A basic course in statistics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
London u.a.
Arnold
1992
|
| Ausgabe: | 3. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003350422&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XX, 451 S. graph. Darst. |
| ISBN: | 0340567724 |
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| 245 | 1 | 0 | |a A basic course in statistics |c G. M. Clarke ; D. Cooke |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a London u.a. |b Arnold |c 1992 | |
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Datensatz im Suchindex
| _version_ | 1819286015387369472 |
|---|---|
| adam_text | A Basic Course in
Statistics
Third edition
G M Clarke
D Cooke
Edward Arnold
A member of the Hodder Headline Group
LONDON MELBOURNE AUCKLAND
Contents
Preface to the third edition
Introduction
List of projects
Notation
Populations and variates
A statistical investigation
Constructing tables and graphs
Tables and diagrams
Exercises on Chapter 1
Computing exercises
Projects
Measures of the centre of a set of observs
Introduction
The median
The arithmetic mean
S-notation
The mean of grouped data
Coding
The mode
The geometric mean
Weighted averages and index numbers
Exercises on Chapter 2
Computing exercises
Projects
Samples and populations
A sampling investigation
Some methods of choosing a sample
Completing the investigation
Random numbers
Pseudo-random numbers
Systematic samples
Some useful terms
Sampling with and without replacement
Exercises on Chapter 3
Computing exercises
Projects
HI
V
xvii
xix
x Contents
4 The measurement of variability 42
4 1 Introduction 42
4 2 Range 42
4 3 Mean deviation 42
4 4 Variance and standard deviation 43
4 5 Variance and standard deviation of a grouped frequency distribution 46
4 6 The semi-inter-quartile range (or quartile deviation) 50
4 7 Quantiles 51
4 8 Exercises on Chapter 4 54
4 9 Computing exercises 55
4 10 Projects 57
Revision exercises A 57
5 Probability 63
5 1 Introduction 63
5 2 Winning the toss 64
5 3 Terminology and notation 66
5 4 Counting methods 69
5 5 Use of counting methods in probability 73
5 6 Exercises on Chapter 5 74
5 7 Computing exercises 75
5 8 Projects 76
6 Probabilities of compound events ^ 77
6 1 Introduction 77
6 2 The intersection of two events 77
6 3 The union of two events 78
6 4 Addition rule for mutually exclusive events 80
6 5 Complementary events 80
6 6 The intersection and union of three or more events 82
6 7 Conditional probability 83
6 8 Independence 87
6 9 Events which may happen in mutually exclusive ways 90
6 10 Possibility spaces for outcomes that are not equally likely 93
6 11 Estimation of probabilities 95
6 12 Simulation 96
6 13 Exercises on Chapter 6 97
6 14 Computing exercises 99
6 15 Projects 99
7 Discrete random variables 101
7 1 Predicting the number of left-handed children in a class 101
7 2 Random variables 103
7 3 Families of random variables 105
7 4 The discrete uniform distribution 105
7 5 The Bernoulli distribution 106
7 6 The binomial distribution 106
7 7 The geometric distribution 109
7 8 Cumulative distribution functions and medians 111
7 9 Distribution of a function g(R) given the distribution of R 112
7 10 Choice of a random sample from a distribution 113
7 11 Exercises on Chapter 7 114
7 12 Computing exercises 116
7 13 Projects 116
Contents xi
8 Expectation of a random variable 118
8 1 Expected values 118
8 2 The means of the binomial and geometric distributions 120
8 3 Expectation of a linear function of a random variable 121
8 4 The expected value of a function of a random variable 123
8 5 Variance as an expected value 126
8 6 The variance of the binomial distribution 126
8 7 Variance of a linear function of a random variable 128
8 8 Probability generating functions 129
8 9 Exercises on Chapter 8 131
8 10 Computing exercises 132
8 11 Projects 133
Revision exercises B 133
9 Joint distributions 138
9 1 Bivariate distributions 138
9 2 Mean of the sum of two random variables 141
9 3 Mean of the product of two independent random variables 144
9 4 The variance of the sum of two independent random variables 146
9 5 Exercises on Chapter 9 148
9 6 Computing exercises 149
9 7 Projects 150
10 Estimation 151
10 1 The distribution of estimates of a proportion 151
10 2 Distribution of estimates ofa mean 153
10 3 The mean and variance of A 154
10 4 Unbiased estimators 155
10 5 Unbiased estimation of variance ^ 156
10 6 Exercises on Chapter 10 158
10 7 Computing exercises 159
10 8 Projects 160
11 Collecting data 162
11 1 Introduction 162
11 2 Surveys 162
11 3 Stratified random sampling 163
11 4 Experiments 164
11 5 Basic principles of experimental design 165
11 6 Exercises on Chapter 11 167
11 7 Projects 168
12 Significance testing 169
12 1 Testing a hypothesis 169
12 2 Another alternative hypothesis 172
12 3 Two types of error 176
12 4 Significance 177
12 5 The Wilcoxon Rank Sum (or Mann-Whitney U) test 178
12 6 The Wilcoxon signed-rank test 182
12 7 Type II errors and the power of a test 184
12 8 Summary and definitions 186
12 9 Exercises on Chapter 12 188
12 10 Computing exercises 190
xii Contents
12 11 Projects 190
Revision exercises C 191
13 Continuous random variables 196
13 1 Modelling continuous variates 196
13 2 The specification of continuous random variables 201
13 3 The mean and variance of continuous random variables 204
13 4 Use of the expectation operator with continuous random variables 205
13 5 The continuous uniform distribution 207
13 6 The exponential distribution 208
13 7 Uses of the exponential distribution 209
13 8 The moment generating function 212
13 9 Generating the moments 213
13 10 Distribution of a function of a random variable 214
13 11 Exercises on Chapter 13 215
13 12 Computing exercises 218
13 13 Projects 218
14 The normal distribution 220
14 1 Introduction 220
14 2 The standard normal distribution 221
14 3 The normal distribution as a model for data 222
14 4 Derivation of mean and variance 224
14 5 The calculation and use of standard variates when data are normally
distributed 226
14 6 Exercises on Chapter 14 230
14 7 Computing exercises 231
14 8 Projects 232
15 Sampling distributions of means and related quantities i 233
15 1 The central limit theorem I 233
15 2 Distribution of sample total 235
15 3 Normal approximation to the binomial distribution 237
15 4 Proportions 240
15 5 Distribution of linear combinations of normal random variables 240
15 6 Exercises on Chapter 15 242
15 7 Computing exercises 245
15 8 Projects 245
Revision exercises D 245
16 Significance tests using the normal distribution 251
16 1 Introduction 251
16 2 The standard normal distribution 251
16 3 A single observation from M Qi, a2) 254
16 4 The mean of n observations from M (n, a2) 255
16 5 Difference between two means from normal distributions 257
16 6 Large-sample tests 258
16 7 One-tail and two-tail tests 259
16 8 Paired comparison data 260
16 9 Tests for proportions 262
16 10 Normal approximations to non-parametric test statistics 264
16 11 Test on sample mean when variance estimated from sample 265
16 12 Paired comparisons using estimated variance 267
Contents xiii
16 13 Test on means of two unpaired samples using estimated variances 269
16 14 Inference when the null hypothesis is the hypothesis of interest 271
16 15 Parametric versus non-parametric tests 271
16 16 Exercises on Chapter 16 272
16 17 Computing exercises 276
16 18 Projects 276
17 Confidence intervals 277
17 1 Introduction 277
17 2 Confidence interval for mean of a normal distribution 278
17 3 Confidence interval for population mean based on a large sample 279
17 4 Confidence interval for a population proportion 280
17 5 Confidence intervals for means of normal distributions when the variance
a2 is unknown and the sample size is small 281
17 6 Investigation of a null hypothesis 283
17 7 Confidence interval for variance of a normal distribution 284
17 8 Exercises on Chapter 17 285
17 9 Computing exercises 287
17 10 Projects 288
18 Hypothesis tests using the ^distribution 289
18 1 Random digits 289
18 2 The ^ family of distributions 290
18 3 The rule for finding degrees of freedom in y2 tests 292
18 4 Why the X2 statistic has an approximate x~ distribution 293
18 5 Testing the fit of a theoretical distribution to observed data 294
18 6 Testing the fit of data to a binomial distribution 295
18 7 Contingency tables 298
18 8 The2x2 table 300
18 9 Testing the fit of a continuous distribution 303
18 10 Exercises on Chapter 18 304
18 11 Computing exercises 306
18 12 Projects 307
Revision exercises E 307
19 The Poisson distribution 315
19 1 Introduction 315
19 2 Two mathematical results 315
19 3 The binomial distribution as n-» oo, ^ - » 0 315
19 4 The Poisson distribution as the outcome of a random process 318
19 5 The conditions for a Poisson distribution 319
19 6 Conditions in which a Poisson model breaks down 320
19 7 The mean and variance of the Poisson distribution 321
19 8 The sum of two Poisson random variables 323
19 9 Tests of goodness-of-fit to a Poisson distribution 324
19 10 The normal approximation to the Poisson distribution 325
19 11 Testing a hypothesis about the mean in a Poisson distribution 326
19 12 Comparing two means 327
19 13 Giving limits to an estimated mean 328
19 14 The index of dispersion 329
19 15 Significance tests when x2 has a very large number of degrees of freedom 330
19 16 Exercises on Chapter 19 331
19 17 Computing exercises 333
19 18 Projects 334
xiv Contents
20 Correlation 335
20 1 Introduction 335
20 2 Scatter diagrams 335
20 3 The correlation coefficient 339
20 4 Correlation between two random variables 341
20 5 Testing values of r for significance 343
20 6 Fallacies in interpreting calculated correlation coefficients 344
20 7 Comparing two correlation coefficients 348
20 8 Confidence interval for p 350
20 9 Rank correlation 351
20 10 Testing rs for significance 352
20 11 Exercises on Chapter 20 354
20 12 Computing exercises 356
20 13 Projects 357
21 Linear regression 359
21 1 Introduction 359
21 2 Fitting a straight line when there is error in only one variable 359
21 3 Fitting a straight line that may not pass through the origin 363
21 4 The distribution of b 366
21 5 Regression 368
21 6 Prediction of the total score on two dice 369
21 7 Prediction of son s height from father s height 370
21 8 Two possible regression lines 373
21 9 Exercises on Chapter 21 375
21 10 Computing exercises 378
21 11 Projects 378
Revision exercises F 379
22 The analysis of variance 386
22 1 Introduction 386
22 2 Comparison of the means of populations: one-way analysis of variance 387
22 3 Confidence intervals and tests on means 390
22 4 The F-distribution and the F-test 391
22 5 A mathematical model for comparing population means 393
22 6 Two-way analysis of variance 394
22 7 An analysis of variance for regression 399
22 8 Exercises on Chapter 22 401
22 9 Computing exercises 404
22 10 Projects 405
Appendix 406
I The binomial series expansion 406
II The exponential function 407
III Derivatives and integrals of the exponential function 408
IV Integrals related to the normal distribution 408
V The limit of (1 +£) as n -* oo 409
VI A derivation of the Poisson distribution 410
Bibliography 411
I Particular topics 411
II Reference texts 411
Contents xv
Answers 412
Hints on computing exercises 424
Tables 435
Al Random digits 435
A2 The standard normal variable, z 437
A3 Student s r-distribution 438
A4 The/distribution 439
A5 The correlation coefficient 440
A6 Spearman s rank correlation coefficient 440
A7 TheF-distribution 441
A8 Common statistical distributions 443
I Discrete distributions 443
II Continuous distributions 444
Index 445
|
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| title | A basic course in statistics |
| title_auth | A basic course in statistics |
| title_exact_search | A basic course in statistics |
| title_full | A basic course in statistics G. M. Clarke ; D. Cooke |
| title_fullStr | A basic course in statistics G. M. Clarke ; D. Cooke |
| title_full_unstemmed | A basic course in statistics G. M. Clarke ; D. Cooke |
| title_short | A basic course in statistics |
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