Statistics in language studies:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1986
|
| Edition: | 1. publ. |
| Series: | Cambridge textbooks in linguistics
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000770099&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000770099&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 322 S. graph. Darst. |
| ISBN: | 0521253268 0521273129 |
Staff View
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Record in the Search Index
| _version_ | 1819270972655534080 |
|---|---|
| adam_text | CONTENTS
page
Preface
xi
ι
Why do linguists need statistics?
ι
8
3
19
20
22
23
*5
27
29
30
34
37
37
40
43
45
46
48
48
49
б2
54
57
S»
2
Tables and graphs
2.1
Categorical data
2.2
Numerical data
2.З
Multi-way tables
2-4
Special cases
Summary
Exercises
3
Summary measures
3·1
The median
З2
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
The problem
4·2
Populations
4-3
The theoretical solution
4-4
The pragmatic solution
Summary
Exercises
Contents
5
Probability
59
5.
ι
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
Estimating from samples
95
7.1
Point estimators for population parameters
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 no
Summary in
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%
level
129
Contents
8.4.2
The value of the test statistic is not significant
130
Summary
130
Exercises
9
Testing the fit of models to data
І32
9.1
Testing how well a complete model fits the data
I32
9.2
Testing how well a type of model fits the data
!37
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
2X2
contingency table
146
9·4·3
Independence of the observations
47
9·4·4
Testing several tables from the same study
149
9-4-5
The use of percentages
!5°
Summary
151
Exercises
152
IO
Measuring the degree of interdependence between
two variables
44
ΐο.ΐ
The concept of covariance
154
10.2
The correlation coefficient
160
іо.з
Testing hypotheses about the correlation coefficient
162
io.
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
II
Testing for differences between two populations
176
II.
І
Independent samples: testing for differences between
means
176
11.
2
Independent samples: comparing two variances
182
•З
Independent samples: comparing two proportions
182
ІІ.4
Paired samples: comparing two means
184
«•5
Relaxing the assumptions of normality and equal var¬
iance: nonparametric tests
188
ІІ.6
The power of different tests
191
Summary
192
Exercises
193
vu
Contents
12
Analysis of variance
- ANOVA
12.
ι
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
ANO VA
215
12.8
Further comments on ANOVA
219
12.8.
ι
Transforming the data
220
12.8.2
Within-subject ANOVAs
221
Summary
222
Exercises
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
viii
Contents
14.8
Linear
discriminant
analysis
265
14.9
The linear discriminant function for two groups
268
14.10
Probabilities of misclassification
269
Summary
271
Exercises
271
15
Principal components analysis and factor analysis
27З
Ï5-1
Reducing the dimensionality of multivariate data
27З
15.2
Principal components analysis
275
*5·3
A principal components analysis of language test scores
278
!5·4
Deciding on the dimensionality of the data
282
ΐ5·5
Interpreting the principal components
284
Ι5.6
Principal components of the correlation matrix
287
15-7
Covariance matrix or correlation matrix?
287
15-8
Factor analysis
290
Summary
295
Appendix
A Statistical tables
296
Appendix
В
Statistical computation
307
Appendix
С
Answers to some of the exercises
314
References
316
Index
319
IX
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 c/iZ-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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| id | DE-604.BV001277187 |
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| indexdate | 2024-12-20T07:33:35Z |
| institution | BVB |
| isbn | 0521253268 0521273129 |
| language | English |
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| spellingShingle | Woods, Anthony Fletcher, Paul Hughes, Arthur 1941- Statistics in language studies Russisch (DE-588)4051038-4 gnd Sprachstatistik (DE-588)4182534-2 gnd |
| subject_GND | (DE-588)4051038-4 (DE-588)4182534-2 |
| title | Statistics in language studies |
| title_auth | Statistics in language studies |
| title_exact_search | Statistics in language studies |
| title_full | Statistics in language studies Anthony Woods ; Paul Fletcher ; Arthur Hughes |
| title_fullStr | Statistics in language studies Anthony Woods ; Paul Fletcher ; Arthur Hughes |
| title_full_unstemmed | Statistics in language studies Anthony Woods ; Paul Fletcher ; Arthur Hughes |
| title_short | Statistics in language studies |
| title_sort | statistics in language studies |
| topic | Russisch (DE-588)4051038-4 gnd Sprachstatistik (DE-588)4182534-2 gnd |
| topic_facet | Russisch Sprachstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000770099&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000770099&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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