Statistical Analysis for Education and Psychology Researchers

6 106 13867.0000 13091.0000 468.674341 130.820755

Average Scores were used for Ties

Kruskal-Wallis Test (Chi-Square Approximation)

CHISQ=12, 110 DF=5 Prob>CHISQ=0.0333

Figure 7.9: Kruskal-Wallis test using

frequency data presented in Table 7.6

(data in the form of an r×k contingency

table)

Interpretation of Computer Output

The Kruskal-Wallis test statistic is 12.110 (Chi-square approximation) and since with
alpha equal to 5%=11.07, it can be concluded that the six distributions are not identical.

7.7 Friedman’s ANOVA by Ranks (for related data)

When to Use

The Friedman’s ANOVA by ranks is the last statistical procedure to be presented in this
chapter. It should be considered when an investigator is interested in testing difference
among related groups (repeated measurements) and when measures are naturally ranked
or can be rank ordered. The test can be considered as an extension of the Wilcoxon
signed ranks test, for more than two conditions. It is particularly suited for within-subject
experimental designs in psychology and education. Often a response variable is a score
representing, for example, the number of correct items, the number of errors, or the
number of tasks completed.
The procedure is most practical when there are at least five subjects and a minimum of
four conditions (repeated measures). With fewer subjects or treatments the exact

sampling distribution of the test statistic, should be consulted (see tables in Siegel

and Castallan, 1988). With more than three treatment groups and more subjects,
approximates to the Chi-square distribution. The test procedure is based on the idea that
under the null-hypothesis of no difference between conditions, we would expect the rank
values to be distributed randomly within each condition. We would also expect the rank
sum and mean rank in each condition to be similar.
The repeated measures design is intended to eliminate intra-subject variability
(subject-to-subject variability) and thereby make comparisons among conditions more
sensitive to treatment effects. If the rank sums for the various conditions are unequal, this
suggests that the scores in each condition are drawn from different populations. The
Friedman’s rank test is particularly sensitive to population differences in central tendency
and is generally considered to be more powerful than Cochran’s Q test.

Statistical analysis for education and psychology researchers 240