MA20033: Statistical Inference 1 
Timetable: 
Lectures 
Monday 
Tutorials 
Monday 16:15 (8W 1.33) for Group 1 in weeks 2, 4, 6, 8, 10. Monday 17:15 (3WN 3.8) for Group 2 in weeks 2, 4, 6, 8, 10. Wednesday 10:15 (3W 3.9) for Group 3 in weeks
2, 4, 6, 8, 10. 

Practicals 
Monday 16:15 (1W 2.25) for Group 1 in weeks 3, 5, 7, 9. Monday 17:15 (1W 2.25) for Group 2 in weeks 3, 5, 7, 9. Wednesday 10:15 (1W 2.25) for Group 3 in weeks
3, 5, 7, 9. 
Lecturer: Simon Shaw;
s.shaw at bath.ac.uk
Tutors: 
Groups 1 and 4 
Simon Shaw; s.shaw at bath.ac.uk 
Group 2 
Vangelis Evangelou; e.evangelou at bath.ac.uk 

Group 3 
Wenyang Zhang; w.zhang at bath.ac.uk 
Aims & Learning Objectives:
Aims: Introduce classical estimation and hypothesistesting
principles.
Objectives: Ability to perform standard estimation procedures and
tests on normal data. Ability to carry out goodnessoffit tests,
analyse contingency tables, and carry out nonparametric tests. Ability
to use R to calculate estimates, carry out hypothesis tests and compute
confidence intervals.
Content:
Point estimation: Maximumlikelihood estimation, including
computational aspects; further properties of estimators, including mean
square error, efficiency and consistency; robust methods of estimation
such as the median and trimmed mean. Confidence intervals. Hypothesis
testing: Size and power of tests; NeymanPearson lemma. Onesided and
twosided tests. Distributions related to the normal: t, chisquare and
F distributions. Interference for normal data: Tests and confidence
intervals for normal means and variances, onesample problems, paired
and unpaired twosample problems. Contingency tables and goodnessoffit
tests. Nonparametric methods: Sign test, signed rank test, MannWhitney
Utest. Examples of all the above, including case studies in R.
Some useful books
We won't follow a book as such but useful references include:
The rather dishevelled appearance of my copy of Rice indicates it as a
personal favourite. The interested student may find other books around
the 512.75 and 512.76 shelfmarks.
For help with programming in R, a recommended reference is:
2009/10 Course summary and material
Lecture 1 (05 Oct 09): Introduction, §1
Point estimation: introduction, estimators and estimates.
Lecture 2 (08 Oct 09): Sampling distribution, maximum likelihood estimation.
Lecture 10 (05 Nov 09): tdistribution, confidence interval for normal mean §4 Hypothesis testing: null and alternative hypothesis.
Lecture 11 (09 Nov 09): Critical region, Type I and Type II errors, significance level. Question Sheet Three handed out.Lecture
17 (30 Nov 09): pvalue for one and twosided tests.
Lecture 18 (03 Dec 09): Investigating µ in onesample problems
(unknown variance): ttests.
Lecture 19 (07 Dec 09): Comparing paired samples. Question Sheet Five handed out.
Lecture 20 (10 Dec 09): Unpaired data, Fdistribution,
investigating the variance for unpaired data.
Lecture 21 (14 Dec 09): Investigating the
means for unpaired data (known and unknown variances), pooled sample
variance.
Lecture 22 (17 Dec 09): §6 Goodnessoffit tests:
multinomial distribution, Pearson's chisquare statistic. Question Sheet Six handed out.
Forthcoming material
The course is now completed.Omitted material
In previous years, the course has contained 24 lectures, the contents of these lectures are shown below.Lecture 23: §7 Nonparametric methods: Signedrank test aka Wilcoxon matchedpairs test.
Lecture 24: MannWhitney Utest.
Lecture notes: pdf or postscript
Handouts  Adding independent normals: pdf or postscript
Tables  
normal: pdf 
chisquared: pdf 
tdistribution: pdf 
Fdistribution: pdf 
(thanks to Ruth Salway)
Homework 
There will be fortnightly question sheets. Question sheets and full solution sheets will be made available.Practicals 
Practical Sheet One: Set in Week 3 practicals 


text file of functions: txt  
Practical Sheet Two: Set in Week 5 practicals  Assessed coursework,
due in Week 6 tutorials 

text file of functions: txt  Coursework Cover Sheet: pdf  
Practical Sheet Three: Set in Week 7 practicals  Assessed coursework, due in Week 8 tutorials  
Practical Sheet Four: Set in Week 9 practicals  Assessed coursework, due in Week 10 tutorials 
Exams  
2008/09 
2007/08 
2006/07 
2005/06 

Paper: 

Solutions:  pdf 
pdf 
pdf 
pdf 
Last revision: 