# Statistics in Language Studies

Cambridge 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.

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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 Derechos de autor