• ECTS

    4 credits

  • Component

    Faculty of Science

Description

Non-parametric methods are important in many statistical applications because they allow to get away from classical approaches which require the specification of valid statistical models. However, establishing the validity of such a model is a complex undertaking.

Non-parametric methods circumvent this problem by using the transformation of data into ranks and by conditioning on certain quantities derived from the observed configuration of these ranks. The statistics thus constructed are independent of the distribution of the raw data, which allows the construction of statistical inference procedures free of the model underlying the data. Moreover, the loss of statistical efficiency is minimal.

This course is a fairly comprehensive presentation of non-parametric methods. It builds on a first course on parametric inferential methods by adapting and developing the theory of several advanced concepts such as conditional testing, comparative power of tests (efficiency measures), and the notion of "effect size". It emphasizes the practical application of these methodologies by providing an overview of the main R commands and their uses.

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Objectives

To help the student understand the limitations of parametric statistical methods, to choose a good non-parametric approach to a given problem based on the underlying statistical principles, to implement the solution to the problem using the R software, and to report the conclusions of the analysis and their significance to the end users.

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Necessary pre-requisites

One M-level inferential statistics course

One L-level probability course
 


 
Recommended prerequisites: A course in descriptive statistics at the L level

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Knowledge control

Continuous control

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Syllabus

  1. Definitions of Nonparametric Statistics

    2. Two tricks to remove dependence on an unknown parameter: conditioning (with application to contingency tables, chi-square tests and Fisher-Yates tests) and rank transformation.

    3. The Wilcoxon-Mann-Whitney 2-sample test: Assumptions and test statistics; Exact and asymptotic behavior under H0, the case of tied data, robustness of the test.

    4. Variants and extensions of the Wilcoxon-Mann-Whitney test: Point and interval estimation of the effect of treatments, the case of paired samples, power of the Wilcoxon-Mann-Whitney test i) when the Student paradigm holds and ii) when it does not. Notions of "effect-size", calculation of sample sizes to obtain a targeted power.

    5. Other tests for the case of 2 samples: Kolmogorov-Smirnov test, Ansari-Bradley test

    6. The case of K >2 samples: Kruskal-Wallis test, Friedman-Tukey test. The problem of multiple comparisons. Control of the p-value : Holm's method, FDR method (false discovery rate)

    7. Independence, correlation and regression: Pearson's correlation coefficient, Spearman, Kruskal, independence test. Application to regression

    Implementation with R software of the main non-parametric tests seen in the course.
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Additional information

Hourly volumes:
CM : 15h
TD : 15h
TP :
Field :

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