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

APPENDIX E | Hypothesis Tests for Ordinal Data: Mann-Whitney, Wilcoxon, Kruskal-Wallis, and Friedman Tests 695
With critical boundaries of ±1.96, the obtained z-score is close to the boundary, but it is
enough to be significant at the .05 level. Note that this is exactly the same conclusion we
reached using the Wilcoxon T table.
E.4 The Kruskal-Wallis Test: An Alternative
to the Independent-Measures ANOVA
The Kruskal-Wallis test is used to evaluate differences among three or more treatment
conditions (or populations) using ordinal data from an independent-measures design. You
should recognize that this test is an alternative to the single-factor ANOVA introduced in
Chapter 12. However, the ANOVA requires numerical scores that can be used to calculate
means and variances. The Kruskal-Wallis test, on the other hand, simply requires that you
are able to rank-order the individuals for the variable being measured. You also should
recognize that the Kruskal-Wallis test is similar to the Mann-Whitney test introduced
earlier in this chapter. However, the Mann-Whitney test is limited to comparing only two
treatments, whereas the Kruskal-Wallis test is used to compare three or more treatments.
■ The Data for a Kruskal-Wallis Test
The Kruskal-Wallis test requires three or more separate samples. The samples can represent
different treatment conditions or they can represent different preexisting populations. For
example, a researcher may want to examine how social input affects creativity. Children are
asked to draw pictures under three different conditions: (1) working alone without supervision,
(2) working in groups where the children are encouraged to examine and criticize each
other’s work, and (3) working alone but with frequent supervision and comments from a
teacher. Three separate samples are used to represent the three treatment conditions with
n 5 6 children in each condition. At the end of the study, the researcher collects the drawings
from all 18 children and rank-orders the complete set of drawings in terms of creativity. The
purpose for the study is to determine whether one treatment condition produces drawings
that are ranked consistently higher (or lower) than another condition. Notice that
the researcher does not need to determine an absolute creativity score for each painting.
Instead, the data consist of relative measures; that is, the researcher must decide which
painting shows the most creativity, which shows the second most creativity, and so on.
The creativity study that was just described is an example of a research study comparing
different treatment conditions. It also is possible that the three groups could be defined
by a subject variable so that the three samples represent different populations. For example,
a researcher could obtain drawings from a sample of 5-year-old children, a sample of
6-year-old children, and a third sample of 7-year-old children. Again, the Kruskal-Wallis
test would begin by rank-ordering all of the drawings to determine whether one age group
showed significantly more (or less) creativity than another.
Finally, the Kruskal-Wallis test can be used if the original, numerical data are converted
into ordinal values. The following example demonstrates how a set of numerical scores is
transformed into ranks to be used in a Kruskal-Wallis analysis.
EXAMPLE E.2
Table E.2(a) shows the original data from an independent-measures study comparing three
treatment conditions. To prepare the data for a Kruskal-Wallis test, the complete set of
original scores is rank-ordered using the standard procedure for ranking tied scores. Each
of the original scores is then replaced by its rank to create the transformed data in
Table E.2(b) that are used for the Kruskal-Wallis test.
■