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Statistical Methods for the Social Sciences STATISTICAL METHODS FOR THE SOCIAL SCIENCES C. A. HESSE, BSc, MPhil, PhD, Senior Lecturer of Statistics Methodist University College Ghana J. B. OFOSU, BSc, PhD, FSS Professor of Statistics Methodist University College Ghana i Statistical Methods for the Social Sciences Copyright © 2017 Akrong Publications Ltd. All rights reserved No part of this publication may be reproduced, in part or in whole, stored in a retrievable system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the publisher. Published and Printed by AKRONG PUBLICATIONS LIMITED P. O. BOX M. 31 ACCRA, GHANA (0244 648 757, 0264 648 757) ISBN: 978–9988–2–6060–6 Published, 2017 akrongh@yahoo.com. ii Statistical Methods for the Social Sciences PREFACE The purpose of this book is to acquaint the reader with the increasing number of applications of statistics in engineering and the social sciences. It can be used as a textbook for a first course in statistical methods in Universities and Polytechnics. The book can also be used by decision makers and researchers to either gain basic understanding or to extend their knowledge of some of the most commonly used statistical methods. Our goal is to introduce the basic theory without getting too involved in mathematical detail, and thus to enable a larger proportion of the book to be devoted to practical applications. Because of this, some results are stated without proof, where this is unlikely to affect the reader’s comprehension. However, we have tried to avoid the cook-book approach to statistics by carefully explaining the basic concepts of the subject, such as probability and sampling distributions; these the reader must understand. The worst abuses of statistics occur when scientists try to analyze their data by substituting measurements into statistical formulae which they do not understand. The book contains ten Chapters. Chapter 1 deals with overview of statistics. In Chapter 2, we discuss how to describe data, using graphical and summary statistics. Chapter 3 covers probability while Chapters 4 and 5 cover probability distributions. Chapters 6, 7, 8 and 9 present basic tools of statistical inference; point estimation, interval estimation, hypothesis testing and analysis of variance. Chapter 10 presents linear regression and correlation. Our presentation is distinctly applications-oriented. A prominent feature of the book is the inclusion of many examples. Each example is carefully selected to illustrate the application of a particular statistical technique and or interpretation of results. Another feature is that each chapter has an extensive collection of exercises. Many of these exercises are from published sources, including past examination iii Statistical Methods for the Social Sciences questions from King Saud University (Saudi Arabia) and Methodist University College Ghana. Answers to all the exercises are given at the end of the book. We are grateful to Ms. Patience Workpor, secretary to the Dean of Informatics and Mathematical Sciences for her editorial assistance. We are also grateful to Professor Abdullah Al-Shiha of King Saud University (Saudi Arabia) for reading a draft of the book and offering helpful comments and for his permission to publish the statistical tables he used the Minitab software package to prepare. These tables are given in the Appendix. Last, but not least, we thank King Saud University and Methodist University College Ghana, for permission to use their past examination questions in Statistics. We have gone to great lengths to make this text both pedagogically sound and error free. If you have any suggestions, or find potential errors, please contact us at jonofosu@hotmail.com or akrongh@yahoo.com. J. B. Ofosu C. A. Hesse July, 2017 iv
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