6 ECTS credits
150 h study time
Offer 1 with catalog number 4017235FNR for all students in the 2nd semester of even academic years (e.g. 2012-2013) at a (F) Master - specialised level.
The following topics are treated, where each topic is illustrated through various practical datasets and examples:
1. General(ized) linear models and exponential dispersion families
The chapter revisits concepts from mathematical statistics needed for data-analysis. We frame the results from earlier statistics courses in a theory of Hilbert spaces and projection operators.
2. One-way analysis of variance designed under the conditions of Fisher, Welch and Scheffé
The chapter treats classical ANOVA theory starting with Fishers version under homoscedasticity of the data. Welch provides a correction to allow heteroscedastic models which is a powerful test but no longer the uniform most powerful test known as the Beherns-Fisher paradox. Finally, we study the analysis of variance for contrasts and introduce the methods of Scheffé.
3. Multi-way analysis of variance and post-hoc tests
The chapter extends the viewpoint of chapter 2 to multiple categorical independent variables where main effects and crossterms or interactions are allowed. We analyze a residual analysis to assess normality and homoscedasticity claims. To formally test this claim, we study Shapiro-Wilk test for normality and homogeinity of variance test of Bartlett. The low robustness of Bartlett's test to departures of normality is solved by the introduction of Levene's test.
4. Sample size calculations and power analysis.
To ensure that practical relevance and statistical significance coincide, one must compute the needed sample size. A sample size too large renders statistical significance for meaningless differences in practice by virtue of the weak law of large numbers, whereas a sample size too small is not able to verify the alternative hypothesis due to a lack of information. We introduce a power analysis for omnibus F-tests and post-hoc tests based on the t-distrubution.
Syllabus is available. The course follows in part [A. Agresti, Foundations of linear and generalized linear models, Wiley, 2015] whose mathematical details are derived from [A. Stuart, K. Ord and S. Arnold, Kendall's advanced theory of statistics - Vol. 2A, Wiley 2004] and scientific work of the teacher.
The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.
Within the Other Exam category, the following assignments need to be completed:
Oral examination with written preparation about the theory.
Per chapter, a group assignment with a written report of a maximal length of 10 A4 pages and presentation of its main results is requested. The group assignment consists of the statistical analysis of real life data with a dedicated research question or hypothesis.
Evaluation:
10 marks on exam.
4 group assignment with a maximal mark 4x5 evaluated through the presentations and reports. Differentiation among members of a group is possible at the oral examination where a discussion is held about the group assignments.
This offer is part of the following study plans:
Master of Mathematics: Financial and Applied Mathematics (only offered in Dutch)
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)
Master of Mathematics: Education (only offered in Dutch)
Master of Teaching in Science and Technology: wiskunde (120 ECTS, Etterbeek) (only offered in Dutch)