Sturdy statistics: Nonparametrics and order statistics
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass.
Addison-Wesley
1973
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV,395 S. |
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MARC
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| 100 | 1 | |a Mosteller, Frederick |d 1916-2006 |e Verfasser |0 (DE-588)118940627 |4 aut | |
| 245 | 1 | 0 | |a Sturdy statistics |b Nonparametrics and order statistics |c Frederick Mosteller ; Robert E. K. Rourke |
| 264 | 1 | |a Reading, Mass. |b Addison-Wesley |c 1973 | |
| 300 | |a XV,395 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Non-parametrische statistiek |2 gtt | |
| 650 | 4 | |a Statistique non paramétrique | |
| 650 | 4 | |a Statistiques d'ordre | |
| 650 | 4 | |a Statistik | |
| 650 | 4 | |a Nonparametric statistics | |
| 650 | 4 | |a Order statistics | |
| 650 | 4 | |a Statistics | |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Rourke, Robert E. K. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804117428130545664 |
|---|---|
| adam_text | Contents
Chapter 1 Normal and Non normal Data
1 1 What are sturdy statistics? 1
1 2 What does this book do? 2
1 3 The shapes of normal distributions 2
1 4 The family of normal distributions 6
1 5 Permutation tests for differences in distributions 12
1 6 Permutation test with large samples; simulation 17
1 7 Normal approximation for permutation test for difference of means 19
Chapter 2 Applications of the Binomial and Multinomial Distributions
2 1 The binomial distribution 24
2 2 The normal approximation for the binomial 25
2 3 The sign test: more work for the binomial 29
2 4 Significance level and power 32
2 5 Power functions for the sign test 35
2 6 An informal and often used approach to testing 38
2 7 The multinomial distribution 41
2 8 Applications and tables of the multinomial distribution. ... 46
2 9 Unbiased and maximum likelihood estimation 48
Chapter 3 Ranking Methods for Two Independent Samples
3 1 A problem and a method 54
3 2 The Mann Whitney two sample test 56
3 3 Tables for the Mann Whitney test 60
3 4 Formulas for n = 1, n = 2 65
3 5 Power of the Mann Whitney test 68
3 6 Tables for computing power for normally distributed alternatives
for Mann Whitney test 68
Chapter 4 Normal Approximation for the Mann Whitney Test
4 1 Mean and variance of 7 , the rank sum of the J? sample ... 73
4 2 Normal approximation for the Mann Whitney test 76
xi
xii Contents
4 3 A closer look at the Mann Whitney statistic 80
4 4 How to rank ties 84
Chapter 5 Wilcoxon s Signed Rank Test
5 1 The Wilcoxon statistic, W 89
5 2 The distribution of W under the null hypothesis 92
5 3 Tables for the distribution of W; the normal approximation ... 94
5—4 Power of the Wilcoxon signed rank test for shift alternative with
normally distributed differences 99
Chapter 6 Rank Correlation
6 1 Correlation coefficient; special case 103
6 2 Rank correlation coefficient; the general case 108
6 3 The null distribution of the rank correlation coefficient, rs . . . 112
6 4 Tables for the distribution of rs; the normal approximation . . 119
6 5 Power of the rank correlation coefficient; the bivariate normal
distribution 122
Chapter 7 Rare Events: The Poisson Distribution
7 1 What processes yield a Poisson distribution? 125
7 2 The Poisson probability distribution: mean and variance . . . 127
7 3 The Poisson approximation for the binomial 133
7 4 Distribution of the sum of two independent Poisson random
variables 135
7 6 Estimation 139
Chapter 8 The Exact Chi Square Distribution
8 1 Sums of squares of standard normal deviates 141
8 2 Chi square distribution with one degree of freedom 144
8 3 Tables for ^ distributions 148
8 4 Shapes of ^ distributions; the normal approximation . . . . 149
8 5 Losing degrees of freedom 154
Chapter 9 Applying Chi Square to Counted Data: Basic Ideas
9 1 The idea of goodness of fit: particular case 159
9 2 Approximation of the exact discrete distribution by the continuous
chi square 164
9 3 Idea of goodness of fit: general discussion 168
9 4 The 1 x 2 contingency table; general p 170
9 5 Continuity correction for one degree of freedom 173
Chapter 10 Applying Chi Square: 1 x * Tables
10 1 The 1 x k contingency table; known p s 175
10 2 The 1 x k table; fitting a parameter 177
10 3 Pooling cells 182
10 4 Goodness of fit for continuous distributions 185
10 5 Chi square when the null hypothesis is false 186
Contents xiii
Chapter 11 Applying Chi Square: Two Way Tables
11 1 2 x 2 contingency tables; some origins 192
11 2 2 x 2 contingency tables; the chi square test for independence . 194
11 3 Correction for continuity 199
11 4 r x c contingency tables 200
11 5 Alternative ways of examining assumptions for several binomial
samples 205
11 6 The estimated values 207
Chapter 12 The Kruskal Wallis Statistic
12 1 Testing three independent samples 210
12 2 The Kruskal Wallis statistic for several independent samples . . 212
12 3 Relation of H to Mann Whitney statistic T; distribution of H. . 216
12 4 Tables for the Kruskal Wallis statistic 219
Chapter 13 The Problem of m Rankings: The Friedman Index
13 1 The problem of more than two rankings; a special case . . . 224
13 2 Average rank correlation coefficient for several pairs of judges . . 226
13 3 Testing for randomness; the Friedman statistic 229
Chapter 14 Order Statistics: Distributions of Probabilities; Confidence
Limits, Tolerance Limits
14 1 What are order statistics and why study them? 234
14 2 Confidence limits for the median and other quantiles of the
population 236
14 3 Distribution of the probability to the left of the z th order statistic;
statistically equivalent blocks 241
Chapter 15 Order Statistics: Point Estimation
15 1 Ideas of point estimation for means and medians 248
15 2 Distribution of Ut 251
15 3 Tables of expected values for the order statistics of the standard
normal distribution 256
15 4 Variances and covariances of the order statistics from a normal
distribution 260
15 5 Use of ranges to estimate a 263
Chapter 16 Designing Your Own Statistical Test or Measure
16 1 First steps: try to avoid invention 266
16 2 Runs up and down; comparing tests for trend 267
16 3 The comparative study of the power of several tests for slippage or
shift in location 269
Appendix I Discrete Distribution of a Random Variable
1 1 What is a random variable? 273
1 2 Probability function of a discrete random variable 274
1 3 The cumulative distribution 275
xiv Contents
1 4 The mean and the variance 276
1 5 Some properties of means and variances 278
Appendix II Continuous Distribution of a Random Variable
II—1 Probabilities represented by areas 279
II 2 The probability density function 280
II—3 Mean and variance of a continuous distribution 281
Appendix III Normal Approximations: Central Limit Theorems
III—1 The value of approximations 284
IH 2 Standardized random variables 284
III—3 The central limit theorem for the binomial 285
IH 4 More general central limit theorems 286
Appendix IV Dependent Random Variables: Covariance and Correlation
IV 1 Covariance 288
JV 2 Properties of covariance 288
IV 3 Correlation 290
Appendix V Variances of Sums of Random Variables
V l Variance of X + KandofX Y 292
V 2 Variance of the sum of n random variables 293
V 3 Variance of weighted sums 295
V 4 Sums and differences of independent normal random variables . 296
V 5 Sums and differences of correlated normal random variables . . 297
Appendix VI Sampling Theory
VI 1 Sampling with replacement 298
VI 2 Sampling without replacement 300
Appendix VII Confidence Limits and Significance Testing
VI I 1 The general idea of statistical inference 303
VII 2 Confidence limits and significance tests on n; known a . . . . 305
VII 3 Confidence limits and significance tests on n; unknown a, large
samples 306
VI1 4 Confidence limits and significance tests with small samples; the
r distributions 306
VI1 5 Differences between means; two samples, known o s .... 308
VI1 6 Differences between means; two samples, unknown cr s . . . . 309
Tables
A l Normal curve areas 313
A 2 Inverse of cumulative normal 314
A 3 Probability levels of r distribution 315
A 4 Values of chi squares 316
A 5 Cumulative binomial distribution 318
Contents xv
A 6 Cumulative binomial for p = | 324
A 7 Multinomial distribution 328
A 8 Poisson distribution 333
A 9 Probabilities for Mann Whitney, T 337
A 10 /i and a for Mann Whitney, T 339
A l 1 Probabilities for Wilcoxon, Wsm Ws 340
A 12 a for Wilcoxon, W 342
A l 3 Probabilities for D and Rs 343
A l 4 Probabilities for Kruskal Wallis, H 344
A l 5 Probabilities for Friedman, X? 354
A l 6 Expected values of order statistics 356
A 17 Covariances between order statistics 360
A l 8 Divisors for the range 363
A l 9 Ordinates of the normal 364
A 20 Squares 365
A 21 Square roots 366
A 22 1000 random digits 367
A 23 200 random normal deviates 368
Glossary 369
References 371
Short Answers to Selected Odd Numbered Exercises . . . 373
Index 385
|
| any_adam_object | 1 |
| author | Mosteller, Frederick 1916-2006 Rourke, Robert E. K. |
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| physical | XV,395 S. |
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| spelling | Mosteller, Frederick 1916-2006 Verfasser (DE-588)118940627 aut Sturdy statistics Nonparametrics and order statistics Frederick Mosteller ; Robert E. K. Rourke Reading, Mass. Addison-Wesley 1973 XV,395 S. txt rdacontent n rdamedia nc rdacarrier Non-parametrische statistiek gtt Statistique non paramétrique Statistiques d'ordre Statistik Nonparametric statistics Order statistics Statistics Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Rourke, Robert E. K. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001970251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mosteller, Frederick 1916-2006 Rourke, Robert E. K. Sturdy statistics Nonparametrics and order statistics Non-parametrische statistiek gtt Statistique non paramétrique Statistiques d'ordre Statistik Nonparametric statistics Order statistics Statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Sturdy statistics Nonparametrics and order statistics |
| title_auth | Sturdy statistics Nonparametrics and order statistics |
| title_exact_search | Sturdy statistics Nonparametrics and order statistics |
| title_full | Sturdy statistics Nonparametrics and order statistics Frederick Mosteller ; Robert E. K. Rourke |
| title_fullStr | Sturdy statistics Nonparametrics and order statistics Frederick Mosteller ; Robert E. K. Rourke |
| title_full_unstemmed | Sturdy statistics Nonparametrics and order statistics Frederick Mosteller ; Robert E. K. Rourke |
| title_short | Sturdy statistics |
| title_sort | sturdy statistics nonparametrics and order statistics |
| title_sub | Nonparametrics and order statistics |
| topic | Non-parametrische statistiek gtt Statistique non paramétrique Statistiques d'ordre Statistik Nonparametric statistics Order statistics Statistics Statistik (DE-588)4056995-0 gnd |
| topic_facet | Non-parametrische statistiek Statistique non paramétrique Statistiques d'ordre Statistik Nonparametric statistics Order statistics Statistics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001970251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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