Presents fundamental concepts in applied probability, exploratory data analysis, and statistical inference, focusing on probability and analysis of one and two samples. Topics include discrete and continuous probability models; expectation and variance; central limit theorem; inference, including hypothesis testing and confidence for means, proportions, and counts; maximum likelihood estimation; sample size determinations; elementary non-parametric methods; graphical displays; and data transformations.
The goal of this course is to equip biostatistics and quantitative scientists with core applied statistical concepts and methods:
1) The course will refresh the mathematical, computational, statistical and probability background that students will need to take the course.
2) The course will introduce students to the display and communication of statistical data. This will include graphical and exploratory data analysis using tools like scatterplots, boxplots and the display of multivariate data. In this objective, students will be required to write extensively.
3) Students will learn the distinctions between the fundamental paradigms underlying statistical methodology.
4) Students will learn the basics of maximum likelihood.
5) Students will learn the basics of frequentist methods: hypothesis testing, confidence intervals.
6) Students will learn basic Bayesian techniques, interpretation and prior specification.
7) Students will learn the creation and interpretation of P values.
8) Students will learn estimation, testing and interpretation for single group summaries such as means, medians, variances, correlations and rates.
9) Students will learn estimation, testing and interpretation for two group comparisons such as odds ratios, relative risks and risk differences.
10) Students will learn the basic concepts of ANOVA.