语言研究中的统计学PDF电子书下载

1 Why do linguists need statistics? 1

2 Tables and graphs 8

2.1 Categorical data 8

2.2 Numerical data 13

References 16

2.3 Multi-way tables 19

2.4 Special cases 20

Summary 22

Exercises 23

3 Summary measures 25

3.1 The median 27

3.2 The arithmetic mean 29

3.3 The mean and the median compared 30

3.4 Means of proportions and percentages 34

3.5 Variability or dispersion 37

3.6 Central intervals 37

3.7 The variance and the standard deviation 40

3.8 Standardising test scores 43

Summary 45

Exercises 46

4 Statistical inference 48

4.1 The problem 48

4.2 Populations 49

4.3 The theoretical solution 52

4.4 The pragmatic solution 54

Summary 57

Exercises 58

5 Probability 59

5.1 Probability 59

5.2 Statistical independence and conditional probability 61

5.3 Probability and discrete numerical random variables 66

5.4 Probability and continuous random variables 68

5.5 Random sampling and random number tables 72

Summary 75

Exercises 75

6 Modelling statistical populations 77

6.1 A simple statistical model 77

6.2 The sample mean and the importance of sample size 80

6.3 A model of random variation:the normal distribution 86

6.4 Using tables of the normal distribution 89

Summary 93

Exercises 93

7.1 Point estimators for population parameters 95

7 Estimating from samples 95

7.2 Confidence intervals 96

7.3 Estimating a proportion 99

7.4 Confidence intervals based on small samples 101

7.5 Sample size 103

7.5.1 Central Limit Theorem 103

7.5.2 When the data are not independent 104

7.5.3 Confidence intervals 105

7.5.4 More than one level of sampling 106

7.5.5 Sample size to obtain a required precision 107

7.6 Different confidence levels 110

Summary 111

Exercises 112

8 Testing hypotheses about population values 113

8.1 Using the confidence interval to test a hypothesis 113

8.2 The concept of a test statistic 117

8.3 The classical hypothesis test and an example 120

8.4 How to use statistical tests of hypotheses:is significance significant? 127

8.4.1 The value of the test statistic is significant at the 1 2.497769e-180vel 129

8.4.2 The value of the test statistic is not significant 130

Summary 130

Exercises 131

9 Testing the fit of models to data 132

9.1 Testing how well a complete model fits the data 132

9.2 Testing how well a type of model fits the data 137

9.3 Testing the model of independence 139

9.4 Problems and pitfalls of the chi-squared test 144

9.4.1 Small expected frequencies 144

9.4.2 The 2×2 contingency table 146

9.4.3 Independence of the observations 147

9.4.4 Testing several tables from the same study 149

9.4.5 The use of percentages 150

Summary 151

Exercises 152

10 Measuring the degree of interdependence between two variables 154

10.1 The concept of covariance 154

10.2 The correlation coefficient 160

10.3 Testing hypotheses about the correlation coefficient 162

10.4 A confidence interval for a correlation coefficient 163

10.5 Comparing correlations 165

10.6 Interpreting the sample correlation coefficient 167

10.7 Rank correlations 169

Summary 174

Exercises 174

11.1 Independent samples:testing for differences between means 176

11 Testing for differences between two populations 176

11.2 Independent samples:comparing two variances 182

11.3 Independent samples:comparing two proportions 182

11.4 Paired samples:comparing two means 184

11.5 Relaxing the assumptions of normality and equal var-iance:nonparametric tests 188

11.6 The power of different tests 191

Summary 192

Exercises 193

12 Analysis of variance-ANOVA 194

12.1 Comparing several means simultaneously:one-way ANOVA 194

12.2 Two-way ANOVA:randomised blocks 200

12.3 Two-way ANOVA:factorial experiments 202

12.4 ANOVA:main effects only 206

12.5 ANOVA:factorial experiments 211

12.6 Fixed and random effects 212

12.7 Test score reliability and ANOVA 215

12.8 Further comments on ANOVA 219

12.8.1 Transforming the data 220

12.8.2 'Within-subject'ANOVAs 221

Exercises 222

Summary 222

13 Linear regression 224

13.1 The simple linear regression model 226

13.2 Estimating the parameters in a linear regression 229

13.3 The benefits from fitting a linear regression 230

13.4 Testing the significance of a linear regression 233

13.5 Confidence intervals for predicted values 234

13.6 Assumptions made when fitting a linear regression 235

13.7 Extrapolating from linear models 237

13.8 Using more than one independent variable:multiple regression 237

13.9 Deciding on the number of independent variables 242

13.10 The correlation matrix and partial correlation 244

13.11 Linearising relationships by transforming the data 245

13.12 Generalised linear models 247

Summary 247

Exercises 248

14 Searching for groups and clusters 249

14.1 Multivariate analysis 249

14.2 The dissimilarity matrix 252

14.3 Hierarchical cluster analysis 254

14.4 General remarks about hierarchical clustering 259

14.5 Non-hierarchical clustering 261

14.6 Multidimensional scaling 262

14.7 Further comments on multidimensional scaling 265

14.8 Linear discriminant analysis 265

14.9 The linear discriminant function for two groups 268

14.10 Probabilities of misclassification 269

Exercises 271

Summary 271

15 Principal components analysis and factor analysis 273

15.1 Reducing the dimensionality of multivariate data 273

15.2 Principal components analysis 275

15.3 A principal components analysis of language test scores 278

15.4 Deciding on the dimensionality of the data 282

15.5 Interpreting the principal components 284

15.7 Covariance matrix or correlation matrix? 287

15.6 Principal components of the correlation matrix 287

15.8 Factor analysis 290

Summary 295

Appendix A Statistical tables 296

Appendix B Statistical computation 307

Appendix C Answers to some of the exercises 314

Index 319

文库索引 323