MA 331 - Intermediate Statistics
An introduction to statistical inference and to the use of basic statistical tools. Topics include descriptive and inferential statistics; review of point estimation, method of moments, and maximum likelihood; interval estimation and hypothesis testing; simple and multiple linear regression; analysis of variance and design of experiments; and nonparametric methods. Selected topics, such as quality control and time series analysis, may also be included. Statistical software is used throughout the course for exploratory data analysis and statistical inference based in examples and in real data relevant for applications.
Prerequisites: MA 222
The main objective in this course is to acquaint the student with the essential ideas and reasoning of applied statistics (data analysis, data production, inference) and with statistical methods for various types of data. The students are also required to learn a statistical package (R) and to complete a project applying the notions learned in the class to real data.
Learning outcomes in this class are divided into three categories:
- Data Production and Summary: In this part of the course the students need to know how to produce random samples, stratified samples and block design samples and they need to know how to summarize the data produced using graphical means (bar charts, stemplots, pie chart, line charts, and histograms) and numerical measures (mean, variance, quantiles etc.).
- Basic Data Analysis and Parameter Estimation: This includes learning how to calculate estimators for the parameters and learning how to evaluate the estimators by creating confidence intervals and tests for many commonly encountered distributions (normal, t, chi-squared, F). Once they understand the basic analysis students are ready for the last part of the course, advanced statistical analysis.
- Advanced Statistical Analysis: In the third part of the course the students learn methods for analyzing relations between variables. The methods they need to know include relationship between categorical variables (one and two way tables), between quantitative variables as responses and categorical as predictors (ANOVA and MANOVA), and between quantitative responses and quantitative predictors (simple and multivariate regression). At the end of the class students are required to learn more complex models such as predictors being a mixture of categorical and quantitative variables (ANCOVA) and the response being categorical and the predictors being quantitative (logistic regression). Students are expected to demonstrate the practical understanding of the advanced topics by analyzing real data using the advanced modeling tools taught in the class.
Moore, D. and G. McCabe, Introduction to the practice of Statistics, fifth edition, WH Freeman and Co, 2005.
Dalgaard, Peter, Introductory Statistics with R, Springer Verlag, 2004.