Data collection, description, and factor "association" versus causal relationship; "Confidence" - statistical versus practical; and Hypothesis testing - All of these covered in a conceptual approach while relying heavily on the mathematical language of probability (e.g., population and sample distributions; sampling; regression on one variable) and use of simulated and real data.
Data collection, description, and factor "association" versus causal relationship; "Confidence" - statistical versus practical; and Hypothesis testing - All of these covered in a conceptual approach while relying heavily on the mathematical language of probability (e.g., population and sample distributions; sampling; regression on one variable) and use of simulated and real data.
Introduction to methods of analyzing data from experiments and surveys; the role of statistics in research, statistical concepts and models; probability and distribution functions; estimation; hypothesis testing; regression and correlation; analysis of single and multiple classification models; analysis of categorical data.
Pedagogical skills for teaching assistants in undergraduate statistics courses and effective communication skills for professional statisticians. Topics include: basic teaching techniques, use of writing assignments to increase understanding of statistical concepts, writing and grading effective exams, and recording and analyzing grades with the aid of software. Videotaped sessions will be conducted and critiqued. May be repeated a maximum of three times.
Sampling distributions, statistical models, point estimates and confidence intervals, significance testing. Experimental Design (randomized blocks, nested/hierarchical models, Latin Squares), ANOVA (one, two, and multiway factorials, fixed and random effects), multiple comparison procedures, rank-based analyses, linear and nonlinear regression, power and sample size calculations, professional presentation of results.
Statistical Packages, numerical methods in maximization and integration, bootstrapping, simulation methods, multivariate normal distribution.
Minimal sufficiency and completeness, Lehamnn-Scheffe Theorem and basic division theory, methods for evaluating interval estimators. Methods for evaluating hypothesis testing procedures, robustness and M-estimation, sequential analysis, censored data, model selection techniques.
Axioms of Probability, conditional probability, distribution functions, density functions, transformations, expectations (expected values, moments, and MGFs), discrete and continuous distributions, multiple random variables (joint marginal, and conditional distributions), bivariate transformations, covariance and correlation, inequalities.
Life Table Analysis. Estimation of survival rates with censored data. Competing Risk Theory. Parameter estimation for commonly encountered reliability distribution with complete censored and truncated data. Maximum likelihood and order statistics techniques. Survivability growth models, comparison of survival distribution, and sample size determination in clinical trials. Extreme value theory.
Linear Model interpretation in vector spaces and projections, use of generalized inverses, identifiability and estimability of contrasts, normal equations, Gauss-Markov Theorem, MVUE, distribution theory for quadratic forms, complex designs such as crossover, split-plot and repeated measures, asymptotics for general linear models, familiarity with nonparametric regression models.
