Statistics II
Deep Understanding: 65 hours
The course consists of concepts of sampling, testing hypothesis, parametric and non parametric tests, correlation and regression, experimental designs and stochastic processes.
Acquire the theoretical as well as practical knowledge of estimation, testing of hypothesis, application of parametric and non-parametric statistical tests, design of experiments, multiple regression analysis, and basic concept of stochastic process with special focus to data/problems related with computer science and information technology.
Course Contents
Sampling distribution; sampling distribution of mean and proportion, Central Limit Theorem, Concept of inferential Statistics, Estimation; Methods of estimation; Properties of good estimator, Determination of sample size; Relationship of sample size with desired level of error, Problems and illustrative examples related to computer Science and IT
Types of statistical hypotheses; Power of the test, concept of p-value and use of p-value in decision making, Steps used in testing of hypothesis, One sample tests for mean of normal population (for known and unknown variance), test for single proportion, test for difference between two means and two proportions, paired sample t-test, Linkage between confidence interval and testing of hypothesis, Problems and illustrative examples related to computer Science and IT
Parametric vs. non-parametric test; Needs of applying non-parametric tests, One-sample test: Run test, Binomial test, Kolmogorov–Smirnov test, Two independent sample test: Median test, Kolmogorov-Smirnov test, Wilcoxon Mann Whitney test, Chi-square test, Paired-sample test: Wilcoxon signed rank test; Cochran’s Q test; Friedman two way analysis of variance test; Kruskal Wallis test, Problems and illustrative examples related to computer Science and IT
Multiple and partial correlation, Introduction of multiple linear regression; Hypothesis testing of multiple regression, Test of significance of regression; Test of individual regression coefficient; Model adequacy tests, Problems and illustrative examples related to computer Science and IT
Experimental design; Basic principles of experimental designs, Completely Randomized Design (CRD); Randomized Block Design (RBD); ANOVA table, Efficiency of RBD relative to CRD, Estimations of missing value (one observation only), Advantages and disadvantages, Latin Square Design (LSD): Statistical analysis of m × m LSD for one observation per experimental unit, ANOVA table, Estimation of missing value in LSD (one observation only), Efficiency of LSD relative to RBD, Advantage and disadvantages, Problems and illustrative examples related to computer Science and IT
Definition and classification; Markov Process: Markov chain, Matrix approach, Steady-State distribution, Counting process: Binomial process, Poisson process, Simulation of stochastic process, Queuing system: Main component of queuing system, Little’s law; Bernoulli single server queuing process: system with limited capacity; M/M/1 system: Evaluating the system performance
Laboratory Works
Sampling distribution, random number generation, and computation of sample size,Methods of estimation (including interval estimation),Parametric tests (covering most of the tests),Non-parametric test (covering most of the tests),Partial correlation,Multiple regression,Design of Experiments,Stochastic process