# Nonparametric Statistics

Overview

This chapter brings us to the end of the course.  Nonparametric statistics represents as alternative technique to conducting inference.  The methods of nonparametric statistics do not require that the data follow a specified distribution – such as the normal distribution.  The methods of nonparametric statistics are referred to as distribution-free techniques because they do not rely on a model based on a distribution to make inferences.  In this chapter, we present methods for conducting inference on a single parameter, dependent samples for a measure of central tendency, independent samples comparing two measures of central tendency, measures of association, and comparing three or more populations.

What to Emphasize

It is worth mentioning that simulation and randomization techniques may be used even if model requirements for the parametric tests are not satisfied.  Many would argue that simulation and randomization techniques are superior to the nonparametric methods. So, if you have limited time, it may be worthwhile to introduce simulation and randomization techniques over nonparametric statistics.

• An Overview of Nonparametric Statistics – Compare and contrast parametric with nonparametric procedures. Spend some time on the advantages and disadvantages of nonparametric statistical procedures.  Finally, spend some time talking about efficiency of the nonparametric test compared with the corresponding parametric test.
• Runs Test for Randomness – If you only have time for one nonparametric test, make it this one. Emphasize that the runs test for randomness is used to test whether it is reasonable to conclude the data occur randomly, not whether the data are collected randomly. The problems on random walks for investment vehicles are interesting.
• Inferences about Measures of Central Tendency – It might be worthwhile to use a data set from Section 10.3 where hypothesis tests about a single mean were introduced and do a side-by-side solution comparing the two methods.
• Inferences about the Difference between Two Medians: Dependent Samples – As suggested for inferences about measures of central tendency, it might be worthwhile to use a data set from Section 11.2 where hypothesis tests about two dependent means were introduced and do a side-by-side solution comparing the two methods. You should also consider assigning some problems where the Wilcoxon Signed-Ranks Test is used on a single sample.
• Inferences about the Difference between Two Medians: Independent Samples – Again, do a side-by-side solution using a data set from Section 11.3.
• Spearman’s Rank-Correlation Test – Do a side-by-side solution that allows for a comparison of Spearman’s rank-correlation test with a hypothesis test on the slope of the least-squares regression line.
• Kruskal-Wallis Test – Do a side-by-side solution that allows for a comparison of one-way ANOVA and the Kruskal-Wallis Test.