|| MA11410 |
|| LOOKING AT DATA |
|| 2004/2005 |
|| Dr John A Lane |
|| Intended for use in future years |
|Next year offered
|| N/A |
|Next semester offered
|| N/A |
|| A-level Mathematics or equivalent. |
| Course delivery
|| Lecture || 11 x 1 hour lectures |
|| Practical || 11 x 2 hour practical classes (duplicate practical sessions). |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Assessment|| Practical Report: Practical assignment reports. ||100%|
|Supplementary Assessment||2 Hours (practical examination) ||100%|
On completion of this module, a student should be able to:
produce suitable graphical representations of data;
perform standard (elementary) analyses of data;
interpret the results of such analyses;
identify and correct misleading analyses and representations;
produce clear reports.
Data analysis is a skill that is important to all disciplines. This module develops techniques and methods at a level leading on from
A-level mathematics, and includes examples of elementary modelling and statistical analysis in a wide range of applications such as economics, biology, medicine, etc. It includes training in the use of computer software, in particular the MINITAB package, which is an ideal tool for this purpose; no previous or other knowledge of computing is necessary. The aim of the module is to use such aids intelligently, and to produce clear interpretations leading to effective presentation and communication of results.
To enable students to acquire the skills of effective data analysis, presentation and interpretation.
1. UNDERSTANDING DATA: Effective summarisation of data; collection and simplification; accuracy; table construction. Pictorial representation via graphs, pie charts and bar charts of various kinds. Use and abuse. Interpretation. [D 1.1-1.5]
2. MATHEMATICAL MODELS: Use of mathematical language to describe a theory in a "perfect" world. Proportionality. The straight line; interpretations of intercept and slope. Simple transformations to achieve a straight line relationship. [D 10.1, 10.2] Dynamic models; simple models for rates of change leading to straight line relationships. Fitting a straight line relationship. Simple probability models; success/fail situations, the Binomial experiment, Poisson as a large-number-of-trials approximation. [D 2.3, 4.1-4.4]
3. RECOGNIZING VARIABILITY: Comparison of expected and observed data; the idea of "goodness-of-fit". The chi-squared goodness of fit test. [D 9.2] Consideration of departures from the expected. Measuring variability. Variance - its measurement and meaning. Informal use of variance as a check on some assumptions, e.g. Binomial and Poisson. [D3.1, 5.3-5.5] Estimation and comparison of proportions. Examples in quality inspection, opinion polls, etc. Informal inference. Informal inferences about means. Paired and unpaired comparisons. More formal inferences including one and two sample t-tests. [D7.3, 8.4]
4. PRACTICAL WORK: Good and bad tables; summarising large data sets; interpretations. Introduction to the graphical capabilities of a computer package. Illustrative examples of mathematical modelling drawn from Physics (e.g. Gas Laws, Hooke's Law, simple equations of motion), biology (growth patterns, dependence on weight, etc.), Economics (elasticity) etc. Growth and decay models. Formulation of models for real-life situations. Examples of informal and formal inference drawn from a variety of situations.
** Recommended Text
F Daly, D J Hand, M C Jones, A D Lunn & K J McConway, [D] Elements of Statistics
D S Moore & G P McCabe Introduction to the Practice of Statistics
This module is at CQFW Level 4