Statistics in Language Studies

Portada
This book demonstrates the contribution that statistics can and should make to linguistic studies. The range of work to which statistical analysis is applicable is vast: including, for example, language acquisition, language variation and many aspects of applied linguistics. The authors give a wide variety of linguistic examples to demonstrate the use of statistics in summarising data in the most appropriate way, and then making helpful inferences from the processed information. The range of techniques introduced by the book will help the reader both to evaluate and make use of literature which employs statistical analysis, and to apply statistics in their own research. Each chapter gives step-by-step explanations of particular techniques using examples from a number of fields, and is followed by extensive exercises. The early part of the book provides a thorough grounding in probability and statistical inference, and then progresses through methods such as chi-squared and analysis of variance, to multivariate methods such as cluster analysis, principal components analysis and factor analysis. None of these techniques requires the reader to have a grasp of mathematics more complex than simple algebra. Students and researchers in many fields of linguistics will find this book an invaluable introduction to the use of statistics, and a practical text for the development of skills in the application of statistics.
 

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Decent but no longer sufficient.

Contenido

Why do linguists need statistics?
1
Tables and graphs
8
22 Numerical data
13
23 Multiway tables
19
24 Special cases
20
Summary
22
Exercises
23
Summary measures
25
102 The correlation coefficient
160
103 Testing hypotheses about the correlation coefficient
162
104 A confidence interval for a correlation coefficient
163
105 Comparing correlations
165
1o6 Interpreting the sample correlation coefficient
167
107 Rank correlations
169
Summary
174
Testing for differences between two populations
176

31 The median
27
32 The arithmetic mean
29
33 The mean and the median compared
30
34 Means of proportions and percentages
34
35 Variability or dispersion
37
37 The variance and the standard deviation
40
38 Standardising test scores
43
Summary
45
Exercises
46
Statistical inference
48
42 Populations
49
43 The theoretical solution
52
44 The pragmatic solution
54
Summary
57
Probability
59
52 Statistical independence and conditional probability
61
53 Probability and discrete numerical random variables
66
54 Probability and continuous random variables
68
55 Random sampling and random number tables
72
Summary
75
Modelling statistical populations
77
62 The sample mean and the importance of sample size
80
the normal distribution
86
64 Using tables of the normal distribution
89
Summary
93
Estimating from samples
95
72 Confidence intervals
96
73 Estimating a proportion
99
74 Conf1dence intervals based on small samples
101
75 Sample size
103
752 When the data are not independent
104
753 Confidence intervals
105
754 More than one level of sampling
106
755 Sample size to obtain a required precision
107
76 Different confidence levels
110
Summary
111
Exercises
112
Testing hypotheses about population values
113
82 The concept of a test statistic
117
83 The classical hypothesis test and an example
120
is significance significant?
127
841 The value of the test statistic is significant at the 1 level
129
842 The value of the test statistic is not significant
130
Exercises
131
Testing the fit of models to data
132
92 Testing how well a type of model fits the data
137
93 Testing the model of independence
139
94 Problems and pitfalls of the chisquared test
144
942 The 2 X 2 contingency table
146
943 Independence of the observations
147
944 Testing several tables from the same study
149
945 The use of percentages
150
Summary
151
Exercises
152
Measuring the degree of interdependence between two variables
154
comparing two variances
182
comparing two means
184
nonparametric tests
188
116 The power of different tests
191
Summary
192
Exercises
193
Analysis of variance ANOVA
194
randomised blocks
200
factorial experiments
202
main effects only
206
factorial experiments
211
126 Fixed and random effects
212
127 Test score reliability and ANOVA
215
128 Further comments on ANOVA
219
1281 Transforming the data
220
1282 Withinsubject ANOVAs
221
Summary
222
Linear regression
224
131 The simple linear regression model
226
132 Estimating the parameters in a linear regression
229
133 The benefits from fitting a linear regression
230
134 Testing the significance of a linear regression
233
135 Confidence intervals for predicted values
234
136 Assumptions made when fitting a linear regression
235
137 Extrapolating from linear models
237
139 Deciding on the number of independent variables
242
1310 The correlation matrix and partial correlation
244
1311 Linearising relationships by transforming the data
245
1312 Generalised linear models
247
Exercises
248
Searching for groups and clusters
249
142 The dissimilarity matrix
252
143 Hierarchical cluster analysis
254
144 General remarks about hierarchical clustering
259
145 Nonhierarchical clustering
261
146 Multidimensional scaling
262
147 Further comments on multidimensional scaling
265
149 The linear discriminant function for two groups
268
1410 Probabilities of misclassification
269
Summary
271
Principal components analysis and factor analysis
273
152 Principal components analysis
275
153 A principal components analysis of language test scores
278
154 Deciding on the dimensionality of the data
282
155 Interpreting the principal components
284
156 Principal components of the correlation matrix
287
158 Factor analysis
290
Summary
295
Statistical tables
296
Statistical computation
307
Answers to some of the exercises
314
References
316
Index
319
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