CHAPTER 13
N 0 N PA RAM ET R I C STAT I ST I CS
In Chapters 6-9 and 12, statistical analyses were given which assumed that the data
were interval or ratio. The data were also assumed to be normally distributed. In
Chapter 10 the binomial distribution was introduced where the data had two possible
outcomes, called successes or failures. In this chapter we describe the three most
widely used nonparametric tests that can be used when the data are ordinal and the
tests given in Chapter 8 cannot be used and also present another measure of correlation
when the correlation coefficient given in Chapter 12 is not appropriate.
The question arises as to what we can do if the data are not from a normal dis-
tribution or any other known distribution and are what is called distribution-free.
Usually, we assume that we know the distribution that the data follow, such as a
normal distribution, or we can transform the data to a normal distribution to test its
parameters o or p, but this is not always possible. The term nonpurumetric was used
before the term distribution free. If we do not know the distribution, we obviously do
not know its parameters. Calling a procedure distribution free or nonparametric does
not mean that no assumptions are made in performing the test. For example, we still
assume that random samples are taken plus other assumptions, depending on which
nonparametric test we use. For a more complete discussion of this terminology, see
Sprent and Smeeton [2007].Basic Statistics: A Primer for the Biomedical Sciences, Fourth Edition.
By Olive Jean Dunn and Virginia A. Clark
Copyright @ 2009 John Wiley & Sons, Inc.189