Statistical concepts and methods:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1977
|
| Series: | Wiley series in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 639 S. graph. Darst. |
| ISBN: | 0471072044 |
Staff View
MARC
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| 245 | 1 | 0 | |a Statistical concepts and methods |c Gouri K. Bhattacharyya ; Richard A. Johnson |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1977 | |
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Record in the Search Index
| _version_ | 1804117937385111552 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 What Is Statistics? 1
1.2 Statistics and Everyday Life, 2
1.3 Elements of Scientific Inquiry, 3
1.4 The Role of Statistics in Scientific Inquiry, 4
1.5 Illustrative Situations of the Collection and Analysis
of Data, 5
1.6 Population and Sample, 6
1.7 Statistics Interacting with Other Fields, 9
References, 10
2 Descriptive Study of Data 11
2.1 Introduction, 11
2.2 Description of Data by Graphs and Tables, 12
2.3 Symbols for Data Sets and the Operation of Addition,
24
2.4 Measures of Center, 27
2.5 Measures of Variation, 32
2.6 Comments on the Choice of Numerical Measures, 38
2.7 Descriptive Measures for Grouped Data, 40
*2.8 Coding the Data, 45
Exercises, 47
Class Projects, 57
Mathematical Exercises, 58
3 Elements of Probability 60
3.1 Introduction, 60
3.2 Sample Space and Events, 61
ix
X CONTENTS
3.3 The Probability of an Event, 64
3.4 Operations with Events and Basic Laws of
Probability, 70
3.5 Rules of Counting and Their Use in Uniform
Probability Models, 78
3.6 Conditional Probability, 87
*3.7 Bayes Theorem, 93
*3.8 General Rules of Probability, 95
Exercises, 97
Class Projects, 106
Mathematical Exercises, 107
4 Random Variables and Probability Distributions 108
4.1 Random Variables, 108
4.2 Graphic Presentation of a Probability Distribution,
113
4.3 Expectation and Its Properties, 117
4.4 Variance: A Measure of Spread, 121
4.5 Joint Distribution of Two Random Variables, 124
4.6 Co variance and Correlation, 129
4.7 Independence of Two Random Variables, 131
Exercises, 133
Mathematical Exercises, 138
5 Distributions for Counts 140
5.1 Idea of a Probability Model, 140
5.2 Bernoulli Trials: Success-Failure, 141
5.3 The Binomial Distribution, 145
5.4 How to Use the Binomial Tables, 150
5.5 The Mean and the Variance of the Binomial
Distribution, 151
5.6 The Hypergeometric Distribution, 152
5.7 The Geometric Distribution for Waiting Time, 154
5.8 Rare Events and the Poisson Distribution, 156
References, 159
Exercises, 159
Mathematical Exercises, 163
6 Basic Concepts of Testing Hypotheses 165
6.1 Introduction, 165
6.2 The Null and the Alternative Hypotheses, 166
CONTENTS xi
6.3 The Two Types of Errors and the Power Function of
a Test, 169
6.4 Selecting Among Several Tests, 172
6.5 Drawing Conclusions from a Test, 174
6.6 Testing with a Two-sided Alternative, 176
6.7 General Steps in Testing Hypotheses, 178
Exercises, 182
7 The Normal Distribution and Random Samples 187
7.1 Probability Models for Continuous Variables, 187
7.2 The Normal Distribution, 193
7.3 The Normal Approximation to the Binomial
Distribution, 202
7.4 Random Sampling, Statistic, and Sampling
Distribution, 205
7.5 Distribution of the Sample Mean and the Central
Limit Theorem, 210
7.6 Checking the Assumption of a Normal Population,
220
7.7 Transforming Observations to Attain Near
Normality, 223
References, 226
Exercises, 226
Class Projects, 232
8. Inferences About a Population 233
8.1 Introduction, 233
8.2 Point Estimation of a Parameter, 235
8.3 Estimation by Confidence Intervals, 243
8.4 Confidence Interval for jx Based on Small Samples
(t Distribution), 250
8.5 Testing Hypotheses About a Mean, 255
8.6 Relationship Between Tests and Confidence Intervals,
264
8.7 Inferences About the Standard Deviation a of a
Normal Population, 266
8.8 The Effect of Violation of Assumptions, 270
8.9 Determination of the Sample Size, 272
Reference, 275
Exercises, 276
Mathematical Exercises, 283
Xii CONTENTS
9 Comparing Two Treatments 286
9.1 Introduction, 286
9.2 Independent Random Samples from Two
Populations, 288
9.3 Randomization and Its Role in Inference, 297
9.4 Paired Comparisons, 300
9.5 Choosing Between Independent Samples and Paired
Samples, 306
9.6 Comparison of Two Binomial Proportions, 308
9.7 Comparing the Variances of Two Normal
Populations. 312
*9.8 Relationships of x2 U and F to the Normal
Distribution, 317
Exercises, 321
10 Regression Analysis: Simple Linear Relation 334
10.1 Objectives of Regression Analysis, 334
10.2 A Simple Regression Problem, 338
10.3 Plotting the Data, 339
10.4 A Straight-line Regression Model, 341
10.5 The Method of Least Squares, 342
*10.6 Derivation of the Least Squares Estimates, 346
10.7 Least Squares Regression Line, 346
10.8 Properties of the Least Squares Estimators, 349
10.9 Important Inference Problems, 351
10.10 What to Do if the Predictor Variable Cannot
be controlled by the Experimenter, 357
10.11 Remarks About the Model, 358
Exercises, 359
Mathematical Exercises, 366
11 Regression Analysis: Model Checking and
Multiple Linear Regression 368
11.1 General Attitude Toward a Statistical Model, 368
11.2 Examining the Residuals, 368
11.3 Further Checks on the Straight-line Model, 372
*11.4 Test of Lack of Fit Based on Repeated Runs, 375
11.5 Nonlinear Relations and Linearizing
Transformations, 379
11.6 Multiple Linear Regression, 384
i
CONTENTS Xiii
*11.7 Further Aspects of Multiple Regression, 388
References, 391
Exercises, 391
Mathematical Exercises, 399
12 Correlation: A Measure of Linear Relationship 400
12.1 Introduction, 400
12.2 The Sample Correlation Coefficient, 402
12.3 Correlation and Causation, 406
12.4 A Population Model for Correlation: The Bivariate
Normal, 408
12.5 Serial Correlation, 411
Exercises, 413
Mathematical Exercises, 418
13 Analysis of Categorized Data 420
13.1 Introduction, 420
13.2 The Multinomial Model, 422
13.3 Pearson s Test for Goodness of Fit, 424
13.4 Contingency Tables, 428
13.5 Contingency Tables with One Margin Fixed
(Test of Homogeneity), 435
13.6 An Exact Test for a 2x2 Contingency Table, 441
References, 444
Exercises, 444
Mathematical Exercises, 451
14 Design of Experiments and Analysis of Variance 453
14.1 Introduction and Basic Terminology, 453
14.2 Comparison of Several Treatments: The Completely
Randomized Design, 456
14.3 Population Model and Inferences for a Completely
Randomized Design, 462
14.4 Randomized Block Experiments for Comparing k
Treatments, 469
14.5 Factorial Experiments, 477
14.6 Two-level Factorial Designs, 483
References, 496
Exercises, 496
Mathematical Exercises, 503
xiv CONTENTS
15 NONPARAMETRIC INFERENCE 505
15.1 Introduction, 505
15.2 The Wilcoxon Rank-Sum Test for Comparing Two
Treatments, 507
15.3 Paired Comparisons, 516
15.4 Confidence Intervals Based on Rank Tests, 523
15.5 Measures of Correlation Based on Ranks, 526
15.6 The Kruskal-Wallis Test for Comparing k Treat¬
ments, 533
15.7 Concluding Remarks, 537
References, 539
Exercises, 539
Class Project, 547
Mathematical Exercises, 547
16 Sample Surveys 550
16.1 Why Take Only a Sample When the Population Is
Finite? 550
16.2 Specification of the Population and the Characteristic
of Interest, 551
16.3 Probability Sampling, 552
16.4 Bias and Its Sources, 552
16.5 Using a Random Number Table, 554
16.6 Simple Random Sampling, 555
16.7 Sampling to Determine a Proportion, 560
16.8 Stratified Random Sampling, 563
16.9 Allocation of Sample Sizes, 569
16.10 Stratified Sampling to Determine a Proportion, 571
16.11 Other Methods of Sampling, 573
16.12 Planning a Survey, 575
References, 577
Exercises, 577
Class Projects, 583
Mathematical Exercises, 583
Appendix 587
Table 1 The Number of Combinations (*), 587
Table 2 Cumulative Binomial Probabilities, 588
Table 3 Cumulative Poisson Probabilities, 595
CONTENTS XV
Table 4 Standard Normal Probabilities, 597
Table 5 Percentage Points of / Distributions, 599
Table 6 Percentage Points of x2 Distributions, 600
Table 7 Percentage Points of F{yx,v^) Distributions, 602
Table 8 Extended Table of Percentage Points of t Distributions,
608
Table 9 Selected Tail Probabilities for the Null Distribution of
Wilcoxon s Rank-Sum Statistic, 610
Table 10 Selected Tail Probabilities for the Null Distribution of
Wilcoxon s Signed-Rank Statistic, 615
Table 11 Confidence Intervals for the Median of a Symmetric
Distribution Using the Wilcoxon Signed-Rank Test, 617
Table 12 Confidence Intervals for Shift Using the Wilcoxon
Rank-Sum Test, 618
Table 13 Selected Tail Probabilities for the Null Distribution of
Spearman s Statistic 2 =1i?,S ,, 621
Table 14 5000 Random Digits, 623
Answers to Selected Odd Numbered Exercises, 625
Index 631
|
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| author | Bhattacharyya, Gouri K. 1940- Johnson, Richard Arnold 1937- |
| author_GND | (DE-588)13004363X (DE-588)130043648 |
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| spelling | Bhattacharyya, Gouri K. 1940- Verfasser (DE-588)13004363X aut Statistical concepts and methods Gouri K. Bhattacharyya ; Richard A. Johnson New York [u.a.] Wiley 1977 XV, 639 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Statistics cabt Statistical Methods cabt Statistique Statistiques - méthodes ram Statistische methoden gtt Statistik Statistics Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s DE-604 Johnson, Richard Arnold 1937- Verfasser (DE-588)130043648 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002284092&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhattacharyya, Gouri K. 1940- Johnson, Richard Arnold 1937- Statistical concepts and methods Statistics cabt Statistical Methods cabt Statistique Statistiques - méthodes ram Statistische methoden gtt Statistik Statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4151278-9 |
| title | Statistical concepts and methods |
| title_auth | Statistical concepts and methods |
| title_exact_search | Statistical concepts and methods |
| title_full | Statistical concepts and methods Gouri K. Bhattacharyya ; Richard A. Johnson |
| title_fullStr | Statistical concepts and methods Gouri K. Bhattacharyya ; Richard A. Johnson |
| title_full_unstemmed | Statistical concepts and methods Gouri K. Bhattacharyya ; Richard A. Johnson |
| title_short | Statistical concepts and methods |
| title_sort | statistical concepts and methods |
| topic | Statistics cabt Statistical Methods cabt Statistique Statistiques - méthodes ram Statistische methoden gtt Statistik Statistics Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistics Statistical Methods Statistique Statistiques - méthodes Statistische methoden Statistik Einführung |
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