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Applied Statistics

Code: MA689 | L-T-P-C: 3-0-0-6

Pre-Requisite: Basic knowledge of Probability and Statistical Distributions

Preamble / Objectives:

Knowledge of statistics is now essential for all academic branches as well as in the industry. This course's objectives are to teach students about different types of data that exist in real life and various statistical methods for them to analyze. This course will enable students to learn the topics in an applied manner so that they can use those methods/techniques in real life using a statistical software (like R).

Course Content/ Syllabus:

Data types: binary, continuous, categorical, ordinal, count, survival, longitudinal with examples. Study types: prospective, retrospective, case-control, cohort, cross-sectional, qualitative studies, randomized controlled trials. Exploratory Data Analysis: data visualization and statistical plots. Statistical Inference: Estimation, Hypothesis testing. Useful Statistical Tests: z-test, t-test, F-test, Chi-Square test, Wilcoxon signed-rank test with applications. Regression: linear regression, logistic regression, count regression. Analysis of Variance (ANOVA): One-way and two-way ANOVA. Bayesian Techniques: Bayes theorem, prior and posterior distributions, Bayesian inference. Survival Analysis: survival function, hazard function, Kaplan–Meier curves,  log-rank test, Cox proportional hazards regression. Statistical Learning: clustering and classification. Statistical traps to avoid: correlation vs causation, misuse of p-values and multiple testing,  handling outliers, misuse of variable selection, misuse of data visualization, ethical issues in statistics. Case studies with real data.

Texts:

1. Wasserman, L. All of statistics: a concise course in statistical inference. Vol. 26. New York: Springer, 2004.
2. Hogg, R.V., Tanis, E.A. and Zimmerman, D.L. Probability and Statistical Inference, 192. Printice Hall, Upper Saddle River, NJ (2014).
3. Gareth, J., Daniela, W., Trevor, H., and Robert, T. An introduction to statistical learning: with applications in R. Spinger, 2013
4. Weisberg, S. Applied linear regression. Vol. 528. John Wiley & Sons, 2005
5. Kleinbaum, D.G., and Klein M. Survival analysis a self-learning text. Springer, 2011
6. Koch, K.R. Introduction to Bayesian statistics. Springer Science & Business Media, 2007
7. Motulsky, H. Intuitive Biostatistics: a Nonmathematical guide to Statistical Thinking. Oxford University Press, USA, 2014
8. Kabacoff, R. Data visualization with R. Quantitative Analysis Center: Wesleyan University, 2020
9. Montgomery, D.C., Peck, E.A., and Vining, G.G. Introduction to Linear Regression Analysis, 5th Ed., Wiley, 2012
10. Rohatgi, V.K. and Saleh, A.K. An Introduction to Probability and Statistics, 3rd Ed., Wiley, 2015.