Next: MC262 Linear Regression Models
Up: Year 2
Previous: MC260 Mathematical Statistics
MC261 Statistical Methods
| Credits: 10 |
Convenor: Dr. M.J. Phillips |
Semester: 1 (weeks 7 to 12) |
| Prerequisites: |
essential: MC160, MC161, MC260 |
|
| Assessment: |
Coursework: 20% |
One and a half hour exam: 80% |
| Lectures: |
18 |
Classes: |
5 |
| Tutorials: |
5 |
Private Study: |
47 |
| Labs: |
none |
Seminars: |
none |
| Project: |
none |
Other: |
none |
| Total: |
75 |
|
|
Explanation of Pre-requisites
The module MC160 provides the basic ideas of probability
which are required to understand statistical methods.
The module MC161 presents the basic concept of a statistic
and its use in estimation and hypothesis testing.
The module MC260 provides the techniques for study of the
joint distributions of random variables which enable the
classical normal theory results of mathematical statistics to be derived.
Course Description
Scientific and mathematical textbooks are filled with deterministic
models of reality, such as Newton's `law' relating the force of a
body to its mass and acceleration, which predict with little error.
In contrast many other models in scientific journals and texts are
not so good. The problem of how to
decide which is the `best' model
to use in these situations and how to use the probability model
to assess the validity of any inferences based on the model is
covered.
An introduction to the elementary statistical methods
for the analysis of data based on the theory of normal
random variables is given. This is extended to the case of two
random samples.
The question of how to explain variation
in two random samples is considered.
The simple linear regression model,
which can be used to study the linear association between two
variables, is briefly explained.
The course concludes with a brief account of
of goodness-of-fit for
frequency data in two-way contingency tables using Pearson's
test statistic.
Aims
This module covers the elementary statistical methods for the
analysis of data based on the theory of the normal (Gaussian)
random variables.
It aims to present the
use the Student's t distribution
and the one-way analysis of variance (ANOVA) table
in making inferences
from random samples from two normal populations.
There is an introduction
to the coefficient of correlation,
which aims to show how it can be used to
investigate the linear association between two variables.
This is followed by a brief introduction to the least
squares estimation of regression lines, which aims to show how
linear relationships can be established between two variables.
The ability to assess goodness-of-fit in two-way
contingency tables is covered.
This module aims to provide the necessary foundation for the
continued study of linear models in MC262 and MC264.
Objectives
To know the distribution of the sample mean and variance for
the normal population.
To understand how to
use the Student's t distribution
and the one-way analysis of variance (ANOVA) table
to make inferences
from random samples from two normal populations.
To understand how the coefficient of correlation can be used to
investigate the linear association between two variables.
To know the assumptions made in using the
simple linear regression model.
To be able to assess goodness-of-fit in two-way
contingency tables.
Transferable Skills
Ability to use the Student's t distribution to make inferences
from random samples from one or two normal populations.
Ability to use the one-way analysis of variance (ANOVA) table
to explain the variation in a normal population.
Knowledge of the coefficient of correlation and its use to
investigate the linear association between two variables.
The ability to make inferences about the parameters of the
simple linear regression model.
Knowledge of how to assess goodness-of-fit in two-way
contingency tables.
Syllabus
An introduction to the distribution of linear combinations of
normal random variables and the chi-square distribution.
The distribution of the sample mean and variance for the
normal population.
The Student's t distribution.
Two sample distributions including Snedecor's F distribution.
The question of how to explain variation is considered
using a one-way analysis of variance (ANOVA) table.
A brief review of significance tests to test hypotheses
using p-values and confidence intervals.
Relationships between variables are considered.
Inferences about the linear association of two variables
are studied using the coefficient of correlation.
The simple linear regression model is briefly explained.
Least squares estimators of slope and intercept parameters
are obtained.
Sampling distributions are derived for these estimators as
well as for `error' variance parameter.
Inference for the model parameters is covered using confidence
intervals and hypothesis tests.
Goodness-of-fit is investigated for
frequency data in two-way contingency tables using Pearson's
test statistic.
Reading list
Essential:
W. Mendenhall, R. L. Scheaffer and D. D. Wackerly,
Mathematical Statistics with Applications,
4th edition,
Duxbury Press, 1990.
Details of Assessment
One and a half hour examination in January consists of four questions.
Next: MC262 Linear Regression Models
Up: Year 2
Previous: MC260 Mathematical Statistics
Roy L. Crole
10/22/1998