This module is an introduction to probability and statistical inference. Statistics deals with the organisation, presentation and interpretation of data and methods from the theory of probability are used as tools in statistical analysis. The emphasis will be practical and will be assisted by a statistical software package.

Learning Outcomes

On successful completion of this module the learner will be able to:

LO1

Apply probability axioms and rules including Bayes theorem.

LO2

Use software to graphically display and numerically summarise data.

LO3

Use probability distributions to model random variables.

LO4

Understand the need for sampling and calculate a regression line.

LO5

Calculate and interpret both confidence intervals and hypothesis tests for both means and proportions.

Pre-requisite learning

Module Recommendations

This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).

Incompatible Modules

These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list.

This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.

No requirements listed

Module Content & Assessment

Indicative Content

Probability

Permutations and combinations. Classical, frequentist and axiomatic definitions. Laws of probability, independence, mutual exclusivity, conditional probability and Bayes' theorem. Tree diagrams.

Review of Descriptive Statistics

Presentation of data. Summary statistics. Histograms. Box plots. Use of software.

Probability Distributions

Random variables. Discrete vs Continuous. Expectation, mode, variance and standard deviation. Linearity of expectation. Binomial, Poisson and normal distributions. Use of software.

Sampling Theory

Sample statistics and sampling distributions. Central limit theorem. Confidence intervals for means and proportions. Determination of sample size. Hypothesis testing for small and large samples. Regression.

Assessment Breakdown

%

Course Work

30.00%

End of Module Formal Examination

70.00%

Course Work

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Short Answer Questions

In-class test: Probability, descriptive statistics and probability distributions.

1,3

15.0

Week 8

Practical/Skills Evaluation

Practical Laboratory Examination

2,3,4

15.0

Week 12

End of Module Formal Examination

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Formal Exam

End of Semester Final Examination

1,3,4,5

70.0

End-of-Semester

Reassessment Requirement

Repeat examination Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment

Module Workload

Workload: Full Time

Workload Type

Workload Description

Hours

Frequency

Average Weekly Learner Workload

Lecture

Exposition of theory illustrated by concrete examples

3.0

Every Week

3.00

Tutorial

Problem solving under the guidance of a tutor.

1.0

Every Second Week

0.50

Lab

Practical with software package

1.0

Every Second Week

0.50

Independent Learning

Completion of theory and practical exercises

3.0

Every Week

3.00

Total Hours

8.00

Total Weekly Learner Workload

7.00

Total Weekly Contact Hours

4.00

Workload: Part Time

Workload Type

Workload Description

Hours

Frequency

Average Weekly Learner Workload

Lecture

Exposition of theory illustrated by concrete examples

1.5

Every Week

1.50

Tutorial

Problem solving under the guidance of a tutor.

1.0

Every Second Week

0.50

Lab

Practical with software package

1.0

Every Second Week

0.50

Independent Learning

Completion of theory and practical exercises

5.0

Every Week

5.00

Total Hours

8.50

Total Weekly Learner Workload

7.50

Total Weekly Contact Hours

2.50

Module Resources

Recommended Book Resources

O'Shea, T. L. 2013, Essential Statistics for Researchers, IT Tralee [ISBN: 0957505906]

Kabacoff, R. 2015, R in Action, 2 Ed., Manning [ISBN: 9781617291388]

Supplementary Book Resources

Clarke G.M. and Cooke D. 1998, A Basic Course in Statistics,, 4 Ed., Arnold [ISBN: 0340719958]

Dalgaard, P 2002, Introductory Statistics with R, Springer [ISBN: 9780387954752]

This module does not have any article/paper resources