Essentials of Biostatistics

ESSENTIALS OF

BIOSTATISTICS FOR UNDERGRADUATE, POSTGRADUATE STUDENTS OF MEDICAL SCIENCE, BIOMEDICAL SCIENCES AND RESEARCHERS

Indranil Saha Associate Professor Department of Community Medicine ESI PGIMSR & ESIC Medical College, Kolkata

Bobby Paul Assistant Professor Department of Preventive and Social Medicine, All India Institute of Hygiene and Public Health, Kolkata

ACADEMIC PUBLISHERS KOLKATA-700 073 E-mail : [email protected] Website : www.academicpublishers.in

© Reserved

First Published April 2010 Second Edition July 2016

ISBN : 978-93-83420-71-1

Price : Rupees two hundred only.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise, without the prior permission of the copyright holders.

Published by B. K. Dhur of Academic Publishers, 5A, Bhawani Dutta Lane, Kolkata-700 073, laser type setting by Studio Michaelangelo, 5A, Bhawani Dutta Lane, Kolkata-700 073 and printed at Rajendra Offset, 11 Panchanan Ghosh Lane, Kolkata-700 009.

Dedicated to our parents and children

Abbreviations used in this book

AIIMS AI

: :

All India Institute of Medical Sciences All India

AIIH&PH

:

All India Institute of Hygiene and Public Health

AP

:

Andhra Pradesh State Entrance Examination

CU

:

Calcutta University State Entrance Examination

DNB

:

Diplomate of National Board

DPH

:

Diploma of Public Health

IA Exam

:

Internal Assessment Examination of 3rd Professional MBBS Part I

IPGME&R

:

Institute of Post Graduate Medical Education and Research

JIPMER

:

Jawaharlal Nehru Institute of Postgraduate Medical Education and Research

MAHE

:

Manipal Medical Entrance Examination

MPH

:

Master of Public Health

PGI

:

Post Graduate Institute, Chandigarh

TN

:

Tamil Nadu State Entrance Examination

UPSC

:

Union Public Service Commission

WBUHS

:

West Bengal University of Health Sciences

Preface to the second edition We welcome the readers who wish to learn biostatistics. The purpose of this book is to give a comprehensive insight into the basic aspects of biostatistics that is easy to read and relevant with useful practical applications. Fundamental concepts are presented in a highly succinct format suitable for students without in depth background in mathematics or statistics. Apart from other conventional statistical books, we have deliberately kept discussion of statistical theory to a minimum. We have emphasized on giving an overview of key concepts of methods of data presentation, scales of measurement, measures of central tendency and dispersion, normal distribution, sample si1ze calculation and sampling techniques, probability, sampling variability, null hypothesis, and details on tests of significance, written in lucid language. The chapter on ‘Art and Science of Research’ provides an insight into research methodology and study designs and the chapter on 'Publication in Journal' provides useful guidelines for publishing one’s research work. This makes it a handbook of essentials of biostatistics for undergraduate and postgraduate students and researchers from the field of medicine, public health, preventive medicine, nursing, dental, psychology, paramedical sciences, biological and social sciences or in a nutshell, anyone who encounters the use of biostatistics in his/her respective field. This text is also helpful for PhD students who are preparing for their examination on research methodology as well as undergraduate and postgraduate students to prepare for their short research projects / thesis and writing answers on biostatistics in their final university examination. The favourable response that the first edition of this book received from teachers and students encouraged us to write the second edition. Based on teaching experience and student feedback, we have transformed the question answer format of the previous book into text format in a simplistic language with a major objective to motivate students and readers to develop a positive attitude towards learning biostatistics. We have aimed to raise this positive attitude by introducing the concepts through simple worked-out examples. Each chapter begins with an introductory note, proceeds on to the details in a concise and clear manner and ends with examples of application of the statistical methods in published literature. In addition, there are exercises at the end of each chapter for the purpose of learning and practice - long questions, short notes, justify / explain with examples, statistical and epidemiological exercises from different university examinations for MBBS students as well as MD students. Multiple choice questions from different postgraduate entrance examinations with their respective answers and explanations along with some new set of questions have also been incorporated. Though ample study materials are available online, though in a fragmented form, it fails to provide a better understanding of this discipline in a comprehensive manner. We humbly submit that in spite of our laborious efforts, there may be some errors, inaccuracies, and ambiguous statements. We would appreciate receiving the comments of our valuable readers. We have a special electronic mail account for your constructive feedback at [email protected] since first edition book. We are especially grateful to the entire team of Academic Publishers for publishing the second edition book. 4th June, 2016 [email protected]

Indranil Saha Bobby Paul

Preface to the first edition Biostatistics - MCQ and Essentials has been designed especially for the MBBS students and postgraduate aspirants who are concentrating both on preparation for entrance examination as well as gaining a good grip on the subject. Each chapter begins with a brief introduction of the topic, and then, instead of going into monotonous explanation, the authors have used the format of MCQ with the answers and their relevant explanation in the form of text. Thus it would be beneficial in writing questions in theory papers as well as to face practical and oral in MBBS Part - I university examination. This book will also be helpful for post graduate students to some extent for preparing their thesis and writing short notes on biostatistics in their final university examination. The topics, such as test of significance, probability, correlation, regression etc. are usually not covered during undergraduate teaching, but are frequenters in post graduate entrance examination. These chapters are dealt with in depth for better understanding which will help them to answer the MCQ. Different MCQ from different examinations for the last 20 years upto 2010 have been discussed along with some new set of questions. This portion is an unique feature of this book. These new sets of questions are included in almost every chapter in an attempt to include many relevant important questions that may come in future. Thus it would be helpful for preparing MD/MS, All India, AIIMS and different state examinations like CU, Karnataka etc. along with DNB and UPSC examinations. Often researchers are interested to know the appropriate statistical test needed to apply in different sets of data. Those researchers as well as students doing dissertation will be benefitted regarding use of different statistical significance tests, which has been dealt lucidly in this book. Suggestions, criticisms and biostatistics MCQ of different entrance examinations from the readers are welcome to make the book more useful, which will be gratefully acknowledged in future editions. We are specially grateful to Mrs. Sandhya Paul, Mrs. Mahua Ghosh, Miss Sneha Saha, Master Rayan Saha & to the staff members of Academic Publishers for publishing the book.

22 March, 2010 Indranil Saha Bobby Paul

ACKNOWLEDGEMENT                            

Dr. Saswati Nandy - R. G. Kar Medical College, West Bengal Prof. Aparajita Dasgupta - All India Institute of Hygiene & Public Health, WB Prof. Jayasri Mitra - ESI PGIMSR & ESIC Medical College, Joka, WB Prof. Ramendra Narayan Chaudhury - All India Institute of Hygiene & Public Health, WB Prof. Akhil Bandhu Biswas - Institute of Health and Family Welfare, Swasthya Bhawan, WB Prof. Gautam Ghose - IQ City Medical College, Durgapur, West Bengal Prof. Saibendu Kumar Lahiri - R. G. Kar Medical College, West Bengal Prof. Samir Dasgupta - North Bengal Medical College, Siliguri, West Bengal Prof. Raghunath Misra - Institute of Post Graduate Medical Education & Research, WB Prof. Dilip Kumar Das - Burdwan Medical College, West Bengal Prof. Rabindra Nath Sinha - All India Institute of Hygiene & Public Health, WB Prof. Arup Kumar Kundu - IQ City, Medical College, Durgapur, West Bengal Prof. Sarmila Mallik - Murshidabad Medical College, West Bengal Late Prof. Ranadeb Biswas - All India Institute of Hygiene & Public Health, WB Dr. Ashish Kumar Yadav - ESI PGIMSR & ESIC Medical College, Joka, WB Dr. Sk. Samim Ferdows - IQ City Medical College, Durgapur, West Bengal Dr. Rabindra Nath Roy - Burdwan Medical College, West Bengal Dr. Sanjit Dey - Rajabazar Science College, West Bengal Dr. Ruchi Yadav - Rural Institute of Medical Sciences, Saifai, Etawah, Uttar Pradesh Dr. Arijit Banerjee - Eastern Coal Field, Durgapur, West Bengal Dr. Prabha Shrivastava - Burdwan Medical College, West Bengal Dr. Lina Bandyopadhyay - All India Institute of Hygiene & Public Health, WB Dr. Shweta Goswami - ESI PGIMSR & ESIC Medical College, Joka, WB Dr. Md. Abdur Rahman - Malda Medical College, West Bengal Dr. Susmita Chaudhuri - ESI PGIMSR & ESIC Medical College, Joka, WB Dr. Sarbajit Ray - Institute of Post Graduate Medical Education & Research, WB Dr. Md. Mehboob Ulislam - Burdwan Medical College, West Bengal Mr. Sudip Karmakar - IQ City Medical College, Durgapur, West Bengal

CONTENTS Chapter 1 : DATA AND ITS PRESENTATION

1-28

Introduction 1; Introduction to some common terminology used in statistics 1; Classification of data 2; Presentation of data 4; Applications 18; Exercises 19; Answers 24. Chapter 2 : DIFFERENT SCALES OF MEASUREMENTS

29-35

Introduction 29; Different scales of measurement 29; Some specific scales 31; Applications 33; Exercises 34; Answers 35. Chapter 3 : CENTRAL TENDENCY Introduction 36; Concept of central tendency 36; Exercises 39; Answers 41.

36-42

Chapter 4 : NORMAL DISTRIBUTION AND MEASURES OF DISPERSION

43-62

Introduction 43; Measures of location 43; Normal curve 44; Skewness 45; Kurtosis 46; Z score 47; Standard normal curve 48; Measures of dispersions/variations 49; Different types of distribution 52; Application 53; Exercises 53; Answers 59. Chapter 5 : SAMPLE SIZE AND SAMPLING TECHNIQUE 63-78 Introduction 63; Some common terminology used in sampling 63; Sample size calculation 64; Sampling technique 66; Sampling bias 74; Design effect 74; Exercises 74; Answers 77. Chapter 6 : PROBABILITY

79-84

Introduction 79; Probability 79; P value 81; Exercises 82; Answers 84. Chapter 7 : SAMPLING VARIABILITY AND NULL HYPOTHESIS

85-94

Introduction 85; Standard error (SE) 85; Tests of significance applying standard error 86; Null hypothesis 87; Sampling error 88; Exercises 89; Answers 93. Chapter 8 : DIFFERENCE BETWEEN PROPORTIONS

95-106

Introduction 95; Chi-square test (Pearson’s chi-square test) 95; Assumptions for pearson’s chi-square test 96; General procedure of chi-square test 96; Different variants of chi-square test 97; Contingency table 100; Degrees of freedom (df) 100; Effect size in chi-square test 100; Z test for proportion 101; Cochran-armitage trend test 101; Test of significance 102; Applications 102; Exercises 103; Answers 105. Chapter 9 : DIFFERENCE BETWEEN MEANS

107-122

Introduction 107; While choosing a statistical test, following statements are taken into consideration 107; Tests relating to comparison of means 107; Z test for mean 108; Student’s t test 108; Mann-whitney u test 111; Wilcoxon matched-pairs signed rank test 111; ANOVA / Analysis of variance 112; Friedman’s ANOVA by rank 114; Kruskal-wallis h test 115; MANOVA / Multivariate analysis of variance 115; Analysis of co-variance (ANCOVA) 116; Effect size 116; Applications 117; Exercises 117; Answers 121.

Chapter 10 : CORRELATION 123-132 Introduction 123; Correlation 123; Interpretation of correlation 124; Correlation coefficient to be used 125; Assumptions for correlation 125; Output of correlation 125; Correlation for nominal scale data 126; Correlation for ordinal scale data 126; Correlation for interval and ratio scale data 127; Universal relationship 127; Correlation matrix 127; Some other types of correlation 127; Applications 129; Exercises 129; Answers 132. Chapter 11 : REGRESSION

133-140

Introduction 133; Regression 133; Types of regression analysis 133; Linear regression 134; Logistic regression 136; Cox regression model 138; Multivariable model versus univariate / bivariate model 138; Applications 139; Exercises 139; Answers 140. Chapter 12 : ART AND SCIENCE OF RESEARCH

141-177

Introduction 141; Some commonly used definitions 141; Research protocol 142; Cardinal steps of preparing a protocol 143; Primary data 144; Secondary data 149; Ethical issues 149; Guidelines to write a research report / thesis 152; Some common study designs 159; Clinical trial 163; Systematic review 165; Meta-analysis 165; Strength and weaknesses of common study designs 167; Evidence based medicine 168; Applications 169; Exercises 170; Answers 174. Chapter 13 : PUBLICATION IN JOURNAL

178-181

Introduction 178; Manuscript preparation 178; Sections of the submitted manuscript 178; Some useful terminologies 180. APPENDIX

182-186

REFERRENCE

187-188

INDEX

189-190

IMPORTANT DAYS

191-192