Statistics in Language StudiesCambridge University Press, 1986 M08 14 - 322 páginas 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. |
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 |
319 | |
Términos y frases comunes
analysis ANOVA average bilingual calculated carried chapter chi-squared child chosen cloze cluster column confidence interval correlation coefficient corresponding covariance covariance matrix critical values cumulative frequency data of table data set degrees of freedom discs discussed dissimilarity epenthesis estimate example expected frequencies F-ratio factor figure formula give Greek teachers H₁ histogram i-th independent variable individual j-th language language-impaired linear regression linguistic male mean score measure median method MINITAB morphemes multidimensional scaling multivariate null hypothesis observed obtained P(male pairs percentage population mean possible principal components principal components analysis probability problem procedure proficiency proportion random sample relative frequencies residual sample mean scattergram significance level standard deviation standard normal distribution standardised statistical population subtest Suppose t-distribution techniques test scores test statistic tion total deviance type I error utterances variance verb X₁ Y₁ zero