Unit information: Statistics 1 in 2013/14

Unit name	Statistics 1
Unit code	MATH11400
Credit points	10
Level of study	C/4
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Professor. Johnson
Open unit status	Not open
Pre-requisites	Normally an A Level in Mathematics or equivalent
Co-requisites	MATH11300
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Statistics is now very important in many fields of human endeavour - in science, medicine, industry, social science, commerce and government. The very basic idea of statistics is that of modelling phenomena in a random way, using the tools of probability theory. Having specified a model, inferences can be made about elements of the model. These cover, not only estimates of quantities of interest, but also assessments of how accurate these estimates are. This unit introduces the basic methods of statistical data analysis and inference. It includes sections on descriptive statistics, estimation, confidence intervals and hypothesis testing, and looks at simple applications of these procedures.

Aims:

To introduce the role of statistics in contemporary applications and to develop an elementary understanding of, and fluency in, the statistical paradigm of data collection, exploration, modelling and inference.

Syllabus

• Modern applications of statistics; Data exploration; Use of R. [2].

• Model formulation; Parametric models; Parameter estimation; Method of moments and maximum likelihood; Assessment of fit. [4]

• The simple linear regression model; Motivation by example and simulation; Least squares estimation; Model assessment (through residuals) and interpretation. [2].

• Sampling variation; Assessment by simulation; Sample mean and variance etc.[2]

• Central limit theorem - mathematical proof and interpretation by simulation; implications for large sample inference; approximation to Binomial.[2].

• Exact Normal theory: the t and chi-squared distributions.[2]

• Confidence intervals; Interpretation via simulation; Exact results for Normal population mean; Effect of sample size and choice of confidence level. [2].

• Hypothesis testing; Interpretation via simulation; Exact theory for Normal population mean; Error types and size of test. [2].

• Theory and examples for paired sample inferences and two-sample inferences. [2].

• Simple linear regression; confidence intervals and hypothesis tests. [2].

Relation to Other Units

This unit is part of the foundation for all statistics units in later years.

Intended Learning Outcomes

Students should be able to:

• Use exploratory techniques to identify simple relationships in data;

• Formulate simple statistical models as appropriate to particular applications;

• Understand the principles of parametric modelling, and be able to derive parameter estimates for simple models using method-of-moments and maximum likelihood;

• Derive the simple linear regression model and implement it in appropriate situations;

• Simulate samples from specified distributions and understand why simulation techniques are a useful statistical tool;

• Use simulation techniques to explore sample variation;

• Calculate and understand confidence intervals for simple models by both exact and simulation methods;

• Formulate and carry out hypothesis tests by exact and simulation methods;

• Use the statistical software system R to support each of the above tasks.

Transferable Skills:

Use of statistical software for elementary statistical analysis on the computer.

Teaching Information

Lectures supplemented by weekly small group tutorials for first year students. Weekly problem sheets, with outline solutions available a fortnight later.

Assessment Information

The final mark for Statistics 1 is calculated from one 1½ -hour written examination in May/June. This examination paper is in two sections.

• Section A contains 5 short questions, ALL of which should be attempted. Section A contributes 40% of the mark for this paper.

Section B has 3 longer questions; you should attempt TWO. If you attempt more than two, your best two answers in Section B will be used for assessment.

• Section B contributes 60% to the mark for this paper. Calculators of the approved type (non-programmable, no text facility) are required for the examination. Statistical tables will NOT be provided or needed for the examination.

Reading and References

The recommended text is:

J. A. Rice, Mathematical statistics and data analysis, Wadsworth and Brooks Cole.

There are many other elementary texts on Probability and/or Statistics that you may find useful. However, the book by Rice may be recommended for the Statistics 2 course as well.

As part of the Statistics syllabus, students are required to develop familiarity with the statistical software package R. The use of R is continued in Statistics units in years 2, 3 and 4. The recommended text for R is:

P. Dalgaard, Introductory Statistics with R, Springer