Graduate Courses

Measures of location and variability. Graphs for presenting discrete and continuous data. Sampling distributions and the central limit theorem. General principles for constructing confidence intervals for parameters in one or two independent populations. Asymptotic confidence intervals for means and proportions. Statistical hypothesis tests for parameters through confidence intervals. Special topics in confidence intervals and related tests. Basic principles of hypothesis testing. Likelihood ratio test and asymptotic likelihood ratio test. Chi-square goodness-of-fit and independence tests, and the Kolmogorov-Smirnov test. Specialized normality tests. Ordered observations, median, percentiles and confidence intervals. Sign test for the median. Tests for equality of distribution of two samples. One-way ANOVA for independent and dependent samples and related tests. Basic principles of experimental designs. Simple and multiple linear models. Correlation coefficients and tests. Modelling bivariate variables: the bivariate normal distribution and copula theory. Applications and laboratory work in R.