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.

The full unit timetable is available here. A schedule for the course is available as either pdf or postscript.
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:
  • Perform standard estimation procedures and tests on normal data.
  • Carry out goodness-of-fit tests and analyse contingency tables.
  • Use R to calculate estimates, carry out hypothesis tests and compute confidence intervals.

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:

  1. J.A. Rice, Mathematical Statistics and Data Analysis, Third Edition, 2007. 512.75 RIC
  2. G. Casella and Berger, R.L., Statistical inference, 1990. 512.76 CAS
  3. L.J. Bain and Engelhardt, M., Introduction to probability and mathematical statistics, 1992. 512.75 BAI
  4. C. Chatfield, Statistics for technology: a course in applied statistics, Third Edition, 1983. 512.760.5 CHA
  5. S.Chatterjee, Handcock, M.S. and Simonoff, J.S., A casebook for a first course in statistics and data analysis, 1995. 512.76 CHA


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:


  1. Peter Dalgaard, Introductory statistics with R, 2002. 512.764 DAL

The book is also available electronically from the University of Bath library by clicking here for the first edition or here for the second edition.

2011/12 Course summary and material


Material covered:
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 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 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.

Forthcoming material:
This course is now completed.
Lecture notes: pdf or postscript

Tables -

normal: pdf

chi-squared: pdf

t-distribution: pdf

F-distribution: pdf

(thanks to Ruth Salway)


Homework -
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

Practicals -
This course has one practical sheet and two pieces of assessed coursework.
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:
pdf pdf pdf pdf pdf
Solutions: pdf
pdf
pdf
pdf
pdf

Last revision:
30/08/12

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