STATISTICAL METHODS FOR APPLIED SCIENCES

Code (Credit) - STAT 0502 (3-1-0)

Course Objectives

To provide students with a comprehensive understanding of statistical methods and their applications in the field of agricultural sciences. Also this subject enhance to applying Advanced Statistical Techniques for Agricultural Decision-Making.

Course outcome (CO-PSO Mapping)

PSO1 : Impart knowledge and understanding of fundamental concepts and techniques of maintaining and enhancing soil fertility, crop production, crop management, crop improvement, biodiversity and sustainability of agriculture worldwide.

PSO3 : Apply knowledge of basic science through Agricultural microbiology, Plant biochemistry and Biotechnology.

PSO4 : Apply knowledge of Agri-business management and finance to develop profitable agricultural system.

Course Syllabus

Theory

Classification, tabulation and graphical representation of data.

Box-plot, Descriptive statistics. Exploratory data analysis.

Theory of probability. Random variable and mathematical expectation.

Discrete and continuous probability distributions: Binomial, Poisson, Negative Binomial, Normal distribution.

Beta and Gamma distributions and their applications.

Concept of sampling distribution: chi-square, t and F distributions.

Tests of significance based on Normal, chi-square, t and F distributions. Large sample theory.

Introduction to theory of estimation and confidence-intervals.

Correlation and regression. Simple and multiple linear regression models.

Estimation of parameters, predicted values and residuals, correlation, partial correlation coefficient.

Multiple correlation coefficients.

Rank correlation

Test of significance of correlation coefficient and regression coefficients.

Coefficient of determination.

Polynomial regression models and their fitting.

Probit regression analysis by least squares and maximum likelihood methods, confidence interval for sensitivity.

Testing for heterogeneity. Non-parametric tests.

Sign, Wilcoxon, Mann-Whitney U-test. Wald Wolfowitz run test.

Run test for the randomness of a sequence. Median test, Kruskal- Wallis test.

Introduction to ANOVA: One way and Two Way, Introduction to Sampling Techniques, Introduction to Multivariate Analysis, Transformation of Data.

Practical

Exploratory data analysis, Different plots.

Fitting of distributions ~Binomial, Poisson, Negative Binomial, Normal.

Large sample tests.

Testing of hypothesis based on exact sampling distributions ~ chi square, t and F.

Confidence interval estimation and point estimation of parameters of binomial, Poisson and Normal distribution.

Correlation and regression analysis.

Fitting of Linear and Quadratic Model.

Non- parametric tests. ANOVA: One way, Two Way, SRS

Reference

Goon AM, Gupta MK &Dasgupta B. 1977. An Outline of Statistical Theory. Vol. I. The World Press.

Goon AM, Gupta MK &Dasgupta B. 1983. Fundamentals of Statistics. Vol. I. The World Press.

Hoel PG. 1971. Introduction to Mathematical Statistics. John Wiley.

Hogg RV & Craig TT. 1978. Introduction to Mathematical Statistics. Macmillan.

Morrison DF. 1976. Multivariate Statistical Methods. McGraw Hill.

Robert V. Hogg, Joseph W. McKean, Allen T. Craig (2012). Introduction to Mathematical Statistics (7th Edition)

Siegel S, Johan N & Casellan Jr. 1956. Non-parametric Tests for Behavior Sciences. John Wiley.

T.W. Anderson(2009) An Introduction to Multivariate Statistical Analysis, 3rd Ed . John Wiley.

Session Plan

Session 1

Classification, tabulation and graphical representation of data, Box-plot, Descriptive statistics, Exploratory data analysis

Session 1

Lecture 1

Lecture 2

Lecture 3

Session 2

Theory of probability, Random variable and mathematical expectation.

Session 2

Lecture 4

Lecture 5

Lecture 6

Session 3

Discrete and continuous probability distributions: Binomial, Poisson, Negative Binomial, Normal distribution, Beta and Gamma distributions and their applications.

Session 3

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Session 4

Concept of sampling distribution: chi-square, t and F distributions.

Session 4

 Lecture 11, 12

Lecture 13, 14

Session 5

Tests of significance based on Normal, chi-square, t and F distributions. Large sample theory. Introduction to theory of estimation and confidence-intervals.

Session 5

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lecture 22

Session 6

Simple and multiple correlation coefficient, partial correlation, rank correlation.

Session 6

Lecture 23, 24, 25

Session 7

Simple and multiple linear regression model, test of significance of correlation coefficient and regression coefficients, Coefficient of determination.

Session 7

Lecture 26

Lecture 27

Lecture 28

Lecture 29

Lecture 30

Lecture 31

Lecture 32

Lecture 33

Lecture 34

Session 8

Non-parametric tests - sign, Wilcoxon, Mann-Whitney U-test, Run test for the randomness of a sequence. Median test.

Session 8

Lecture 35

Lecture 36

Lecture 37

Lecture 38

Lecture 39

Session 9

Introduction to ANOVA: One way and Two Way, Introduction to Sampling Techniques

Session 9

Lecture 40

Lecture 41

Lecture 42

Session 10

Introduction to Multivariate Analysis, Transformation of Data.

Session 10

Lecture 43

Lecture 44

Lecture 45

Lecture 46, 47, 48

Assignment

Assignment 1

Assignment 2

Assignment 3

Question Bank

Question Bank 1

Question Bank 2

Course E- Material

E-Material 1

E-Material 2