Greg W. Corder is Adjunct Instructor in the Department of Physics and Astronomy at James Madison University. He is also Adjunct Instructor of graduate education at Mary Baldwin College. Dale I. Foreman is Professor Emeritus in the School of Education and Human Development at Shenandoah University.
Nonparametric Statistics: An Introduction
In this chapter, you will learn the following items:
The difference between parametric and nonparametric statistics.
How to rank data.
How to determine counts of observations. 1.2 Introduction
If you are using this book, it is possible that you have taken some type of introductory statistics class in the past. Most likely, your class began with a discussion about probability and later focused on particular methods of dealing with populations and samples. Correlations, z -scores, and t -tests were just some of the tools you might have used to describe populations and/or make inferences about a population using a simple random sample.
Many of the tests in a traditional, introductory statistics text are based on samples that follow certain assumptions called parameters. Such tests are called parametric tests . Specifically, parametric assumptions include samples that
are randomly drawn from a normally distributed population,
consist of independent observations, except for paired values,
consist of values on an interval or ratio measurement scale,
have respective populations of approximately equal variances,
are adequately large, and
approximately resemble a normal distribution.
If any of your samples breaks one of these rules, you violate the assumptions of a parametric test. You do have some options, however.
You might change the nature of your study so that your data meet the needed parameters. For instance, if you are using an ordinal or nominal measurement scale, you might redesign your study to use an interval or ratio scale. (See Box 1.1 for a description of measurement scales.) Also, you might seek additional participants to enlarge your sample sizes. Unfortunately, there are times when one or neither of these changes is appropriate or even possible.
Box 1.1 Measurement Scales.
We can measure and convey variables in several ways. Nominal data, also called categorical data, are represented by counting the number of times a particular event or condition occurs. For example, you might categorize the political alignment of a group of voters. Group members could either be labeled democratic, republican, independent, undecided, or other. No single person should fall into more than one category.
A dichotomous variable is a special classification of nominal data; it is simply a measure of two conditions. A dichotomous variable is either discrete or continuous. A discrete dichotomous variable has no particular order and might include such examples as gender (male vs. female) or a coin toss (heads vs. tails). A continuous dichotomous variable has some type of order to the two conditions and might include measurements such as pass/fail or young/old.
Ordinal scale data describe values that occur in some order of rank. However, distance between any two ordinal values holds no particular meaning. For example, imagine lining up a group of people according to height. It would be very unlikely that the individual heights would increase evenly. Another example of an ordinal scale is a Likert-type scale. This scale asks the respondent to make a judgment using a scale of three, five, or seven items. The range of such a scale might use a 1 to represent strongly disagree while a 5 might represent strongly agree . This type of scale can be considered an ordinal measurement since any two respondents will vary in their interpretation of scale values.
An interval scale is a measure in which the relative distances between any two sequential values are the same. To borrow an