| MA20226: Statistics 2A |
| Timetable: | Lectures: | Monday 15:15 (EB 1.1) and Thursday 12:15 (EB 1.1) in weeks 1-11. |
| Tutorials: | Monday 11:15 (3E 3.11) for Group A in weeks 2, 4, 5, 7, 8, 10, 11. Tuesday 17:15 (1WN 3.11) for Group B in weeks 2, 4, 5, 7, 8, 10, 11. Tuesday 13:15 (1WN 3.23) for Group C in weeks 2, 4, 5, 7, 8, 10, 11. Wednesday 12:15 (8W 1.33) for Group D in weeks 2, 4, 5, 7, 8, 10, 11. Thursday 10:15 (8W 2.6) for Group E in weeks 2, 4, 5, 7, 8, 10, 11. Wednesday 10:15 (1WN 3.23) for Group F in weeks 2, 4, 5, 7, 8, 10, 11. Wednesday 11:15 (1W 4.39) for Group G in weeks 2, 4, 5, 7, 8, 10, 11. Thursday 09:15 (8W 1.33) for Group H in weeks 2, 4, 5, 7, 8, 10, 11. | |
| Practicals: |
Monday 11:15 (3E 3.1) for Group A in weeks 3, 6, 9. Tuesday 17:15 (3E 3.1) for Group B in weeks 3, 6, 9. Tuesday 13:15 (EB 0.9) for Group C in weeks 3, 6, 9. Wednesday 12:15 (3E 3.1) for Group D in weeks 3, 6, 9. Thursday 10:15 (EB 0.9) for Group E in weeks 3, 6, 9. Wednesday 10:15 (EB 0.9) for Group F in weeks 3, 6, 9. Wednesday 11:15 (3E 3.1) for Group G in weeks 3, 6, 9. Thursday 09:15 (EB 0.9) for Group H in weeks 3, 6, 9. |
| Lecturer: | Simon Shaw; s.shaw at bath.ac.uk | |
| Tutors: | Groups A and G: | Simon Shaw; s.shaw at bath.ac.uk |
| Groups B and C: | Merrilee Hurn; m.a.hurn at bath.ac.uk | |
| Groups D and F: | Nicole Augustin; n.h.augustin at bath.ac.uk | |
| Groups E and H: | Steve Raper; s.l.raper at bath.ac.uk |
| Credits: | 6 |
| Level: | Intermediate |
| Period: | Semester 1 |
| Assessment: | CW25EX75 There will be two pieces of assessed coursework. The first will be handed out in the lecture of 03 Nov 11 with a deadline of 17 Nov 11. The second will be handed out in the lecture of 24 Nov 11 with a deadline of 08 Dec 11. |
| Other work: | There will be seven question sheets. These will be set in tutorials and handed in one week later. There is also one practical sheet which serves as preparation for the coursework and will be set in the lab session of week three and handed in the following week. Any work submitted by the hand-in deadline will be marked by your tutor and returned to you. Full solutions to all exercises will be made available. |
| Requisites: | Before taking this unit you must take MA10211 (home-page) and take MA10212 (moodle home-page) or equivalent units from MA10001 - MA10006. You may not take this unit if you have already taken MA20033. |
| Description: | Aims: Introduce classical estimation and hypothesis-testing principles. Learning Outcomes: After taking this unit, students should be able to:
Content: Point estimation: Maximum-likelihood 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; Neyman-Pearson lemma. One-sided and two-sided tests. Distributions related to the normal: t, chi-square and F distributions. Interference for normal data: Tests and confidence intervals for normal means and variances, one-sample problems, paired and unpaired two-sample problems. Contingency tables and goodness-of-fit tests. 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:
2011/12 Course summary and material
| Lecture 1 (03 Oct 11): | Introduction, §1 Point estimation: introduction, estimators and estimates. |
| Lecture 2 (06 Oct 11): | Sampling distribution, maximum likelihood estimation. |
| Lecture 3 (10 Oct 11): | Log-likelihood, examples of mle for Poisson and Normal distribution. |
| Lecture 4 (13 Oct 11): | §2 Evaluating point estimates: bias. |
| Lecture 5 (17 Oct 11): | Mean square error, relative efficiency. |
| Lecture 6 (20 Oct 11): | Consistency, robustness, measures of location. |
| Lecture 7 (24 Oct 11): | Trimmed mean, §3 Interval estimation: principle of interval estimation. |
| Lecture 8 (27 Oct 11): | Pivot, confidence interval, confidence interval for normal mean (variance known). |
| Lecture 9 (31 Oct 11): | Chi-squared distribution, confidence interval for normal variance. |
| Lecture 10 (03 Nov 11): | t-distribution, confidence interval for normal mean. |
| Lecture 11 (07 Nov 11): | §4 Hypothesis testing: null and alternative hypothesis, critical region. |
| Lecture 12 (10 Nov 11): | Type I and Type II errors, significance level, power of a test, Neyman-Pearson lemma and examples of use. |
| Lecture 13 (14 Nov 11): | One-sided alternative hypotheses uniformly most powerful test. |
| Lecture 14 (17 Nov 11): | Two-sided alternative hypotheses, duality between hypothesis test and confidence interval. |
| Lecture 15 (21 Nov 11): | Power function, §5 Inference for normal data: investigating the variance in one-sample problems. |
| Lecture 16 (24 Nov 11): | Investigating µ in one-sample problems (known variance). |
| Lecture 17 (28 Nov 11): | p-value for one and two-sided tests. |
| Lecture 18 (01 Dec 11): | Investigating µ in one-sample problems (unknown variance): t-tests. |
| Lecture 19 (05 Dec 11): | Comparing paired samples. |
| Lecture 20 (08 Dec 11): | Unpaired data, F-distribution, investigating the variance for unpaired data. |
| Lecture 21 (12 Dec 11): | Investigating the means for unpaired data (known and unknown variances), pooled sample variance. |
| Lecture 22 (15 Dec 11): | §6 Goodness-of-fit tests: multinomial distribution, Pearson's chi-square statistic. |
|
Tables - |
normal: pdf |
chi-squared: pdf |
t-distribution: pdf |
F-distribution: pdf |
(thanks to Ruth Salway)
| Question Sheet One: pdf or postscript | Feedback Sheet One: pdf or postscript |
| Question Sheet Two: pdf or postscript | Feedback Sheet Two: pdf or postscript |
| Question Sheet Three: pdf or postscript | Feedback Sheet Three: pdf or postscript |
| Question Sheet Four: pdf or postscript | Feedback Sheet Four: pdf or postscript |
| Question Sheet Five: pdf or postscript | Feedback Sheet Five: pdf or postscript |
| Question Sheet Six: pdf or postscript | |
| Question Sheet Seven: pdf or postscript |
| Practical Sheet One: pdf or postscript | Feedback on Practical Sheet One: pdf or postscript |
| Coursework Sheet One: pdf or postscript | |
| Coursework Sheet Two: pdf or postscript |
|
Exams - |
2010/11 | 2009/10 |
2008/09 |
2007/08 |
2006/07 |
| Paper: |
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| Solutions: | pdf |
pdf |
pdf |
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Last revision: |