# Statistical Theory II

Course category:
2nd year
Module code:
0590020
Year:
2009/10
Term:
Spring
Credits:
10
Lecturer:
Dr Stephen Connor

## Aims

To continue the development of statistical concepts and techniques learnt in Statistical Theory I and to provide students with a solid grounding in statistical theory, thereby providing the necessary background for advanced third year statistics modules. The course will also provide an introduction to the statistical software package R.

## Learning objectives

By the end of the module you are expected to:

• be able to calculate confidence intervals for means and variances in a number of settings;
• understand the basic concepts of statistical inference, the concept of a hypothesis, how one might go about testing it and the trade-off between the size and power of such a hypothesis test;
• have knowledge of the basic theory associated with correlation analysis and simple linear regression;
• be able to fit a simple linear regression model to data, estimate parameters and interpret them;
• understand the principles of analysis of variance;
• be confident at implementing the above theory using R.

## Syllabus

• Confidence intervals for means, proportions, difference in means, variances;
• Hypothesis testing: Hypotheses, critical regions, size and power. Likelihood ratio tests. Neyman-Pearson lemma and UMP tests. Consistent tests. Power calculation for fixed size. Determination of sample size needed to achieve a desirable level of power. Test for the mean with known variance (Z test). Test for the mean with unknown variance (t test). Test for the difference of two means. Test for the variance (F test);
• Correlation coefficient and its interpretation;
• The simple linear regression model: Fitting a straight line. Parameter estimation using least squares. Distributional properties of least squares estimators and the residual sum of squares. Testing the significance of a regression relationship. One-way Analysis of Variance.

## Recommended texts

• ** R V Hogg and A T Craig, Introduction to Mathematical Statistics (5th edn), Prentice-Hall (SF HOG)
• ** Casella, G., and Berger, R.L. (1990). Statistical Inference. Duxbury Press. (SF 2 CAS)
• ** Hoel, P.G. Introduction to Mathematical Statistics, Wiley. (SF HOE)
• * R V Hogg and E A Tanis, Probability and Statistical Inference (4th edn), Macmillan (S 9 HOG)
• * D C Montgomery, E A Peck, Introduction to linear regression analysis (2nd edn), Wiley (SF 2.5 MON)

In addition, students may find it useful to obtain a copy of the following tables:

• H R Neave, Statistics tables for mathematicians, engineers, economists and the behavioural and management sciences (SF 0.83 NEA and REF SF 0.83 NEA).

## Teaching

• Spring Term
• 2 lectures per week
• Weekly seminar

## Assessment

One and a half hour closed examination in week 1 Summer Term (90%). Coursework (10%). Note that coursework submitted after the advertised deadlines will be given a mark of zero.

## Elective information

Please check prerequisites carefully before asking to take this module as an elective.

## Postrequisites

The following modules use material from this module