The course is specifically designed to introduce students to multivariate techniques. It helps students to handle multivariate data effectively. Specific areas include: Structure of multivariate data. Inferences about multivariate means - Hotelling’s ; likelihood ratio tests, etc. Comparisons of several multivariate means - paired comparisons; one-way MANOVA; profile analysis. Principal component analysis - graphing; summarizing sample variation, etc. Factor analysis. Discriminant analysis - separation and classification for two populations; Fisher’s discriminant function; Fisher’s method for discriminating among several populations Cluster analysis - hierarchical clustering; non-hierarchical clustering; multi-dimensional scaling.
Further methods for discrete data: examples and formulation - binomial, multinomial and Poisson distributions. Comparison of two binomials; McNeyman’s test for matched pairs; theory and transformations of variables; multiple linear regression; selection of variables ; use of dummy variables. Introduction to logistic regression and generalized linear modeling. Non-parametric methods. Use of least squares principle; estimation of contrasts, two-way crossed classified data.
Estimation theory - unbiased estimators; efficiency; consistency; sufficiency; robustness. The method of moments. The method of maximum likelihood. Bayesian estimation - prior and posterior distributions; Bayes’ theorem; Bayesian significant testing and confidence intervals. Applications - point and intervals. Estimations of means, variances, differences between means, etc. Hypothesis testing theory - test functions; the Neyman - Pearson Lemma; the power function of tests, Likelihood ratio test.
Report writing and presentation ― organization, structure, contents and style of report. Preparing reports for oral presentation. Introduction to word processing packages, e.g., word for windows and latex. Single- and two-sample problems; Poisson and binomial models. Introduction to the use of generalized linear modeling in the analysis of binary data and contingency tables. Simple and multiple linear regression methods; dummy variables; model diagnostics; one and two-way analysis of variance. Data exploration method - summary and graphical displays. Simple problems in forecasting.
This course will introduce students to the sampling methods. The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size;
estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc. Stratified random sampling - proportional and optimum allocations.
Cluster sampling, systematic sampling, multistage sampling.
This course will introduce students to the sampling methods. The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size; estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc. Stratified random sampling - proportional and optimum allocations. Cluster sampling, systematic sampling, multistage sampling.
Introduction to Statistical Software: Eg. SPSS, Minitab, R, Matlab. Statistical data – Data from designed experiments; sample surveys; observational studies. Data exploration - sample descriptive techniques: measures of location and spread; correlation, etc. Diagrammatic representation of data: the histogram; stem - and leaf -; box-plot; charts, etc. Tabulation, interpretation of summary statistics and diagrams. Regression and Correlation Analysis: Simple Linear Regression. Interpretation of coefficients, Correlation and coefficient of determination. One-way ANOVA.
Vector random variables: expected values of random vectors and matrices; covariance matrices; linear transforms of random vectors; further properties of the covariance matrix; singular and non-singular distributions; quadratic functions of random vectors. Distribution concepts: distribution of a random vector; multivariate moment generating functions. Transformation of random variables: vector transformation and Jacobian; change of variables in multiple integrals; distribution of functions of random vectors; some applications – the Beta-distribution family; the Chi-square, t – and F – distributions. Order statistics: order transformation; joint distributions of order statistics; marginal distributions; alternative methods. Multivariate normal distribution: definition and examples; singular and non-singular distributions; properties of the multivariate normal distribution; multivariate normal density; independence of multivariate normal vectors. Conditional distribution:
Sources of information. Report writing: Structure – title, summary, introduction, results, conclusions, recommendations, methods, general discussion, references, appendices;
Content; Presentation; Style. Oral presentation: Preparation – logistical requirements, e.g., Flip charts, transparencies, overhead projector, slides, etc. Delivery – use of Power Point software;
Introduction to proposal writing.
Basic concepts/terminologies – e.g., units, treatments, factors. Completely randomized designs. Randomized block designs-efficiency, missing data. Latin squares. Sensitivity of randomized block and Latin square experiment. Factorial experiments-several factors at two levels; effects and interactions; complete and partial confounding of factorial experiments. Split-plot experiments-efficiency; missing data; split-plot confounding.