Statistical Technique In Agricultural Research - pocketboek

STATISTICAL TECHNIQUE IN AGRICULTURAL RESEARCH A Simple Exposition of Practice and Procedure in Biometry BY D. D. PATERSON, B. Sc., B. Sc. AGRIC., EDIN. Reader in Agriculture at the Imperial College of Tropical Agriculture, Trinidad, B. W. I. FIRST EDITION FOURTH IMPRESSION McGRAW-HILL BOOK COMPANY, INC. NEW YORK AND LONDON 1939 PREFACE Recent advances in statistical method have given the research biologist a new and valuable weapon to aid him in the accurate interpretation of his data. Statistics is a branch of applied mathematics, and a comprehensive understanding of the theory is possible only to those of a mathematical turn of mind. In consequence, a full appreciation of the fundamental mathematics must remain the prerogative of the few. On the other hand, there is no reason why those who are interested in statistics solely as an aid to scientific research should forego the advantages of applying statistical methods to research data derived from any standardized experimental design. The interpretation of the results by means of the appropriate statistical formulas should then become a purely routine operation. The available literature is rather technical in character, and several years experience with postgraduate students has shown that there is a real demand for a more elementary exposition of statistical technique. This book is an attempt to meet this demand and is essentially the detailed analysis of data from a representative series of experi ments typical of some of the commoner statistical problems encountered by the average research worker. In certain exam ples, the original data have been slightly simplified in order to make it easy to follow the successive stages in thearithmetical calculations. It is hoped that these representative examples may serve as a practical guide to the research worker in the design and interpretation of his experiments. For the student who has to study the subject more deeply, they may even help toward an easier understanding of statistical theory as expounded in the more technical works. In compiling this handbook, the writer has made liberal use of the relevant literature. To the authors of the various theoretical and practical memoirs consulted, he wishes to express his deep indebtedness. In particular, grateful acknowledgment is made to Professor R. A. Fisher and to his publishers, Messrs. Oliver and Boyd, for permission to reproduce some of the fundamental tables from Statistical Methods for Research Workers. TRINIDAD, B. W. I., D. D. PATERSON. January, 1939. CONTENTS PAGE PREFACE v CHAPTER I GENERAL PRINCIPLES 1 Calculation of Mean and Standard Deviation 3 Normal Curve of Error 6 Standard Error 12 Statistical Significance 13 Sampling 16 Analysis of Small Samples 17 Analysis of Correlated Samples Students Method 19 Coefficient of Variation 22 Probable Error 23 Short Methods of Computation 24 Formulas 28 CHAPTER II ANALYSIS OF VARIANCE 31 Analysis of Variance in Its Simplest Form 31 The F Test for Comparing Component Variances 38 The z Test 42 Affinity between the z and i Tests 44 Interactions 45 Direct Calculation of an Interaction 50 Analysis of Data Divided into Subunits 52 A Complex Experiment 58 Experimental Precision 63 r Useful Formulas in Analysis of Variance 67 CHAPTER III GOODNESS OF FIT AND CONTINGENCY TABLES 70 The Chi-squared Test x 2 70 .. Binomial Distribution 72 S Contingency Tables 77 Problems inGenetics 81 CHAPTER IV DIAGRAMS 89 Graphs 90 Growth Measurements 93 Frequency Distributions 96 vii viii CONTENTS PAOB Evaluation of Standard Deviation from a Frequency Table .....