A computational methods course in the theory and techniques of data analysis and error propagation, with emphasis on applications common to the physical sciences: the treatment of statistical errors, the maximum- likelihood method, the chi-square distribution, and curve fitting. Students will learn computer programming, and they will prepare a set of analysis programs for use in subsequent lab courses.
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 and moment generating functions, expected values, discrete and continuous distributions, joint marginal, and conditional distributions, transformations, covariance, and correlation, inequalities, properties of sums from a random sample.
This course presents statistical techniques for analyzing longitudinal studies and repeated measures experiments that occur frequently in public health, clinical trials, and outcomes research. This course will cover linear mixed models, generalized linear mixed models and an introduction to nonlinear models as they apply to the analysis of correlated data.
