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