STATISTICAL THEORY The Relationship of Probability Credibility and. Error LANCELOT HOGBEN, F. R. S Statistical Theory The Relationship of PROBABILITY, CREDIBILITY AND ERROR AN EXAMINATION OF THE CONTEMPORARY CRISIS IN STATISTICAL THEORY FROM A BEHAVIOURIST VIEWPOINT V-W-NORTON COMPANY INC Publishers New York CONTENTS Foreword page 7 1 The Contemporary Crisis or the Uncertainties of Uncertain Inference 13 PART I. THE FOUNDING FATHERS 2 The Founding Fathers and the Natural History of Gambling 33 3 Randomness and the Relevance of the Rule 59 4 Division of the Stakes and the Lottery of Life and Death 83 5 The Backward Look and the Balance Sheet of Thomas Bayes no 6 The Place of Laplace and the Grand Climacteric of the Classical Tradition 133 PART II. THE CALCULUS OF ERROR AND THE CALCULUS OF EXPLORATION 7 The Normal Law comes into the Picture 159 8 The Method of Least Squares and the Concept of Point Estimation 182 9 Error, Variation and Natural Law 210 10 Stochastic Models for Simple Regression 232 11 The Impasse of Factor Analysis 257 PART III. THE CALCULUS OF AGGREGATES 12 Maxwell and the Urn of Mature 279 13 Mendelism and the Two Meanings of Probability 297 PART IV. THE CALCULUS OF JUDGMENTS 14 Statistical Prudence and Statistical Inference 319 1 5 Decision Indecision and Sample Economy 345 1 6 Induction and Design, Stochastic and Non-stochastic 370 1 7 Recipe and Rule in Stochastic Induction 399 1 8 The Confidence Controversy and the Fifth Canon 433 1 9 Epilogue 454 Appendix I 477 Appendix II 480 Appendix III 485 Appendix IV 7 Index 07 FOREWORD THE USE of the word behaviourist in my sub-title calls for clari fication. It came into current usage chiefly through the writings of J. B.Watson, in the first fine flush of enthusiasm following the reception of Pavlovs work on conditioned reflexes. Watson conveyed the impression that all forms of animal including human behaviour are ultimately explicable in terms of neural or humoral co-ordination of receptors and effectors. Neither this proposition nor its denial is susceptible of proof. A comet may destroy the earth before we have completed a research programme of such magnitude as the operative adverb ultimately suggests. Many years ago, and in what now seems to me a very im mature volume of essays written as a counter-irritant to the mystique of Eddingtons Nature of the Physical World, I suggested a more restricted definition of the term and offered an alter native which seemingly did not commend itself to my con temporaries. By behaviourist in this context I mean what Ryle means in the concluding section of his recent book The Concept of Mind. What Ryle speaks of as the behaviourist viewpoint and what I had previously preferred to call the publicist outlook has no concern with structure and mechanism. Our common approach to the problem of cognition is not at the ontological level. The class of questions we regard as profitable topics of enquiry in this context arise at the level of epistemology, or, better still, what G. P. Meredith calls epistemics. If one wishes to discuss with any hope of reaching agreement what one means by knowledge or preferably knowing the two main topics of the agenda for our public symposium will be recognition and communication and we shall discuss them as different facets of the same problem, neither meaningful in isolation. A simple illustration will suffice to make clear, both at theemotive level of non-communicable private conviction and at the public or communicable level of observable be haviour, the difference between knowing, conceived as a process, and knowledge, conceived as a static repository. The Nature of Living Matter 1930. 7 STATISTICAL THEORY We shall suppose that B is colour-blind to differences in the red and green regions of the visible spectrum, A being normal in the customary sense of the term in the relevant context...

Encompassing the areas of economics, sociology, social biology and genetics, and drawing on studies from the UK and Australia, this volume charts and analyses the factors affecting population growth. Chapters include: * The international decline in fertility * The changing structure of the family * Educational opportunities * Concepts of race.

First published in 1937, What is Ahead of Us? is a collection of essays, which were originally presented as lectures before the Fabian Society. Conceived in an era of growing fascism and economic despair, the essays urge the reader to imagine more equitable alternatives to capitalism. The authors offer socialism as a solution but what is more interesting is their criticism of capitalism and the connections they draw between capitalism and fascism using examples from the West. This book will be of interest to students of history, economics and political science.

Hogben escaped from a background of religious bigotry by the academic ladder and gained a major scholarship at Cambridge and graduated in 1916. During a noteworthy academic career, he found time to be active in the Fabian Society and in the London Labour Party. He also founded the Journal of Experimental Biology along with Julian Huxley and J.B.S. Haldane. He is most widely known for Mathematics for the Million and Science for the Citizen, and he played a big part in creating The Loom of Language.

One of the most illuminating, useful and exciting books ever published in the mathematical field Taking only a modicum of knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus. His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order - a language Hogben shows one can both master and enjoy.

Encompassing the areas of economics, sociology, social biology and genetics, and drawing on studies from the UK and Australia, this volume charts and analyses the factors affecting population growth. Chapters include: * The international decline in fertility * The changing structure of the family * Educational opportunities * Concepts of race.

"It makes alive the contents of the elements of mathematics."—Albert Einstein

Taking onlyl the most elementary knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus. His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed dificulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

"A great book, a book of first-class importance."—H. G. Wells

A Study Of The Lives Of Prehistoric Peoples For Children.

A Study Of The Lives Of Prehistoric Peoples For Children.

PRINCIPLES OF ANIMAL BIOLOGY BY LANCELOT HOGBEN, F. R. S. MASON PROFESSOR OF ZOOLOGY IN THE UNIVERSITY OF BIRMINGHAM, FORMERLY RFGIUS PROFESSOR OF NATURAL HISTORY IN THE UNIVERSITY OF ABERDEEN, RESEARCH PROFESSOR OF SOCIAL BIOLOGY IN THE UNIVERSITY OF LONDON, AND PROFESSOR OF ZOOLOGY IN THE UNIVERSITY OF CAPE TOWN SECOND EDITION revised and with new illustrations throughout by J. F. HORRABIN LONDON GEORGE ALLEN UNWIN LTD MUSEUM STREET TWO EXTREMES OF COLOUR CHANGE IN THE COMMON FROG Showing the influence of pituitary hormone on colour-change in frogs. Left Control specimen, in dry, light surroundings. Right Specimen kept in the same surroundings, but injected with extract of ox-pituitary posterior lobe. See Chapter VI. First published in 1930 by Christophers, Ltdi COMPLETELY REVISED SECOND EDITION IQ4O REPRINTED IQ42 REPRINTED IQ45 COMPLETE CONFORMITY WITH THE AUTHORIZED ECONOMY STANDARDS ALL RIGHTS RESERVED PRINTED IN GREAT BRITAIN in n-Point Imprint Type BY UNWIN BROTHERS LIMITED WOKING PREFACE TO SECOND EDITION PRINCIPLES OF ANIMAL BIOLOGY was pub-- lished first in 1930. It was based on the plan of elemen tary instruction adopted in the University of Cape Town during the authors tenure of the chair of zoology. Its object was not then, and is not now, to supplant the many excellent dissecting manuals available for use in the labora tory. It aims at supplementing laboratory work with a general introduction based on evolutionary principles with emphasis on function throughout. While the original plan remains, each chapter has been extensively revised or, where necessary, entirely rewritten. The chapter in which the Vertebrate skeleton is used to illustrate the principles of geologicalsuccession by reference to the fossil record has been recast to take advantage of the many new discoveries which have been made during the past ten years. The author is greatly indebted to Dr. Westoll, Lecturer in Palaeontology in the University of Aberdeen, for advice and information, especially with reference to the design of new illustrations. All the illustrations in the previous edition have been redrawn by Mr. Horrabin, and many new ones have been added or substituted. To help students to practise methodical methods of memorizing essential facts new tabular matter has been introduced in various places. Dr. H. Waring who saw the new edition through the press is responsible for many valuable suggestions. THE UNIVERSITY LANCELOT HOGBEN ABERDEEN Nov. 1939 CONTENTS PART I The Vertebrate Body as a Going Concern CHAPTER PAGE I. LIVING MATTER AND REPRODUCTION 15 II. THE MACHINERY OF RESPONSE 45 III. THE MACHINERY OF CO-ORDINATION 73 IV. THE SOURCES OF ENERGY OF THE ANIMAL BODY 98 V. DIGESTION, RESPIRATION AND EXCRETION 114 VI. THE TRANSPORT OF MATERIALS IN THE ANIMAL BODY 129 VII. THE DEVELOPMENT OF A NEW ORGANISM 155 VIII. THE MACHINERY OF INHERITANCE 1 86 PART II How Animals Differ IX. THE DIVERSITY OF ANIMAL LIFE 345 X. THE PRINCIPLE OF UNITY OF TYPE 371 XI. UNITY OF TYPE AMONG INVERTEBRATES 291 XII. THE PRINCIPLE OF SUCCESSION WITH SPECIAL REFERENCE TO THE VERTEBRATE SKELETON 331 XIII. EVOLUTIONARY THEORY TO-DAY 367 APPENDIX I. CLASSIFICATION OF CRUSTACEA 389 APPENDIX II. KEYS TO THE ORDERS OF INSECTS 394 APPENDIX III. SERIAL HOMOLOGY 400 APPENDIX IV. PARTS OF THE BRAIN 403 INDEX 405 ILLUSTRATIONS Two Extremes of Colour Change in the Common Frog Frontispiece FIG. PAGE 1. Set-up ofExperiment to show the Dependence of the Heart-beat on Metallic Ions 16 2. Paramcecium Dividing 23 3. Reproductive and Associated Organs of the Frog 24 4. Fertilization in the Starfish 25 5. Human Egg and Sperm 26 6. Spermatozoa of Different Animals 27 7. Stages in the Development of the Frogs Egg 28 8. Cellular Structure of the Animal Body 29 9. The Cellular Structure of the Testis 31 10. Immature Ova of Different Vertebrate Types 33 11. Early Stages in the Segmentation of the Egg of the Sea Urchin, Sturgeon and Fowl 36 12...

STATISTICAL THEORY The Relationship of Probability Credibility and. Error LANCELOT HOGBEN, F. R. S Statistical Theory The Relationship of PROBABILITY, CREDIBILITY AND ERROR AN EXAMINATION OF THE CONTEMPORARY CRISIS IN STATISTICAL THEORY FROM A BEHAVIOURIST VIEWPOINT V-W-NORTON COMPANY INC Publishers New York CONTENTS Foreword page 7 1 The Contemporary Crisis or the Uncertainties of Uncertain Inference 13 PART I. THE FOUNDING FATHERS 2 The Founding Fathers and the Natural History of Gambling 33 3 Randomness and the Relevance of the Rule 59 4 Division of the Stakes and the Lottery of Life and Death 83 5 The Backward Look and the Balance Sheet of Thomas Bayes no 6 The Place of Laplace and the Grand Climacteric of the Classical Tradition 133 PART II. THE CALCULUS OF ERROR AND THE CALCULUS OF EXPLORATION 7 The Normal Law comes into the Picture 159 8 The Method of Least Squares and the Concept of Point Estimation 182 9 Error, Variation and Natural Law 210 10 Stochastic Models for Simple Regression 232 11 The Impasse of Factor Analysis 257 PART III. THE CALCULUS OF AGGREGATES 12 Maxwell and the Urn of Mature 279 13 Mendelism and the Two Meanings of Probability 297 PART IV. THE CALCULUS OF JUDGMENTS 14 Statistical Prudence and Statistical Inference 319 1 5 Decision Indecision and Sample Economy 345 1 6 Induction and Design, Stochastic and Non-stochastic 370 1 7 Recipe and Rule in Stochastic Induction 399 1 8 The Confidence Controversy and the Fifth Canon 433 1 9 Epilogue 454 Appendix I 477 Appendix II 480 Appendix III 485 Appendix IV 7 Index 07 FOREWORD THE USE of the word behaviourist in my sub-title calls for clari fication. It came into current usage chiefly through the writings of J. B.Watson, in the first fine flush of enthusiasm following the reception of Pavlovs work on conditioned reflexes. Watson conveyed the impression that all forms of animal including human behaviour are ultimately explicable in terms of neural or humoral co-ordination of receptors and effectors. Neither this proposition nor its denial is susceptible of proof. A comet may destroy the earth before we have completed a research programme of such magnitude as the operative adverb ultimately suggests. Many years ago, and in what now seems to me a very im mature volume of essays written as a counter-irritant to the mystique of Eddingtons Nature of the Physical World, I suggested a more restricted definition of the term and offered an alter native which seemingly did not commend itself to my con temporaries. By behaviourist in this context I mean what Ryle means in the concluding section of his recent book The Concept of Mind. What Ryle speaks of as the behaviourist viewpoint and what I had previously preferred to call the publicist outlook has no concern with structure and mechanism. Our common approach to the problem of cognition is not at the ontological level. The class of questions we regard as profitable topics of enquiry in this context arise at the level of epistemology, or, better still, what G. P. Meredith calls epistemics. If one wishes to discuss with any hope of reaching agreement what one means by knowledge or preferably knowing the two main topics of the agenda for our public symposium will be recognition and communication and we shall discuss them as different facets of the same problem, neither meaningful in isolation. A simple illustration will suffice to make clear, both at theemotive level of non-communicable private conviction and at the public or communicable level of observable be haviour, the difference between knowing, conceived as a process, and knowledge, conceived as a static repository. The Nature of Living Matter 1930. 7 STATISTICAL THEORY We shall suppose that B is colour-blind to differences in the red and green regions of the visible spectrum, A being normal in the customary sense of the term in the relevant context...

STATISTICAL THEORY The Relationship of Probability Credibility and. Error LANCELOT HOGBEN, F. R. S Statistical Theory The Relationship of PROBABILITY, CREDIBILITY AND ERROR AN EXAMINATION OF THE CONTEMPORARY CRISIS IN STATISTICAL THEORY FROM A BEHAVIOURIST VIEWPOINT V-W-NORTON COMPANY INC Publishers New York CONTENTS Foreword page 7 1 The Contemporary Crisis or the Uncertainties of Uncertain Inference 13 PART I. THE FOUNDING FATHERS 2 The Founding Fathers and the Natural History of Gambling 33 3 Randomness and the Relevance of the Rule 59 4 Division of the Stakes and the Lottery of Life and Death 83 5 The Backward Look and the Balance Sheet of Thomas Bayes no 6 The Place of Laplace and the Grand Climacteric of the Classical Tradition 133 PART II. THE CALCULUS OF ERROR AND THE CALCULUS OF EXPLORATION 7 The Normal Law comes into the Picture 159 8 The Method of Least Squares and the Concept of Point Estimation 182 9 Error, Variation and Natural Law 210 10 Stochastic Models for Simple Regression 232 11 The Impasse of Factor Analysis 257 PART III. THE CALCULUS OF AGGREGATES 12 Maxwell and the Urn of Mature 279 13 Mendelism and the Two Meanings of Probability 297 PART IV. THE CALCULUS OF JUDGMENTS 14 Statistical Prudence and Statistical Inference 319 1 5 Decision Indecision and Sample Economy 345 1 6 Induction and Design, Stochastic and Non-stochastic 370 1 7 Recipe and Rule in Stochastic Induction 399 1 8 The Confidence Controversy and the Fifth Canon 433 1 9 Epilogue 454 Appendix I 477 Appendix II 480 Appendix III 485 Appendix IV 7 Index 07 FOREWORD THE USE of the word behaviourist in my sub-title calls for clari fication. It came into current usage chiefly through the writings of J. B.Watson, in the first fine flush of enthusiasm following the reception of Pavlovs work on conditioned reflexes. Watson conveyed the impression that all forms of animal including human behaviour are ultimately explicable in terms of neural or humoral co-ordination of receptors and effectors. Neither this proposition nor its denial is susceptible of proof. A comet may destroy the earth before we have completed a research programme of such magnitude as the operative adverb ultimately suggests. Many years ago, and in what now seems to me a very im mature volume of essays written as a counter-irritant to the mystique of Eddingtons Nature of the Physical World, I suggested a more restricted definition of the term and offered an alter native which seemingly did not commend itself to my con temporaries. By behaviourist in this context I mean what Ryle means in the concluding section of his recent book The Concept of Mind. What Ryle speaks of as the behaviourist viewpoint and what I had previously preferred to call the publicist outlook has no concern with structure and mechanism. Our common approach to the problem of cognition is not at the ontological level. The class of questions we regard as profitable topics of enquiry in this context arise at the level of epistemology, or, better still, what G. P. Meredith calls epistemics. If one wishes to discuss with any hope of reaching agreement what one means by knowledge or preferably knowing the two main topics of the agenda for our public symposium will be recognition and communication and we shall discuss them as different facets of the same problem, neither meaningful in isolation. A simple illustration will suffice to make clear, both at theemotive level of non-communicable private conviction and at the public or communicable level of observable be haviour, the difference between knowing, conceived as a process, and knowledge, conceived as a static repository. The Nature of Living Matter 1930. 7 STATISTICAL THEORY We shall suppose that B is colour-blind to differences in the red and green regions of the visible spectrum, A being normal in the customary sense of the term in the relevant context...