|Unit level:||Level 2|
|Teaching period(s):||Semester 2|
|Offered by||School of Mathematics|
|Available as a free choice unit?:||N
- MATH20802 - Statistical Methods (Compulsory)
Additional RequirementsMATH20812 co-requisites
This course unit aims to introduce essential statistical concepts and techniques and to provide the students with experience in the use of the statistical system R.
In this course statistical methods and concepts are put in the context of their practical application with emphasis on model selection and diagnostics. Students do a series of small projects in class and as homework. Some projects are complete data analysis exercises centred around particular statistical topic
On completion of this unit students will be able to:
- estimate the sample correlation coefficient from a sample of bivariate data and make inferences about the true population value,
- formulate a simple linear regression model and use least squares to estimate the parameters,
- to carry out appropriate goodness-of-fit tests to assess distributional assumptions about sample data,
- to make inferences about the characteristics of an underlying bivariate distribution when the data is categorical,
- use the statistical software R to explore and interpret data using graphical presentations, data summaries, model fitting, confidence intervals and test statistics,
- to be able to use R to conduct simple Monte Carlo experiments to estimate parameter values and the sampling distribution of their estimators,
- to present informatively and discursively the results of computations arising from data analysis.
Assessment Further Information
100% coursework consisting of in-class tests and homework projects.
Exploratory data analysis (3 lectures)
- Data collection and presentation. 
- Organisation of data analysis in R: transformations, scripts and functions. 
Correlation (3 lectures)
- Sample correlation coefficient: numerical properties and interpretation. 
- Estimation of population correlation and test for zero correlation. 
- Rank correlation. 
Linear regression (4 lectures)
- Simple linear regression. 
- Transformations of predictor and response variables. 
Writing projects (1 lecture)
Goodness of fit tests (5 lectures)
- Testing for a single distribution (K-S test). 
- Testing for a family of distributions. 
- Analysis of residuals. 
- Chi-square test for discrete distributions. 
Tests for bivariate data (3 lectures)
- Two-way contingency tables: chi-square test of independence, testing homogeneity, inference about the odds ratio. 
Introduction to Monte Carlo methods (3 lectures)
- Estimating standard errors of estimators. 
- Evaluation of integrals by simple Monte Carlo. 
- Estimating distributions of estimators. 
This course unit is not based on a single book, some suggestions are given below.
- A reference text for probability and statistical concepts studied in the first 3 semesters is a necessity, for example: Miller, Irwin; Miller, Marylees(2004) John E. Freund's mathematical statistics with applications. 7th ed. Upper Saddle River, N.J. : Pearson Prentice Hall.
- Conover, W.J. (1999) Practical nonparametric statistics, 3rd edition (mainly Chapter 3 and Chapter 6).
- Dalgaard, Peter (2002) Introductory statistics with R, New York : Springer.
- Devore, Jay; Peck, Roxy Introductory statistics, 2nd edition, 1994 (Chapters 11 and 12 cover simple linear regression and correlation.). There are more recent books by these authors with slightly different names.
Joaquim P. Marques de SÃ¡ (2007) Applied Statistics Using SPSS, STATISTICA, MATLAB and R. Springer Berlin Heidelberg New York.
Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturers, for example during the lecturers’ office hours.
- Lectures - 22 hours
- Tutorials - 11 hours
- Independent study hours - 67 hours