Postgraduate Certificate in StatisticsCourse Structure
The emphasis is on statistical thinking rather than mathematical techniques, consequently statistical or mathematical theory are not discussed. The conceptual basis of the methods is emphasised; the aim is to develop an intuitive understanding of how the methods work. Underlying assumptions of the standard methods and what can be done when these assumptions are invalid are discussed. While it is likely that most participants will have some previous exposure to statistics as undergraduates, the course does not assume prior knowledge of statistical ideas and methods. However, because all participants are graduates, the coverage is conceptually more sophisticated than most undergraduate first level courses.
For Whom is the Course Intended?
The course is intended for graduates of disciplines, other than statistics, who want to develop and deepen their knowledge of statistical methods for solving problems involving data arising in business and industry, in public service agencies or in research agencies. Applications will be considered from degree level graduates in any discipline. While the mathematical level of the course is kept to a minimum, some background in mathematics is essential; Leaving Certificate mathematics is an acceptable standard for most modules.
Many people taking research degrees in other disciplines in Trinity College take the Postgraduate Certificate as a means of developing their research methods skills. This is encouraged by the College and in such cases the tuition fees for the Postgraduate Certificate are waived. Note, though, that students need to register separately for the Postgraduate Certificate - registration for the research degree is not sufficient.
Students taking taught postgraduate courses are NOT NORMALLY GIVEN PERMISSION to take the Postgraduate Certificate in parallel. Students who wish to do so need to apply to the Dean of Graduate Studies for permission. In doing so they should provide a letter/email indicating the support of their Course Director for their request. SUCH PERMISSION IS ONLY GRANTED EXCEPTIONALLY.
The Postgraduate Certificate is designed to be a challenging course for graduates of disciplines other than Statistics. The great majority of participants will have studied some Statistics at undergraduate level, but this will often have been taught in a cookbook fashion by non-statisticians. The course aims to develop and enhance the data analytic skills of non-statistical graduates by teaching in a unified and coherent way the inferential ideas and methods of Applied Statistics. It is not designed for Statistics graduates. Neither is it an entry point for postgraduate study in Statistical Science and it does not lead on to a Masters level degree in the discipline of Statistics.
All students take the Base Module, which is taught on Mondays and Wednesdays during the first 12 week semester, before Christmas. Students must then take two elective modules to complete the course. For the first six weeks of the second semester (after Christmas) there will be a module entitled Introduction to Regression (Tuesdays and Thursdays). This will be followed by a six-week module on the Design and Analysis of Experiments (also Tuesdays and Thursdays) and a module on Time Series (Mondays and Wednesdays) - these two modules will be taught from weeks 7 to 12. Note that the Time Series module is a bit more technical than the others and may not be a suitable choice for students with a weak mathematical background.
ST7001: Base Module
Michaelmas Term (Semester 1): Monday and Wednesday: (18.00-20.00) Lecturer: Mimi Zhang Topics covered:
- Data summaries and graphs
- Statistical models
- Sampling distributions: confidence intervals and tests
- Comparative experiments: t-tests, confidence intervals, design issues
- Counted data: confidence intervals and tests for proportions, design issues
- Cross-classified frequency data: chi-square tests
- Introduction to Regression Analysis
- Introduction to Analysis of Variance
- Statistical computing laboratory
ST7002: Introduction to Regression
Hilary Term (Semester 2) Weeks 1-6: Monday and Wednesday (18.00-20.00)
Lecturer: Dr Myra O'Regan
- Statistical versus deterministic relationships
- Simple linear regression model: assumptions, model fitting, estimation of coefficients and their standard errors
- Confidence intervals and statistical significance tests on model parameters
- Prediction intervals
- Analysis of variance in regression: F-tests, r-squared
- Model validation: residuals, residual plots, normal plots, diagnostics
- Multiple regression analysis - short introduction
- Statistical computing laboratories
ST7003: Design and Analysis of Experiments
Hilary Term (Semester 2): Weeks 7-12: Tuesday and Thursday (18.00 - 20.00)
This module is concerned with the design of data collection exercises for the assessment of the effects of changes in factors associated with a process and the analysis of the data subsequently produced.
In order to assure that the experimental changes caused the observed effects, strict conditions of control of the process must be adhered to. Specifically, the conditions under which the experimentation is conducted must be as homogeneous as possible with regard to all extraneous factors that might affect the process, other than the experimental factors that are deliberately varied.
The simplest experiments involve comparison of process results when a single factor is varied over two possible conditions. When more than two factors are involved, issues regarding the most efficient choice of combinations of factor conditions and ability to detect interactions between factors become important. With many factors and many possible experimental conditions for each factor, the scale of a comprehensive experimental design becomes impractical and suitable strategies for choosing informative subsets of the full design are needed.
The analysis of data resulting from well designed experiments is often very simple and graphical analysis can be very effective. Standard statistical significance tests may be used to assure that apparent effects are real and not due simply to chance process variation. Confidence intervals are used in estimating the magnitude of effects. In cases with more complicated experimental structure, a more advanced technique of statistical inference, Analysis of Variance, may be used.
Minitab is well equipped to assist both with design set up and with analysis of subsequent data, both graphical and formal. There will be two laboratory sessions involving the use of Minitab.
Case studies and illustrations from a range of substantive areas will be discussed
On successful completion of this module, students should be able to:
- compare and contrast observational and experimental studies,
- describe and explain the roles of control, blocking, randomisation and replication in experimentation,
- explain the advantages of statistical designs for multifactor experiments,
- describe and explain the genesis of basic experimental design structures,
- implement and interpret the analysis of variance for a selection of experimental designs,
- describe the models underlying the analysis of variance for a selection of experimental designs,
- produce and interpret graphs for data summary and model diagnostics,
- provide outline descriptions of more elaborate designs and data analyses,
- describe and discuss strategic issues involved in the design and implementation of experiments.
Specific topics addressed in this module include:
The need for experiments
experimental and observational studies
cause and effect
Basic design principles for experiments
Analysis of experimental data
Exploratory data analysis
Parameter estimation and significance testing
Analysis of variance
Statistical models, fixed and random effects
Model validation, diagnostics
Block structure and treatment structure
Analysis of Covariance
Response surface designs
Strategies for Experimentation
Assessment One 3-hour examination
Mullins, E., Statistics for the Quality Control Chemistry Laboratory, Royal Society of Chemistry, 2003, particularly Chapters 4-5, 7-8. Detailed coverage of much of the module, in a specific context.
Mead, R., The design of experiments: statistical principles for practical applications, Cambridge University Press, 1988. Comprehensive text, with extensive discussion of fundamentals.
Box, G.E.P., Hunter, J.S. and Hunter, W.G., Statistics for Experimenters, 2nd. ed., Wiley, 2005. Includes many gems of wisdom from these masters of the genre, though not a course text.
Daniel, C., Applications of Statistics to Industrial Experimentation, Wiley, 1976. Includes many gems of wisdom from this master of the genre, using methodology appropriate for an industrial setting. Robinson, G.K., Practical Strategies for Experimenting, Wiley, 2000. A comprehensive review of the non-statistical aspects of planning and conducting experiments and interpreting and using their results.
ST7004: Aspects of Survey Design (N.B. THIS MODULE IS NOT AVAILABLE IN 2018/2019)
Lecturer: Dr. Myra O'Regan (Myra.ORegan@tcd.ie)
This module will focus on data collection using questionnaires. The following topics will be addressed on the course.
• The survey process
• Sample selection
• Measurement issues
• Designing paper and web based questionnaires
This module will include a computer laboratory element that will show students how to develop online questionnaires.
The model will be assessed on the basis of a project. Each student will be required to carry out a survey of their choice and write a detailed report on the development of the questionnaire. The number of students is limited to 30. Should more than 30 students apply, participants will be chosen at random.
ST7005: Time Series Analysis (N.B. THIS MODULE IS NOT AVAILABLE IN 2018/2019)
Hilary Term (Semester 2): Weeks 7-12: Monday and Wednesday (18.00 - 20.00) Lecturer: Dr. Rozenn Dahyot (Rozenn.Dahyot@scss.tcd.ie)
Several methods of forecasting will be examined, including exponential smoothing and its Hot-Winters extension, auto-regression, moving average, and further regression based methods that take into account seasonal trends of lagged variables. The module will be practical, and will involve every student in extensive analysis of case study material for a variety of time series data.
When students have successfully completed this module they should be able to:
- Define and describe the different patterns that can be found in times series and propose the methods that can be used for their analysis.
- Program, analyse and select the best model for forecasting.
- Interpret output of data analysis performed by a computer statistics package.
- Introduction to times series
- Autoregressive Models
- Data Transformations
- Modelling Seasonality
- Exponential Smoothing
- RMSE and MAPE performance measures
- Holt-Winters Models for Seasonality
- Brief Introduction to ARIMA
Bibliography: Forecasting - Methods and Applications, S. Makridakis, S.C. Wheelwright and R. J. Hyndman, Wiley
Elective modules may vary from year to year. The department reserves the right to cancel a module if there is not sufficient demand.
Note that the information regarding lectures and lecture times, while correct when published, may be subject to change due to unforeseen circumstances.