This is a session of Topic 4: Statistics education at the post-secondary level

Rank-based inference, association measures and nonparametric statistics

Organizers

• Irène Gijbels (Belgium)
• Kathryn Prewitt (United States) : Session chair

Abstract

There are several specific challenges attached to the teaching of statistics nowadays. One of them is that a well-founded motivation of a statistical concept should go hand in hand with details of how to use these methods as well as expectations of performance and workability.. This requires paying attention, in a balanced manner, to theoretical foundations (or refer to them) and also to computational aspects, such as ease of computation and/or available software.

In statistical inference a crucial issue is the statistical modeling assumptions. If the model is wrong, then the conclusions are conceivably worthless. It is therefore important to teach about powerful distribution-free methods such as the Wilcoxon (one or) two-sample test (and its distributional properties, exact or even asymptotically), and association measures such as Kendall’s tau, Spearman’s rho, Gini index, etc. These association measures are among the basic tools to investigate global (and local) dependencies between variables in data analysis. In general, rank-based methods are a reasonable approach to analysis. Another possibility with the goal of less reliance on model assumptions is nonparametric statistics. Teaching nonparametric statistics in this day and age goes far beyond teaching about means, medians and histograms (and the previously mentioned topics). A topic such as kernel estimation is naturally introduced together with a histogram. In a regression context the classical (parametric) least squares fit goes hand in hand with the nonparametric local linear regression fit. Even in a bivariate setting basic ideas around regressograms and surface smoothing can then be given.

When teaching about these topics, one cannot leave out to teach students the intuition behind the statistical concepts. Rank-based procedures and nonparametric methods leave a lot of room for the teacher to also try to develop a good common sense for statistics. In addition, links towards state-of-the-art research are easily made.

Papers