This week, we'll be covering non-parametric (or assumption-free) statistical tests. Parametric techniques, which include the correlation r and the t-test, refer to the use of sample statistics to estimate population parameters (e.g., rho, mu). Thus far, we've come across a number of assumptions that technically are required to be met for doing parametric analyses, although in practice there's some leeway in meeting the assumptions.

Assumptions for parametric analyses, which are also described within the first few pages of Chapter 21, are as follows:

*Data for a given variable are normally distributed in the population.

*Equal-interval measurement.

*Random sampling is used.

*Homogeneity of variance between groups (for t-test).

As discussed in the chapter, one would generally opt for a non-parametric test when there's violation of one or more of the above assumptions and sample size is small. In other words, if assumptions are violated but sample size is large, you still may be able to use parametric techniques. We'll be doing a neat demonstration that conveys the role of large samples in salvaging data from the normal-distribution assumption.

To a large extent, the different non-parametric techniques represent analogues to parametric techniques. As one example, the non-parametric Mann-Whitney U test is analogous to the parametric t-test, when comparing data from two groups. I've even written a song for the occasion...

Mann-Whitney U (Video of Dr. Reifman performing it; thanks to Selen for filming)
Lyrics by Alan Reifman
(May be sung to the tune of “Suzie Q.,” Hawkins/Lewis, covered by John Fogerty)
Mann-Whitney U,
When your groups are two,
If your scaling’s suspect, and your cases are few,
Mann-Whitney U,

The cases are laid out,
Converted to rank scores,
You then add these up, done within each group,
Mann-Whitney U,

(Instrumental)

There is a formula,
That uses the summed ranks,
A distribution’s what you, compare the answer to,
Mann-Whitney U