This book is an introductory resource on biometry, focusing on the application of statistical methods to biological problems in fields like human biology, medicine, public health, agriculture, and experimental studies. It emphasizes the practical use of statistics in biological measurements, covering essential topics, such as measures of central tendency and dispersion, correlation and regression, probability, random variables and distributions, hypothesis testing, and experimental design. Designed for undergraduate and post-graduate students in Biological Sciences, Agriculture, Veterinary Sciences, B.Tech, and Data Science, it provides a foundational understanding of statistical tools for analyzing biological data. The book is structured to suit learners new to biometry while serving as a comprehensive reference for advanced studies. By bridging theoretical concepts and real-world applications, it highlights the importance of statistical techniques in research and experimentation across various scientific disciplines, making it an invaluable resource for students and professionals alike.
Dr. R. Elangovan, M.Sc., M.Phil., Ph.D. (Statistics)., M.Ed. (Education)., M.B.A., Ph.D., (Business Administration). from Annamalai University. Graduated during 1982 and competed M.Sc. (Statistics) during 1984. Completed M.Ed in Education during 1994 and M.B.A. (Business Administration) during 2013 from Annamalai University. He was awarded Ph.D. in Statistics during 2000 and Ph.D., in Business Administration during 2021 from Annamalai University. He has 33 years of PG teaching experience at Annamalai University. Currently he is working as a Professor, School of Management at SASTRA Deemed University, SASTRA, Thanjavur, Tamil Nadu. He has published 79 papers in International, 31 papers in National journals and 20 papers in Conference proceedings, 30 papers in Scopus/Web of Science/ UGC care refereed journals. A total of 160 papers published. Visited countries USA (Five times), France, Paris, Nantes, U.K, U.A.E, Sri Lanka, China, Hong Kong in connection with delivering talks in the International Conferences, and in Connections with Annamalai Univerity Examinations. He did his Leadership Academicians Program (LEAP), domestic phase at I.I.T., Varanasi and International National Phase at Judge Business School, Cambridge University, London, U.K. during 2019 and 2020. He has an excellent record of guiding 24 students and awarded Ph.D. since 2009, 43 students and awarded M.Phil. since 2001. He has delivered 80 invited talk in connection with international conferences India and abroad. He has presented 102 papers in the National Conferences and 40 Webinar/Workshop/Seminar/Colloquium attended. He chaired 40 sessions in the National and International Conferences in India and Abroad. He has received the Dr. Radha Krishnan Best Teacher National Award during 2020. He has received the Ratna Prasad Multidisciplinary Research and Education Society Iconic Professor and Research award during January 2023. Recently he has received the Peter Drucker Legendary International Education and Research Excellence Award 2024 in Business Administration. He has organized two National Conferences and one Workshop sponsored by CSIR, UGC, New Delhi during 2002, 2018 and 2019. He has organized three days International Workshop sponsored by NBHM, Department of Atomic Energy, Government of India during 2014. He has organized two days faculty training programme and one day “Hands on Experience SPSS’’ during 2015. He was the coordinator for UGC-SAP-DRS I Programme during April 2016 to March 2022 and DST-FIST during March 2018 to February 2021. He has worked as a Statistician in Arvind Eye Hospital, Madurai during 1987 to 1988, as Assistant Technical Officer in Christian Medical College, Vellore during 1988 to 1989 before joining as a Lecturer, Annamalai University during 1990 as Lecturer. Currently working as a Professor, School of Management, SASTRA Deemed University, SASTRA, Thanjavur. He has gained the reputation of being an Excellent teacher and researcher.
Dr. R. Singaravel, M.Sc.(Ag.), Ph.D., Post Doc. ( Aus.), Professor of Soil Science and Agricultural Chemistry, Faculty of Agriculture, Annamalai University Graduated during 1988 and completed M.Sc.(Ag.) during 1990 and Ph.D. in Soil Science and Agricultural chemistry during 1999. He did his Post Doc. at Murdoch University, Australia during 2010 under Endeavour Research Fellowship awarded by the Govt. of Australia. He was awarded with the Indian Society of Soil Science Award for the best Ph.D. during 1999. He has 31 years of research and teaching experience. He has published about 86 research papers in National and International Journals. Visited countries like USA, Australia, China, Thailand, Paris, Dubai and Sri Lanka for the presentation of research papers at International Conferences. He has participated in national and international conferences and presented 98 papers. He has guided 9 Post Graduate and 5 Ph.D. scholars. He has prepared 5 research manual and published 4 books with ISBN No. He has operated several research projects funded by UGC, DST, NMPB, TN State Govt. and other Private Agencies. He has chaired Scientific sessions and Delivered Key Note address in the Conferences. He has served as Joint Controller of Examinations, Director, Distance Education and Registrar in Annamalai University.
Dr. A. K. Rajalakshmi is an accomplished Assistant Professor in the Department of Botany at Government Arts College, Chidambaram. With a robust academic foundation— holding an M.Sc., B.Ed., M.Phil., and Ph.D. and over 17 years of teaching experience and 20 years of research expertise. She has dedicated her career to advancing knowledge in plant physiology, biometry and biochemistry. An active researcher and mentor. She has successfully supervised one Ph.D., three M.Phil., and three M.Sc. projects and is currently guiding one Ph.D. scholar. Her research contributions include 11 publications, reflecting her commitment to academic excellence. She has also made significant contributions to academia through her authorship of comprehensive textbooks and practical manuals. These include titles on plant physiology, anatomy, embryology, and biochemistry for undergraduate and post-graduate students, some of which were published under the auspices of Annamalai University’s Directorate of Distance Education. Her active participation in scholarly discourse is evident from her attendance at numerous international and national conferences, symposia, seminars, and workshops. She has dedication to education and research continues to inspire her students and peers alike.
Dr. M. Govindhan is a distinguished statistician specializing in Stochastic processes and biostatistics, having completed a Ph.D. in Statistics at Annamalai University since July 2019. They began their academic career as an assistant professor in statistics at the Aravindhar Agricultural Institute of Technology, Tiruvannamalai, from August 2019 to December 2019, later moving to the PSG College of Arts and Science, Coimbatore, where they served as an assistant professor until January 2023. Currently, he is working as a Guest Lecturer in Statistics at Government Arts College, Dharmapuri, since January 2023. He has received the best research Paper Award on the occasion of National Science Day at Annamalai University in 2019, and he has received P. C. Mahalanobis Young Scientist Award on the occasion of the 9th national conference on natural science Pushkaram College of Agriculture Sciences, Pudukkottai, in the same year, and the Best Researcher Award on the occasion of Sakya Awards 2022 at Sakya Charitable Trust, Madurai, highlighting their significant contributions to the field of Stochastic processes and advancements in biostatistics, reflected his extensive publications and ongoing research endeavours, and are dedicated to inspiring and educating students and colleagues alike, driven by a passion for statistics and a commitment to excellence in research.
1 FREQUENCY DISTRIBUTIONS AND MEASURES OF CENTRAL TENDENCY......................................................................1
1.1 Introduction .................................................................................1
1.2 Formation of a Frequency Distribution........................................3
1.3 Graphs for Frequency Distributions.............................................6
1.4 Measure of Central Tendency.....................................................12
1.5 Median........................................................................................18
1.6 Mode...........................................................................................22
1.7 Empirical Relationship Connecting the Mean, Median and Mode ......................................................................23
1.8 Geometric Mean.........................................................................25
1.9 Harmonic Mean..........................................................................25
1.10 Important Characteristics of a Good Average ...........................26
2 MEASURES OF DISPERSION.........................................................29
2.1 Various Measures of Dispersion.................................................30
2.2 Range..........................................................................................30
2.3 Quartile Deviation......................................................................31
2.4 Mean Deviation..........................................................................37
2.5 Standard Deviation ....................................................................40
2.6 Co-efficient of Dispersion (C.D.) ..............................................42
2.7 Co-efficient of Variation (C.V.) .................................................43
3 CORRELATION AND REGRESSION ............................................49
3.1 Correlation .................................................................................50
3.2 Nature of Correlation ................................................................50
3.3 Scatter Diagram .........................................................................51
3.4 Karl Pearson’s Co-efficient of Correlation or Product Moment Correlation Co-efficient...............................................53
3.5 Computing ‘r’ ............................................................................55
3.6 Regression .................................................................................59
4 PROBABILITY...................................................................................73
4.1 Random Experiment ..................................................................73
4.2 Mathematical Probability ..........................................................75
4.3 Statistical Probability ................................................................76
4.4 Axiomatic Approach to Probability ...........................................76
4.5 Addition Theorem .....................................................................80
4.6 Conditional Probability .............................................................82
4.7 Multiplication Theorem .............................................................83
4.8 Random Variable .......................................................................85
5 RANDOM VARIABLE AND ITS DISTRIBUTION .......................89
5.1 Random Variable and its Distribution .......................................89
5.2 Binomial Distribution ................................................................91
5.3 Poisson Distribution ..................................................................96
5.4 Normal Distribution ................................................................101
5.5 Sampling Distribution and Standard Error ..............................111
6 ESTIMATION, TESTING OF HYPOTHESIS CONCERNING MEAN, VARIANCE AND PROPORTION ....................................115
6.1 Estimation.................................................................................115
6.2 Tests of Hypothesis ..................................................................123
6.3 Statistical Test...........................................................................124
6.4 Normal Test .............................................................................130
6.5 T-Test........................................................................................133
6.6 F-Test........................................................................................141
6.7 Chi-Square Test ........................................................................144
6.8 Chi-Square Test for Goodness of Fit........................................146
6.9 Large Sample Tests...................................................................151
7 DESIGN OF EXPERIMENTS.........................................................157
7.1 Basic Principles of Experimental Designs...............................157
7.2 Uniformity Trial .......................................................................160
7.3 Choice of Experimental Design ...............................................163
7.4 Control of Mechanical Errors...................................................163
7.5 Analysis of Variance.................................................................164
7.6 Description of Completely Randomized Design (One Way Classification) .............................................169
7.7 Randomized Complete Block Design (Two Way Classification) .........................................................176
APPENDIX ........................................................................................181
