)
186(3)
Average Deviations
189(5)
Bivariate Distributions
194(8)
Several Variables
202(3)
Covariance and Correlation
205(3)
Independence
208(6)
Conditional Distributions
214(5)
Moment Generating Functions
219(9)
Chapter Perspective
227(1)
Families of Continuous Distributions
228(28)
Normal Distributions
228(9)
Exponential Distributions
237(3)
Gamma Distributions
240(6)
Chi-Square Distributions
246(2)
Distributions for Reliability
248(8)
Chapter Perspective
255(1)
Organizing and Describing Data
256(50)
Frequency Distributions
256(4)
Data on Continuous Variables
260(11)
Order Statistics
271(7)
Data Analysis
278(7)
The Sample Mean
285(4)
Measures of Dispersion
289(6)
Correlation
295(11)
Chapter Perspective
304(2)
Samples, Statistics, and Sampling Distributions
306(61)
Random Sampling
307(4)
Likelihood
311(7)
Sufficient Statistics
318(6)
Sampling Distributions
324(2)
Simulating Sampling Distributions
326(4)
Order Statistics
330
Moments of Sample Means and Proportions
316(23)
The Central Limit Theorem
339(8)
Using the Moment Generating Function
347(3)
Normal Populations
350(2)
Updating Prior Probabilities via Likelihood
352(3)
Some Conjugate Families
355(4)
Predictive Distributions
359(8)
Chapter Perspective
365(2)
Estimation
367(51)
Errors in Estimation
368(5)
Determining Sample Size
373(5)
Consistency
378(3)
Large-Sample Confidence Intervals
381(4)
Small-Sample Confidence Intervals for μ
385(2)
The Distribution of T
387(2)
Pivotal Quantities
389(2)
Estimating a Mean Difference
391(3)
Estimating Variability
394(4)
Deriving Estimators
398(7)
Bayes Estimators
405(4)
Efficiency
409(9)
Chapter Perspective
416(2)
Significance Testing
418(33)
Hypotheses
420(1)
Assessing the Evidence
421(8)
One-Sample Z-Tests
429(5)
One-Sample t-Tests
434(4)
Some Nonparametric Tests
438(7)
Probability of the Null Hypothesis
445(6)
Chapter Perspective
449(2)
Tests as Decision Rules
451(35)
Rejection Regions and Errors
452(6)
The Power Function
458(2)
Choosing the Sample Size
460(2)
Quality Control
462(4)
Most Powerful Tests
466(4)
Randomized Tests
470(3)
Uniformly Most Powerful Tests
473(2)
Likelihood Ratio Tests
475(5)
Bayesian Testing
480(6)
Chapter Perspective
484(2)
Comparing Two Populations
486(34)
Treatment Effects
486(4)
Large-Sample Comparison of Means
490(3)
Comparing Proportions
493(5)
Two-Sample t-Tests
498(3)
Two-Sample Nonparametric Tests
501(7)
Paired Comparisons
508(4)
The F-Distribution
512(2)
Comparing Variances
514(6)
Chapter Perspective
518(2)
Goodness of Fit
520(41)
Fitting a Distribution with Two Categories
520(2)
The Chi-Square Test
522(7)
Tests Based on Distribution Functions
529(7)
Testing Normality
536(7)
Testing Independence
543(7)
A Likelihood Ratio Test for Goodness of Fit
550(4)
Testing Homogeneity Using Paired Data
554(7)
Chapter Perspective
560(1)
Analysis of Variance
561(28)
One-Way ANOVA: The Method
561(7)
One-Way ANOVA: The Theory
568(7)
Multiple Comparisons
575(4)
Two-Way ANOVA
579(10)
Chapter Perspective
588(1)
Regression
589(56)
Models with a Single Explanatory Variable
590(3)
Least Squares
593(8)
Distribution of the Least-Squares Estimators
601(4)
Inference for the Regression Parameters
605(5)
Predicting y from x
610(6)
Residuals
616(5)
Bivariate Normal Distributions
621(5)
The Regression Effect
626(5)
Multiple Regression
631(14)
Chapter Perspective
645(1)
References and Further Readings 645(2)
Appendix 1 Tables 647(40)
Appendix 2 Answers to Selected Problems 687(12)
Index 699

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