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A Statistical Manual for Forestry Research

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A Statistical Manual for Forestry Research A Statistical Manual For Forestry Research FORESTRY RESEARCH SUPPORT PROGRAMME FOR ASIA AND THE PACIFIC A Statistical Manual For Forestry Research FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS REGIONAL OFFICE FOR ASIA AND THE PACIFIC BANGKOK May 1999 FORESTRY RESEARCH SUPPORT PROGRAMME FOR ASIA AND THE PACIFIC A STATISTICAL MANUAL FOR FORESTRY RESEARCH By K. JAYARAMAN Kerala Forest Research Institute Peechi, Thrissur, Kerala, India FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS REGIONAL OFFICE FOR ASIA AND THE PACIFIC BANGKOK i ACKNOWLEDGEMENTS The author is deeply indebted to the FORSPA for having supported the preparation of this manual. The author is also indebted to the Kerala Forest Research Institute for having granted permission to undertake this work and offering the necessary infrastructure facilities. Many examples used for illustration of the different statistical techniques described in the manual were based on data generated by Scientists at the Kerala Forest Research Institute. The author extends his gratitude to all his colleagues at the Institute for having gracefully co-operated in this regard. The author also wishes to thank deeply Smt. C. Sunanda and Mr. A.G. Varghese, Research Fellows of the Division of Statistics, Kerala Forest Research Institute, for patiently going through the manuscript and offering many helpful suggestions to improve the same in all respects. This manual is dedicated to those who are determined to seek TRUTH, cutting down the veil of chance by the sword of pure reason. March, 1999 K. Jayaraman ii INTRODUCTION This manual was written on a specific request from FORSPA, Bangkok to prepare a customised training manual supposed to be useful to researchers engaged in forestry research in Bhutan. To that effect, a visit was made to Bhutan to review the nature of the research investigations being undertaken there and an outline for the manual was prepared in close discussion with the researchers. Although the content of the manual was originally requested to be organised in line with the series of research investigations planned under the Eighth Five Year Plan for Bhutan, the format was so designed that the manual is useful to a wider set of researchers engaged in similar investigations. The manual is intended to be a source of reference for researchers engaged in research on renewable natural resources especially forests, agricultural lands and livestock, in designing research investigations, collecting and analysing relevant data and also in interpreting the results. The examples used for illustration of various techniques are mainly from the field of forestry. After some introductory remarks on the nature of scientific method and the role of statistics in scientific research, the manual deals with specific statistical techniques starting from basic statistical estimation and testing procedures, methods of designing and analysing experiments and also some standard sampling techniques. Further, statistical methods involved in certain specific fields like tree breeding, wildlife biology, forest mensuration and ecology many of which are unique to forestry research, are described. The description of the methods is not exhaustive because there is always a possibility of utilizing the data further depending on the needs of the investigators and also because refinements in methodology are happening continuously. The intention of the manual has been more on introducing the researchers to some of the basic concepts and techniques in statistics which have found wide application in research in forestry and allied fields. There was also a specification that the manual is to be written in as simple a manner as possible with illustrations so that it serves as a convenient and reference manual for the actual researchers. For these reasons, description of only simple modes of design and analysis are given with appropriate illustrations. More complicated techniques available are referred to standard text books dealing with the topics. However, every effort has been made to include in the manual as much of material required for a basic course in applied statistics indicating several areas of application and directions for further reading. Inclusion of additional topics would have made it just unwieldy. Any body with an elementary knowledge in basic mathematics should be able to follow successfully the description provided in the manual. To the extent possible, calculus and matrix theory are avoided and where unavoidable, necessary explanation is offered. For a beginner, the suggested sequence for reading is the one followed for the different chapters in the manual. More experienced researchers can just skim through the initial sections and start working on the applications discussed in the later sections. 1 NOTATION Throughout this book, names of variables are referred in italics. The symbol å is used to represent ‘the sum of’. For example, the expression G = y1 + y2 +...+yn can be n written as G = å yi or simply G = å y when the range of summation is understood i=1 from the context. In the case of summation involving multiple subscripts, the marginal sums are denoted by placing a dot (.) over that subscript, like, å yij = yi. , å yij = y.j ,å yij = y.. j i ij When two letters are written side by side such as ab, in equations, it generally indicates product of a and b unless otherwise specified or understood from the context. Multiplication with numerals are indicated by brackets e.g., (4)(5) would mean 4 multiplied 5. Division is indicated either by slash (/) or a horizontal mid-line between the numerator and the denominator. Equations, tables and figures are numbered with reference to the chapter numbers. For instance, Equation (3.1) refers to equation 1 in chapter 3. Certain additional notations such as those pertaining to factorial notation, combinatorics, matrices and related definitions are furnished in Appendix 7. 2 A Statistical Manual For Forestry Research 1. STATISTICAL METHOD IN SCIENTIFIC RESEARCH Like in any other branch of science, forestry research is also based on scientific method which is popularly known as the inductive-deductive approach. Scientific method entails formulation of hypotheses from observed facts followed by deductions and verification repeated in a cyclical process. Facts are observations which are taken to be true. Hypothesis is a tentative conjecture regarding the phenomenon under consideration. Deductions are made out of the hypotheses through logical arguments which in turn are verified through objective methods. The process of verification may lead to further hypotheses, deductions and verification in a long chain in the course of which scientific theories, principles and laws emerge. As a case of illustration, one may observe that trees in the borders of a plantation are growing better than trees inside. A tentative hypothesis that could be formed from this fact is that the better growth of trees in the periphery is due to increased availability of light from the open sides. One may then deduce that by varying the spacing between trees and thereby controlling the availability of light, the trees can be made to grow differently. This would lead to a spacing experiment wherein trees are planted at different espacements and the growth is observed. One may then observe that trees under the same espacement vary in their growth and a second hypothesis formed would be that the variation in soil fertility is the causative factor for the same. Accordingly, a spacing cum fertilizer trial may follow. Further observation that trees under the same espacement, receiving the same fertilizer dose differ in their growth may prompt the researcher to conduct a spacing cum fertilizer cum varietal trial. At the end of a series of experiments, one may realize that the law of limiting factors operate in such cases which states that crop growth is constrained by the most limiting factor in the environment. The two main features of scientific method are its repeatability and objectivity. Although this is rigorously achieved in the case of many physical processes, biological phenomena are characterised by variation and uncertainty. Experiments when repeated under similar conditions need not yield identical results, being subjected to fluctuations of random nature. Also, observations on the complete set of individuals in the population are out of question many times and inference may have to be made quite often from a sample set of observations. The science of statistics is helpful in objectively selecting a sample, in making valid generalisations out of the sample set of observations and also in quantifying the degree of uncertainty in the conclusions made. Two major practical aspects of scientific investigations are collection of data and interpretation of the collected data. The data may be generated through a sample survey on a naturally existing population or a designed experiment on a hypothetical population. The collected data are condensed and useful information extracted through techniques of statistical inference. This apart, a method of considerable importance to forestry which has gained wider acceptance in recent times with the advent of computers is simulation. This is particularly useful in forestry because simulation techniques can replace large scale field experiments which are extremely costly and time consuming. Mathematical models are developed which capture most of the 220 A Statistical Manual For Forestry Research relevant features of the system
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