語言研究中的統(tǒng)計學(xué)（英文）

Preface by HaUiday
王宗炎序
導(dǎo)讀
Preface
1 Why do linguists need statistics
2 Tables and graphs
2.1 Categorical data
2.2 Numerical data
2.3 Multi-way tables
2.4 Special cases
Summary
Exercises
3 Summary measures
3.1 Themedian
3.2 The arithmetic mean
3.3 The mean and the median compared
3.4 Means of proportions and percentages
3.5 Variability or dispersion
3.6 Central intervals
3.7 The variance and the standard deviation
3.8 Standardising test scores
Summary
Exercises
4 Statistical inference
4.1 Theproblem
4.2 Populations
4.3 The theoretical solution
4.4 The pragmatic solution
Summary
Exercises
5 Probability
5.1 Probability
5.2 Statistical independence and conditional probability
5.3 Probability and discrete numerical random variables
5.4 Probability and continuous random variables
5.5 Random sampling and random number tables
Summary
Exercises
6 Modelling statistical populations
6.1 A simple statistical model
6.2 The sample mean and the importance of sample size
6.3 A model of random variation: the normal distribution
6.4 Using tables of the normal distribution
Summary
Exercises
7 Estimating from samples
7.1 Point estimators for population parameters
7.2 Confidenceintervais
7.3 Estimating a proportion
7.4 Confidence intervals based on small samples
7.5 Sample size
7.5.1 Central Limit Theorem
7.5.2 When the data are not independent
7.5.3 Confidence intervals
7.5.4 More than one level of sampling
7.5.5 Sample size to obtain a required precision
7.6 Different confidence levels
Summary
Exercises
8 Testing hypotheses about population values
8.1 Using the confidence interval to test a hypothesis
8.2 The concept of a test statistic
8.3 The classical hypothesis test and an example
8.4 How to use statistical tests of hypotheses: is significance
significant
8.4.1 The value of the test statistic is significant at the z%
level
8.4.2 The value of the test statistic is not significant
Summary
Exercises
9 Testing the fit of models to data
9.1 Testing how well a complete model fits the data
9.2 Testing how well a type of model fits the data
9.3 Testing the model of independence
9.4 Problems and pitfalls of the chi-squared test
9.4.1 Smallexpected frequencies
9.4.2 The 2 x 2 contingency table
9.4.3 Independence of the observations
9.4.4 Testing several tables from the same study
9.4.5 The use of percentages
Summary
Exercises
10 Measuring the degree of interdependence between
two variables
10.1 The concept of covariance
10.2 The correlation coefficient
10.3 Testing hypotheses about the correlation coefficient
10.4 A confidence interval for a correlation coefficient
10.5 Comparing correlations
10.6 Interpreting the sample correlation coefficient
10.7 Rank correlations
Summary
Exercises
11 Testing for differences between two populations
11.1 Independent samples: testing for differences between
means
11.2 Independent samples: comparing two variances
11.3 Independent samples: comparing two proportions
11.4 Paired samples: comparing two means
11.5 Relaxing the assumptions of normality and equal var-
iance: nonparametrie tests
11.6 The power of different tests
Summary
Exercises
12 Analysis of variance- ANOVA
12.1 Comparing several means simultaneously: one-way
ANOVA
12.2 Two-way ANOVA: randomised blocks
12.3 Two-way ANOVA: factorial experiments
12.4 ANOVA: main effects only
12.5 ANOVA: factorial experiments
12.6 Fixed and random effects
12.7 Test score reliability and ANOVA
12.8 Further commentson ANOVA
12.8.1 Transforming the data
12.8.2 ''Within-subject''ANOVAs
Summary
Exercises
13 Linear regression
13.1 The simple linear regression model
13.2 Estimating the parameters in a linear regression
13.3 The benefits from fitting a linear regression
13.4 Testing the significance of a linear regression
13.5 Confidence intervals for predicted values
13.6 Assumptions made when fitting a linear regression
13.7 Extrapolating from linear models
13.8 Using more than one independent variable: multiple
regression
13.9 Deciding on the number of independent variables
13.10 The correlation matrix and partial correlation
13.11 Linearising relationships by transforming the data
13.12 Generalised linear models
Summary
Exercises
14 Searching for groups and clusters
14.1 Multivariate analysis
14.2 The dissimilarity matrix
14.3 Hierarchical cluster analysis
14.4 General remarks about hierarchical clustering
14.5 Non-hierarchical clustering
14.6 Multidimensional scaling
14.7 Further comments on multidimensional scaling
14.8 Linear discriminant analysis
14.9 The linear discriminant function for two groups
14.10 Probabilities of misclassification
Summary
Exercises
15 Principal components analysis and factor analysis
15.1 Reducing the dimensionality of multivariate data
15.2 Principal components analysis
15.3 A principal components analysis of language test scores
15.4 Deciding on the dimensionality of the data
15.5 Interpreting the principal components
15.6 Principal components of the correlation matrix
15.7 Covariance matrix or correlation matrix
15.8 Factor analysis
Summary
Appendix A Statistical tables
Appendix B Statistical computation
Appendix C Answers to some of the exercises
References
Index
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