Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

Hypothesis Tests for Ordinal
Data: Mann-Whitney, Wilcoxon,
Kruskal-Wallis, and Friedman Tests
APPENDIX
E
PREVIEW
E.1 Data from an Ordinal Scale
E.2 The Mann-Whitney U-Test: An Alternative
to the Independent-Measures t Test
E.3 The Wilcoxon Signed-Ranks Test: An Alternative
to the Repeated-Measures t Test
E.4 The Kruskal-Wallis Test: An Alternative
to the Independent-Measures ANOVA
E.5 The Friedman Test: An Alternative
to the Repeated-Measures ANOVA
E.1 Data from an Ordinal Scale
Occasionally, a research study generates data that consist of measurements on an ordinal scale.
Recall from Chapter 1 that an ordinal scale simply produces a rank ordering for the individuals
being measured. For example, a kindergarten teacher may rank children in terms of their
maturity, or a business manager may classify job applicants as outstanding, good, and average.
■ Ranking Numerical Scores
In addition to obtaining measurements from an ordinal scale, a researcher may begin with
a set of numerical measurements and convert these scores into ranks. For example, if you
had a listing of the actual heights for a group of individuals, you could arrange the numbers
in order from greatest to least. This process converts data from an interval or a ratio
scale into ordinal measurements. In Chapter 17 (page 562), we identify several reasons
for converting numerical scores into nominal categories. These same reasons also provide
justification for transforming scores into ranks. The following list should give you an idea
of why there can be an advantage to using ranks instead of scores.
1. Ranks are simpler. If someone asks you how tall your sister is, you could reply
with a specific numerical value, such as 5 feet 7 3 4 inches tall. Or you could answer,
“She is a little taller than I am.” For many situations, the relative answer would
be better.
2. The original scores may violate some of the basic assumptions that underlie
certain statistical procedures. For example, the t tests and ANOVA assume that
the data come from normal distributions. Also, the independent-measures tests
assume that the different populations all have the same variance (the homogeneityof-variance
assumption). If a researcher suspects that the data do not satisfy these
assumptions, it may be safer to convert the scores to ranks and use a statistical
technique designed for ranks.
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