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# MMath Mathematics and Statistics / Course details

Year of entry: 2021

## Course unit details:Practical Statistics

Unit code MATH20811 10 Level 2 Semester 1 Department of Mathematics No

### Overview

In this course statistical methods and concepts are put in the context of their practical, computational application with an emphasis on model selection, hypothesis testing and diagnostics. Students study a series of small projects in class and in example classes.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Probability 1 MATH10141 Pre-Requisite Compulsory
Probability 2 MATH20701 Pre-Requisite Compulsory
Introduction to Statistics MATH10282 Pre-Requisite Compulsory

### Aims

This course unit aims to introduce some important statistical concepts and methodology and to provide the students with experience in the use of the statistical system R in applying them to data.  Skills in report writing are to be developed.

### Learning outcomes

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.

### Syllabus

Exploratory data analysis (3 lectures) Data collection and presentation, Organisation of data analysis in R.

Correlation (3 lectures)  Sample correlation coefficient: numerical properties and interpretation, Estimation of population correlation and test for zero correlation, Rank correlation.

Linear regression (5 lectures) Simple linear regression, Multiple regression, Inference and diagnostics, Transformations of predictor and response variables.

Discrete data analysis (3 lectures) Discrete data; univariate probability models, Chi-squared goodness-of-fit test for univariate data;  bivariate discrete data and probability models, testing independence, testing the homogeneity hypothesis.

Monte Carlo Integration (1 lecture)

Assessing Goodness-of-Fit (7 lectures) The cumulative distribution function (cdf); distribution quantiles; sample order statistics and their properties; the probability integral transformation; the empirical cdf; empirical quantile function; quantile-quantile plots, simulating the sampling distribution of a statistic; Kolmogorov-Smirnov goodness-of-fit test.

### Assessment methods

100% coursework based on three take-home projects worth 30%, 30% and then 40%.

### Feedback methods

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.

This course unit is not based on a single book, some suggestions are given below.
John Rice (1994) Mathematical Statistics and Data Analysis, Edition 2 (Duxbury Resource Center)
M Crawley (2005)  Statistics An Introduction using R (Wiley)
Christian Heumann and Michael Schomaker Shalabh (2016) Introduction to Statistics and Data Analysis With Exercises, Solutions and Applications in R (Springer)
Maria Kateri (2014) Contingency Table Analysis, Methods and Implementation Using R (Chapters 1 and 2) (Springer New York)

### Study hours

Scheduled activity hours
Lectures 22
Practical classes & workshops 11
Independent study hours
Independent study 67

### Teaching staff

Staff member Role
Peter Foster Unit coordinator