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Arising from the 2019 Darwin College Lectures, this book presents essays from seven prominent public intellectuals on the theme of vision. Each author examines this theme through the lens of their own particular area of expertise, making for a lively interdisciplinary volume including chapters on neuroscience, colour perception, biological evolution, astronomy, the future of technology, computer vision, and the visionary core of science. Featuring contributions by professors of neuroscience Paul Fletcher and Anya Hurlbert, professor of zoology Dan-Eric Nilsson, the futurist Sophie Hackford, Microsoft distinguished scientist Andrew Blake, theoretical physicist and author Carlo Rovelli, and Dr Carolin Crawford, the Public Astronomer at the University of Cambridge, this volume will be of interest to anybody curious about how we see the world.

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.

In the previous chapter we defined the idea of a multivariate observation and looked at multivariate analysis techniques for discovering and confirming the presence of special groups among the observed individuals. In the present chapter we will look at methods designed specifically to reduce the dimensionality of the data. Reducing the dimensionality of multivariate data Suppose that their scores on p variables, X 1 , X 2 , …, X p , have been observed for each of n subjects (see §15.3 for a language testing example). Typically, the variables will be intercorrelated, each variable having a higher correlation with some of the other variables than it does with the remainder. It is quite common that the pattern of intercorrelations is rather complex. As is often the case, the major statistical interest will lie in considering the differences between individuals. The special problem to be faced now is that the subjects can be different in a variety of ways. Two subjects may have similar scores for some of the variables and quite dissimilar scores on some of the others. If the number of variables is large, then it may be difficult to decide whether subject A differs more from subject B than from subject C since the pattern of differences may be quite dissimilar in the two cases.

Preface Part I. Contexts and Determinants: 1. Psychosocial aspects of language acquisition Maya Hickmann 2. Language acquisition and cognition Robin N. Campbell 3. Language acquisition and linguistic theory Helen Goodluck 4. Conversations with children Catherine E. Snow 5. Learnability Martin Atkinson 6. Variation in child language Gordon Wells Part II. The Development of Linguistic Systems: Phonology: 7. Prespeech segmental feature development Rachel E. Stark 8. Prosodic development David Crystal 9. Early strategies for the perception and production of words and sounds Paula Menyuk, Lise Menn and Ronnie Silber 10. Phonological development: production David Ingram 11. Speech perception and the emergent lexicon: an ethological approach John L. Locke 12. Phonological development: a crosslinguistic perspective Marlys A. Macken Part III. The Development of Linguistic Systems: Grammar: 13. Early vocabulary Patrick Griffiths 14. Early syntax Ann M. Peters 15. Assessing morphological development Bruce L. Derwing and William J. Baker 16. Personal pronouns Shulamuth Chiat 17. Tense and aspect Richard M. Weist 18. Modality Ursula Stephany 19. Deixis Roger Wales 20. A crosslinguistic perspective: morphology and syntax Ruth A. Berman Part IV. Later Language Development: 21. Some fundamental aspects of language development after age 5 Annette Karmiloff-Smith 22. The development of reading: the acquisition of a cognitive skill Philip T. Smith 23. Language acquisition and writing Katherine Perera Notes to chapters Bibliography and citation index General index.

In the last chapter we explained how it was possible to test whether two sample means were sufficiently different to allow us to conclude that the samples were probably drawn from populations with different population means. When more than two different groups or experimental conditions are involved we have to be careful how we test whether there might be differences in the corresponding population means. If all possible pairs of samples are tested using the techniques suggested in the previous chapter, the probability of type i errors will be greater than we expect, i.e. the ‘significance’ of any differences will be exaggerated. In the present chapter we intend to develop techniques which will allow us to investigate possible differences between the mean results obtained from several (i.e. more than two) samples, each referring to a different population or collected under different circumstances. Comparing several means simultaneously: one-way ANOVA Imagine that an investigator is interested in the standard of English of students coming to Britain for graduate training. In particular he wishes to discover whether there is a difference in the level of English proficiency between groups of distinct geographical origins – Europe, South America, North Africa and the Far East. As part of a pilot study he administers a multiple choice test to 40 graduate students (10 from each area) drawn at random from the complete set of such students listed on a central file. The scores obtained by these students on the test are shown in table 12.1.