**DESCRIPTION OF COURSES**

**AS 501 BASIC STATISTICAL METHODS (2L+1P) I**

**Objective**

This course is meant for students who do not have sufficient background of statistical methods. The students would be exposed to concepts of statistical methods and statistical inference that would help them in understanding the importance and need of statistics. It would also help them in understanding the concepts involved in data presentation, analysis and interpretation. The students would get an exposure to presentation of data, probability distributions, parameter estimation, tests of significance, regression and multivariate analytical techniques.

**Theory**

UNIT I

Classification, tabulation and graphical representation of data. Descriptive statistics. Theory of probability. Random variable and mathematical expectation. Box-plot, Stem & leaf plot.

UNIT II

Probability distributions: Binomial, Poisson, Negative binomial, Normal distributions and their applications. Concept of sampling distribution: t, χ2 and F distributions. Tests of significance based on normal, t, χ2 and F distributions.

UNIT III

Theory of estimation and confidence-intervals. Correlation and regression. Simple and multiple linear regression model. Estimation of parameters. Predicted values and residuals. Correlation, partial correlation coefficient, multiple correlation coefficient, rank correlation. Test of significance of correlation coefficient. Coefficient of determination. Polynomial regression models and their fitting. Selection of variables. Validation of models. Probit regression analysis by least squares and maximum likelihood methods. Confidence interval for sensitivity. Testing for heterogeneity.

UNIT IV

Introduction to multivariate analytical tools: dimension reduction techniques (Principal Component Analysis), cluster and discriminant function analysis.

**Practicals**

Descriptive statistics, Box- plots, Stem & leaf plot. Fitting of distributions: Binomial, Poisson, Negative Binomial, Normal. Large sample tests, testing of hypothesis based on exact sampling distributions: χ2, t and F. Confidence interval estimation and point estimation of parameters of Binomial, Poisson and Normal distribution, Correlation and regression analysis, fitting of orthogonal polynomials. Applications of dimensionality reduction, cluster and discriminant function analysis.

**Suggested Readings**

- Anderson, T.W. 1958.
*An Introduction to Multivariate Statistical Analysis.*John - Wiley. Campbell, R.A. 1974.
*Statistics for Biologists.*Cambridge University Press. - Dillon, W.R. and Goldstein, M. 1984.
*Multivariate Analysis: Methods and Applications.*John - Wiley. Electronic Statistics Text Book: http://www.statsoft.com/textbook/stathome.html.
- Goon, A.M., Gupta, M.K. and Dasgupta, B. 1977.
*An Outline of Statistical Theory.*Vol. I. The World Press Pvt. Ltd. - Goon, A.M., Gupta, M.K. and Dasgupta, B. 1983.
*Fundamentals of Statistics.*Vol. I. The World Press Pvt. Ltd., - Gupta, S.C. and Kapoor, V.K. 2007.
*Fundamentals of Mathematical Statistics.*Sultan Chand and Sons. - Hoel, P.G. 1971.
*Introduction to Mathematical Statistics.*John Wiley. - Hogg, R.V. and Craig, T.T. 1978.
*Introduction to Mathematical Statistics.*Macmillan. - Learning Statistics: http://freestatistics.altervista.org/en/learning.php. Morrison, D.F.
- 1976.
*Multivariate Statistical Methods.*McGraw Hill. - Murray, R. 2000.
*Schaum’s Outline of Theory and Problems of Probability and Statistics.*McGraw Hill. - Snedecor, G.W. and Cochran, W.G. 1936.
*Statistical Methods.*Oxford University*.*