语言研究中的统计学【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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1 Why do linguists need statistics?1

2 Tables and graphs8

2.1 Categorical data8

2.2 Numerical data13

References16

2.3 Multi-way tables19

2.4 Special cases20

Summary22

Exercises23

3 Summary measures25

3.1 The median27

3.2 The arithmetic mean29

3.3 The mean and the median compared30

3.4 Means of proportions and percentages34

3.5 Variability or dispersion37

3.6 Central intervals37

3.7 The variance and the standard deviation40

3.8 Standardising test scores43

Summary45

Exercises46

4 Statistical inference48

4.1 The problem48

4.2 Populations49

4.3 The theoretical solution52

4.4 The pragmatic solution54

Summary57

Exercises58

5 Probability59

5.1 Probability59

5.2 Statistical independence and conditional probability61

5.3 Probability and discrete numerical random variables66

5.4 Probability and continuous random variables68

5.5 Random sampling and random number tables72

Summary75

Exercises75

6 Modelling statistical populations77

6.1 A simple statistical model77

6.2 The sample mean and the importance of sample size80

6.3 A model of random variation:the normal distribution86

6.4 Using tables of the normal distribution89

Summary93

Exercises93

7.1 Point estimators for population parameters95

7 Estimating from samples95

7.2 Confidence intervals96

7.3 Estimating a proportion99

7.4 Confidence intervals based on small samples101

7.5 Sample size103

7.5.1 Central Limit Theorem103

7.5.2 When the data are not independent104

7.5.3 Confidence intervals105

7.5.4 More than one level of sampling106

7.5.5 Sample size to obtain a required precision107

7.6 Different confidence levels110

Summary111

Exercises112

8 Testing hypotheses about population values113

8.1 Using the confidence interval to test a hypothesis113

8.2 The concept of a test statistic117

8.3 The classical hypothesis test and an example120

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-180vel129

8.4.2 The value of the test statistic is not significant130

Summary130

Exercises131

9 Testing the fit of models to data132

9.1 Testing how well a complete model fits the data132

9.2 Testing how well a type of model fits the data137

9.3 Testing the model of independence139

9.4 Problems and pitfalls of the chi-squared test144

9.4.1 Small expected frequencies144

9.4.2 The 2×2 contingency table146

9.4.3 Independence of the observations147

9.4.4 Testing several tables from the same study149

9.4.5 The use of percentages150

Summary151

Exercises152

10 Measuring the degree of interdependence between two variables154

10.1 The concept of covariance154

10.2 The correlation coefficient160

10.3 Testing hypotheses about the correlation coefficient162

10.4 A confidence interval for a correlation coefficient163

10.5 Comparing correlations165

10.6 Interpreting the sample correlation coefficient167

10.7 Rank correlations169

Summary174

Exercises174

11.1 Independent samples:testing for differences between means176

11 Testing for differences between two populations176

11.2 Independent samples:comparing two variances182

11.3 Independent samples:comparing two proportions182

11.4 Paired samples:comparing two means184

11.5 Relaxing the assumptions of normality and equal var-iance:nonparametric tests188

11.6 The power of different tests191

Summary192

Exercises193

12 Analysis of variance-ANOVA194

12.1 Comparing several means simultaneously:one-way ANOVA194

12.2 Two-way ANOVA:randomised blocks200

12.3 Two-way ANOVA:factorial experiments202

12.4 ANOVA:main effects only206

12.5 ANOVA:factorial experiments211

12.6 Fixed and random effects212

12.7 Test score reliability and ANOVA215

12.8 Further comments on ANOVA219

12.8.1 Transforming the data220

12.8.2 'Within-subject'ANOVAs221

Exercises222

Summary222

13 Linear regression224

13.1 The simple linear regression model226

13.2 Estimating the parameters in a linear regression229

13.3 The benefits from fitting a linear regression230

13.4 Testing the significance of a linear regression233

13.5 Confidence intervals for predicted values234

13.6 Assumptions made when fitting a linear regression235

13.7 Extrapolating from linear models237

13.8 Using more than one independent variable:multiple regression237

13.9 Deciding on the number of independent variables242

13.10 The correlation matrix and partial correlation244

13.11 Linearising relationships by transforming the data245

13.12 Generalised linear models247

Summary247

Exercises248

14 Searching for groups and clusters249

14.1 Multivariate analysis249

14.2 The dissimilarity matrix252

14.3 Hierarchical cluster analysis254

14.4 General remarks about hierarchical clustering259

14.5 Non-hierarchical clustering261

14.6 Multidimensional scaling262

14.7 Further comments on multidimensional scaling265

14.8 Linear discriminant analysis265

14.9 The linear discriminant function for two groups268

14.10 Probabilities of misclassification269

Exercises271

Summary271

15 Principal components analysis and factor analysis273

15.1 Reducing the dimensionality of multivariate data273

15.2 Principal components analysis275

15.3 A principal components analysis of language test scores278

15.4 Deciding on the dimensionality of the data282

15.5 Interpreting the principal components284

15.7 Covariance matrix or correlation matrix?287

15.6 Principal components of the correlation matrix287

15.8 Factor analysis290

Summary295

Appendix A Statistical tables296

Appendix B Statistical computation307

Appendix C Answers to some of the exercises314

Index319

文库索引323