Statistical Analysis for Education and Psychology Researchers

8 34.5 18 7.14143 2.31046 0.0268

This SAS programme is useful even for small samples (the z-value would not be used)
because it enables T+ and T− to be easily computed from the column of ranked differences
in the output. The difference column gives the sign + or − associated with an observation,
so that the two rank sums can be evaluated, that is the sum of the + rank differences and
the sum of the − rank differences.

Comment on Use of the Wilcoxon Signed Ranks Test

The assumption of rankability of the differences is frequently not met with operational
measures. Kornbrot (1990) discusses this point in some detail with particular reference to
operational measures of times, rates and counts. These are common operational measures
in psychology and education for example, time as an index of information processing,
and counts are often used to determine errors on tasks. Kornbrot presents a practical
alternative statistical test to the Wilcoxon Signed Ranks test called the rank difference
test. This procedure is applicable when operational measures do not meet the assumptions
underlying use of the Wilcoxon Signed Ranks test, in particular if there is doubt about
rankability of the difference scores. Both exact sampling distributions and large sample
approximations for the sample statistic D are given in Kornbrot’s paper.

7.6 Kruskal-Wallis One-way ANOVA

When to Use

A common research problem is to decide whether or not sample differences in central
tendency reflect true differences in parent populations (Walsh and Toothaker, 1974). The
Kruskal-Wallis test is often the chosen procedure to test two or more (k-sample case)
independent groups for location equality when assumptions of a one-way ANOVA
(analysis of variance) are suspect (non-normality and heterogeneity of variance, see
Chapter 8 for details) or when the observations are naturally in the form of ranks. The
rationale underpinning this procedure is that if all scores are considered initially as one
group, assigned a rank value, and the rank values are then reallocated into the
independent (or treatment) groups, then under the null hypothesis of chance the sum of
the ranks in each group will be about the same, apart from sampling variation.
Researchers use this test as they would a one-way ANOVA to determine whether two
or more groups have similar score distributions, Ciechalski (1988) suggests that the
Kruskal-Wallis test is not a substitute for a parametric procedure, but an additional
decision tool.
This procedure is also useful for analyzing count data in contingency tables when the
response variable is categorical and ordered. Traditionally this type of data is analyzed by
a Chi-square procedure, however, provided there is an underlying continuity to the
response variable, the Kruskal-Wallis test is a more powerful alternative than an r×k Chi-
square test.

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