# Module 9: Nonparametric Methods

## Dates

Two and a half days: Monday May 22 and Tuesday May 23, 2017, from 10 am to 1 pm and from 2 pm to 5 pm, and Wednesday May 24, 2017 from 10 am to 1 pm.

## Venue

Faculty of Science , Site Sterre, Krijgslaan 281, Building S9, Ghent

## Description

Nonparametric methods are often used in situations where the assumptions of parametric methods do not hold or cannot be assessed (e.g. in small samples). The focus of this course is on nonparametric tests for comparative studies (e.g. comparing two treatments).

In the first lecture the basics of statistical hypothesis testing are illustrated on the parametric two-sample t-test. From there we move on to exact permutation tests.

The second lecture is devoted to rank tests. After a traditional introduction to rank tests, we spend time on some typical pitfalls related to the use and the interpretation of rank tests. In particular, the roles of the location-shift assumption and the probabilistic index are explained. The connection between rank tests and effect size estimation is also part of this lecture.

An extensive overview of the most popular nonparametric tests is the topic of the third lecture. We also stress the relationship between the study design and the choice of the statistical method. All tests and their interpretations are illustrated using R and/or SAS.

In the fourth lecture some more advanced methods are briefly discussed: probabilistic index models (PIM), rank tests for clustered data and sample size calculation.

Finally, a few methods for nonparametric regression are discussed in the fifth lecture: basics of smoothers and (generalized) additive models.

The following topics are included:

• rank and permutation tests: general principles (permutation null distribution, asymptotic distributions, power, efficiency...)
• some classical rank tests: Wilcoxon-Mann-Whitney, Kruskal-Wallis, Friedman, Mantel-Haenszel, ...
• interpretation of the hypotheses and the effect sizes: location-shift model, probabilistic index
• how nonparametric are nonparametric methods? Assumptions and pitfalls, semiparametric interpretation
• nonparametric estimators for effect sizes: Hodges-Lehman, rank regression, probabilistic index models
• multiple comparisons of means: family wise error rate (FWER), false discovery rate (FDR), permutation methods
• correcting for continuous covariates: rank tests for stratified designs, rank regression, probabilistic index models
• on the relation between the design and the (nonparametric) statistical analysis: Friedman (randomized complete blocks), Mack-Skillings (randomized complete block with recurrences), Skillings-Mack (balanced incomplete block designs), ...
• rank tests for clustered data
• sample size calculation
• nonparametric regression: smoothers, bandwidth selection, generalized additive models

The course consists of 5 theoretic lessions of 2 hours and 5 practical sessions of 1 hour in which SAS or R can be used.

## Target audience

This course targets all researchers who need to analyze small data sets or data for which the common assumptions of parametric methods do not hold.

## Exam

Participants can, if they wish, take part in an exam. Upon succeeding in this test a certificate from Ghent University will be issued to participants with a university degree at the bachelor level or an equivalent degree.

To qualify for reimbursement from the UGent Doctoral Schools one must attend all classes and pass the exam. Additional conditions and procedure.

## Course prerequisites

Participants are expected to be familiar with the basic principles of statistical inference, particularly hypothesis testing and linear regression.

## Teachers

Prof. dr. Olivier Thas is Professor of Statistics at Ghent University, Department of Mathematical Modelling, Statistics and Bioinformatics. He is chairing the Program Committee of the Advanced Master of Statistical Data Analysis. He teaches courses in basic statistics, multivariate and high dimensional data analysis, experimental design and statistical genomics. His research focuses on the development and application of nonparametric and semiparametric statistical methods for the bio and life sciences.

## Course material

Copies of lecture notes.

## Fees

A different price applies, depending on your main type of employment.

EmploymentModule 9Exam
Industry/Private sector1 600 30
Non-profit, government, university outside AUGent2 270 30
(Doctoral)student outside AUGent2 210 30

1 If three or more employees from the same company enrol simultaneously for this course a reduction of 10% on the module price is taken into account.

2 AUGent staff and AUGent doctoral students who pay through use of an SAP internal order/invoice can participate at these special prices.