Applied statistical methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1974
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| Schriftenreihe: | Operations research and industrial engineering
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 479 S. Illustrationen |
| ISBN: | 0121461505 |
Internformat
MARC
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| 245 | 1 | 0 | |a Applied statistical methods |c Irving W. Burr |
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1974 | |
| 300 | |a XIX, 479 S. |b Illustrationen | ||
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| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
Preface xvii
Acknowledgments xix
Chapter 1 Introduction
1.1 Why Statistical Methods ? 1
1.2 Advice to the Student 2
Chapter 2 The Frequency Distribution
A Tool and a Concept
2.1 Introduction 4
2.2 An Example of a Frequency Distribution 4
2.3 Frequency Class Nomenclature and Tabulation 6
2.4 Discrete versus Continuous Data 8
2.5 Graphical Representation of a Frequency Distribution 8
2.6 The Cumulative Frequency Graph 10
2.7 What a Frequency Distribution Shows 12
2.8 Some Examples of Use of Frequency Tables and Graphs 13
2.9 Sample versus Population 16
2.10 Summary 19
Problems 19
Chapter 3 Summarization of Data by Objective Measures
3.1 Introduction 33
3.2 Some Averages 33
3.3 Some Measures of Variability 35
3.4 Efficient Calculation of Averages and Standard Deviations 38
3.4.1 Calculations for Frequency Data 41
3.5* Further Descriptive Measures of Frequency Distributions,
Third and Fourth Moments 42
3.6 Summary 45
Problems 46
vii
viii Table of Contents
Chapter 4 Some Elementary Probability
4.1 Introduction 48
4.2 Sample Spaces of Outcomes 49
4.3 Events 50
4.3.1 Relations of Events 51
4.3.2 Combinations of Events 52
4.4 Probabilities of Events 55
4.5 Probabilities on Discrete Sample Spaces 57
4.5.1 Countably Infinite Spaces 58
4.5.2 Events over Discrete Spaces 58
4.6 Independent and Dependent Events 59
4.6.1 Conditional Probabilities 62
4.6.2 Repeated Trials 63
4.7 Discrete Probabilities 66
4.7.1 Permutations and Combinations 66
4.7.2 Discrete Probability Examples 69
4.8 Probabilities on Continuous Spaces 77
4.9 Applied Bayes Probabilities—Posterior Probabilities 80
4.10 Interpretation of a Probability 82
4.11 Random Variables 83
4.12 Summary 83
Problems 84
Chapter 5 Some Discrete Probability Distributions
5.1 Theoretical Populations 90
5.2 Discrete Probability Distributions in General 91
5.2.1 Expected Values for Y and Functions of Y 92
5.2.2* Population Curve Shape Characteristics 93
5.2.3 Algebra of Expectations 93
5.2.4* Further on Population Moments 95
5.3 The Binomial Distribution 95
5.3.1 Examples of the Binomial Distribution 97
5.3.2 Population Moments for Binomial Distributions 99
5.3.3 Use of Binomial Tables 101
5.3.4 Calculation of a Binomial Distribution 101
5.3.5 Approximations to the Binomial Distribution 103
5.3.6 Conditions of Applicability of the Binomial Distribution 103
5.4 The Poisson Distribution 103
5.4.1 * A Derivation of the Poisson Probability Function 106
5.4.2 Examples of the Poisson Distribution 107
Table of Contents ix
5.4.3 Tables of the Poisson Distribution 109
5.4.4 Using the Poisson Distribution to Approximate the Binomial 109
5.4.5* Derivation of the Poisson as a Limit of the Binomial 109
5.4.6 Conditions of Applicability of the Poisson Distribution 110
5.5 The Hypergeometric Distribution 111
5.5.1 Tables for the Hypergeometric Distribution 113
5.5.2 Examples of the Hypergeometric Distribution 114
5.5.3* Moments for the Hypergeometric Distribution 115
5.5.4* Binomial Approximations to the Hypergeometric Distribution 116
5.5.5* Poisson Approximations to the Hypergeometric Distribution 117
5.5.6 Approximations to Sums of Terms of the Hypergeometric
Distribution 118
5.5.7 Conditions of Applicability of the Hypergeometric Distribution 118
5.5.8 Applications of the Hypergeometric Distribution 119
5.6 The Uniform Distribution 119
5.7* The Geometric Distribution 120
5.8* The Negative Binomial Distribution 122
5.9 Generating Samples from Discrete Distributions 124
5.10 Summary 125
References 125
Problems 126
Chapter 6 Some Continuous Probability Distributions
6.1 Continuous Probability Distributions 131
6.2 Some General Properties of Continuous Distributions 131
6.2.1 Moments for a Continuous Distribution 134
6.3 The Normal Curve 135
6.3.1 Properties of the Normal Distribution 136
6.3.2 The General Normal Curve 138
6.3.3 Sketching a Normal Curve 138
6.3.4 Approximating Probabilities by a Normal Distribution 139
6.4 The Rectangular Distribution 141
6.5 The Exponential Distribution 142
6.6* The Gamma Distribution 144
6.6.1 * Tables of the Gamma Distribution 146
6.6.2* Relation to the Normal Distribution 146
6.6.3* Use of the Gamma Distribution to Approximate Discrete
Distributions 146
6.7* The Beta Distribution 148
6.8* The Weibull Distribution 150
6.9* The Pearson System of Distributions 151
6.10* An Easily Fitted General System of Frequency Curves 152
6.11 Sums and Averages and a Central Limit Theorem 152
x Table of Contents
6.12* TchebychefFs Theorem 155
6.13 Summary 156
6.14* Proofs of Some Relations in Section 6.11 157
References 160
Problems 161
Chapter 7 Some Sampling Distributions
7.1 Distribution of Sample Statistics from Populations 166
7.2 Choice of Sample 167
7.2.1* Sampling from a Probability Distribution 168
7.2.2* Machine Generation of Random Samples 169
7.3 Sampling Distributions of a Sample Statistic 169
7.4 Distribution of Sample Means 171
7.4.1 Standardized Distribution for Means 111
7.4.2 Distribution of Means when Standard Demotion Is Unknown 171
7.4.3 Areas for the t Distribution 173
7.4.4* Interpolation Note 173
7.4.5 Distribution of Means from Nonnormal Populations 174
7.5 Distribution of Sample Variances 174
7.5.1 Distribution of Sample Standard Deviation 176
7.5.2* Population of y s Nonnormal 176
7.5.3 Tables of Chi Square 111
7.6* Joint Distribution of y and s from a Normal Population 177
7.7 Two Normal Populations, Independent Samples 177
7.7.1 Sum and Difference of Two Means, Standard Deviations Known 111
7.7.2 Sums and Differences of Two Means, Standard Deviations
Unknown but Equal 178
7.7.3 Two Variances, F Distribution 119
1.1.4* Two Variances, Large Samples 180
7.8 Sampling Aspects of the Binomial and Poisson Distributions 181
7.9* Sum of Two Independent Chi Square Variables 182
7.10* Noncentral Distributions 182
7.11 Summary 183
References 183
Problems 184
Chapter 8 Statistical Tests of Hypotheses
General and One Sample
8.1 Introduction 187
8.2 An Example 188
8.2.1 Approach 1 Given n, Set Significance Level x 189
8.2.2 Approach 2 Set Two Risks: a. and a ftp , and Find n 192
Table of Contents xi
8.3 Summary of the Elements in Tests of Hypotheses on One Parameter 194
8.4 Summary of Significance Testing for One Mean with a Unknown 196
8.5 Interpretation of Decisions in Hypothesis Testing 197
8.6 Nonnormal Populations of y s 198
8.7 Significance Testing for Mean /j., with a Unknown 198
8.7.1 Example 200
8.7.2 Operating Characteristic Curve 201
8.8 Significance Tests for Variability 202
8.8.1 An Example of First Approach 203
8.8.2 The Second Approach of 4, in Section 8.8 204
8.8.3* Operating Characteristic Curves for Variability Tests 206
8.8.4* Large Samples 206
8.9 Significance Testing for Attributes 207
8.9.1 The Binomial Tests 207
8.9.2 The Poisson Tests 209
8.9.3* Other Attribute Distributions 210
8.9.4 Operating Characteristic Curves 211
8.10 Relation of Significance Testing to Decision Theory 212
8.11 Summary 214
References 217
Problems 218
Chapter 9 Significance Tests Two Samples
9.1 The General Problem 223
9.2 Tests on Two Variances The F Test 225
9.2.1 An Example 226
9.2.2 Large Sample Tests 227
9.2.3 A Large Sample Example 227
9.3 Differences between Means 228
9.3.1 Standard Deviations Known 228
9.3.2 Standard Deviations Equal but Unknown 230
9.3.3* Standard Deviations Unknown and Possibly Unequal 232
9.4 Significance of Differences Binomial Data 234
9.5 Significance of Differences Poisson Data 236
9.5.1 Unequal Areas of Opportunity 237
9.6 Matched Pair Data. Importance of Experimental Design 239
9.6.1 * Matched Pair Model 241
9.7 Sample Sizes Needed for Tests of Two Means 242
9.8 Summary 246
References 246
Problems 247
xii Table of Contents
Chapter 10 Estimation of Population Characteristics
10.1 Point Estimates General Idea 253
10.2 Which Estimator to Use Characteristics of Estimation 254
10.2.1* Consistency and Sufficiency 256
10.3* How to Find a Desirable Estimator 256
10.4 Point Estimates Common Cases 256
10.5 Interval Estimation in General 257
10.5.1* Geometrical Argument for Confidence Intervals 258
10.6 Confidence Intervals for /x 259
10.7 Confidence Intervals for a 261
10.7.1 * Large Confidence Limits for a 262
10.8 How to Have Narrower Confidence Intervals 263
10.9 Confidence Intervals for Functions of Two Parameters
Two Samples 263
10.9.1 Confidence Limits on the Difference of Means 264
10.9.2* Confidence Limits on the Ratio of a s 266
10.9.3 Paired Differences 267
10.10 Confidence Limits for Attribute Data 267
10.10.1 Exact Method for Binomial Population 268
10.10.2 Normal Approximation for Confidence Limits for the Binomial 269
10.10.3 Exact Method for Poisson Population 270
10.10.4 Normal Approximation for Confidence Limits for the Poisson 211
10.10.5 Tables of Confidence Limits 271
10.10.6* Confidence Limits for Two Samples of Attribute Data 272
10.11 Relation between Interval Estimation and Significance Testing 273
10.12 Summary 275
References 275
Problems 278
Chapter 11 Simple Regression
11.1 Regression, A Study of Relationship 285
11.2 The Scatter Diagram 286
11.3 Line of Best Fit to Linear Data 287
11.3.1 Least Squares Fitting 287
11.3.2 Calculational Aspects 290
11.3.3 The Linear Model and Its Parameters 292
11.4 Sampling Distributions for Estimates 293
11.5 Significance Tests and Confidence Intervals for Parameters in
Linear Regression 295
11.5.1 Slope 296
Table of Contents xiii
11.5.2 Intercept 297
11.5.3 Mean of Y s: fiy 297
11.5.4 Error Variance oe°, and ae 297
11.5.5 Regression Line Mean: pY.x = f y + fi{X — X) 298
11.6 Correlational Aspects 298
11.7* Grouped Bivariate Data 300
11.8 Special Case M.x = PiX 304
11.9* Significance of Differences between Two Slopes 305
11.10 Nonlinearity Test 305
11.11 * Use of Least Squares Fitting for Other Trends 306
11.11.1* Functions Linear in the Parameters 306
11.11.2* Least Squares after a Transformation 307
11.11.3* Intrinsically Nonlinear Cases 310
11.12 Applications to Industry and the Laboratory 310
11.13 Summary 312
References 312
Problems 313
Chapter 12 Simple Analysis of Variance
12.1 General Concept of Analysis of Variance 322
12.2 One Factor Analysis of Variance 323
12.2.1 The Model 323
12.2.2 The Formulas and Test 325
12.2.3 The Case of Unequal Sample Sizes 329
12.2.4* Orthogonal Contrasts 331
12.3 Orthogonal Polynomials and Tests 334
12.4 A Method of Multiple Contrasts 341
12.4.1 The Newman Keuh Multiple Range Test 341
12.4.2 Example 343
12.4.3 Interpretation of Risk a. 344
12.5* Testing Homogeneity of Variances 345
12.5.1 An Example 346
12.5.2 Q Test with Unequal Degrees of Freedom 347
12.5.3 Q Test for Ranges 347
12.6 Types of Factors 348
12.7 Analysis of Variance for Two Factors 349
12.7.1 An Example 349
12.7.2 The Models and Assumptions 355
12.7.3 Expected Mean Squares and Significance Tests 356
12.7.4 Interpretation of Significant Factors 348
12.7.5 Case of Unreplicated Two Factor Experiments 348
12.7.6 Example of an Unreplicated Two Factor Completely
Randomised Design 360
xiv Table of Contents
12.8 Other Models 362
12.9 Summary 363
References 363
Problems 365
Chapter 13 Multiple Regression
13.1 Introduction 372
13.2 First Approach 374
13.2.1 Data Table Format 374
13.2.2 Fitting the Equation 31A
13.2.3 Alternative Forms of Normal Equations and Regression 376
13.2.4 Describing Goodness of Fit 379
13.2.5 Systematic Solution of the Normal Equations 380
13.2.6 Significance Tests on the Explained Variation 384
13.2.7 Simple Example 385
13.2.8 Second Example 387
13.3 Second Approach 388
13.3.1 Vectors and Matrices 388
13.3.2 The Matrix Approach 391
13.3.3 Selection of a Set of Predictors 396
13.3.4 Calculation of an Inverse 397
13.4 Summary of Approach 397
13.5 Adequacy of Regression Model 398
13.6 Comments and Precautions 399
References 400
Problems 401
Chapter 14 Goodness of Fit Tests, Contingency Tables
14.1 Introduction 407
14.2 The Chi square Test for Cell Frequencies, Observed versus
Theoretical 408
14.2.1 An Example 409
14.3 Testing Goodness of Fit of Theoretical Distributions 409
14.3.1 A Binomial Example 411
14.3.2 Examples of Tests of Normality 412
14.3.3* Example of a Gamma Distribution Fit 414
14.3.4 Example of a Poisson Distribution 415
14.4* Other Goodness of Fit Tests 416
14.5 Contingency Tables 417
14.5.1 An Example 417
14.5.2 The General Setup of a Contingency Table 418
14.5.3 A 2 ¦ 2 Contingency Table 420
14.5.4 Case of a 2 ¦ b Contingency Table 421
Table of Contents xv
14.6 The Sign Test 422
14.7 Summary 423
References 423
Problems 424
Appendix 429
Answers to Odd Numbered Problems 461
Index 469
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| indexdate | 2024-07-09T15:38:17Z |
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| isbn | 0121461505 |
| language | English |
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| spelling | Burr, Irving W. 1908- Verfasser (DE-588)133527093 aut Applied statistical methods Irving W. Burr New York [u.a.] Acad. Press 1974 XIX, 479 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Operations research and industrial engineering Statistik (DE-588)4056995-0 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Statistik (DE-588)4056995-0 s Anwendung (DE-588)4196864-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001290924&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burr, Irving W. 1908- Applied statistical methods Statistik (DE-588)4056995-0 gnd Anwendung (DE-588)4196864-5 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4196864-5 |
| title | Applied statistical methods |
| title_auth | Applied statistical methods |
| title_exact_search | Applied statistical methods |
| title_full | Applied statistical methods Irving W. Burr |
| title_fullStr | Applied statistical methods Irving W. Burr |
| title_full_unstemmed | Applied statistical methods Irving W. Burr |
| title_short | Applied statistical methods |
| title_sort | applied statistical methods |
| topic | Statistik (DE-588)4056995-0 gnd Anwendung (DE-588)4196864-5 gnd |
| topic_facet | Statistik Anwendung |
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