NO (4) 1 4 (^3204)
Definitely NO (5) (^1 03111)
Total 16 46 (^372219106)
- Data originally collected as part of an evaluation study described in Dagenais and Marascuilo
(1981)^
Educational researchers typically collect questionnaire data in which respondents are
asked to answer a question or state an opinion and to give their response on an ordered
response scale. For example, data shown in Table 7.6 is in response to the question:
Has the integration of Berkeley’s schools been successful?
The ordered response scale is:
Definitely Not No Too soon to tell Yes Definitely yes
These are mutually exclusive categories which can be treated as ordered categories.
Typically this kind of data would be analyzed using an r×k Chi-square analysis. The
majority of two-dimensional contingency tables that appear in edu-cational journals are
analyzed by the traditional Chi-square procedure. Researchers, therefore, generally fail to
use the inherent information contained in an ordered response variable.
If the response variable is a qualitative (categorical) variable which has a theoretically
underlying continuum, the original nominal categories can be replaced by rank values 1,
2, 3...N and a more powerful Kruskal-Wallis test could be applied. Looking at the data in
Table 7.6, the number of subjects with each response in each group is given in each of the
cells of the table, for example, 11 subjects belonging to the group Isolates/Asian gave the
response YES. If we now create a response score for each subject, based on the frequency
in a cell, for example, for the Isolates/ Asian group with the response YES, 11 response
scores of 2 (YES) would be created. These response scores can then be ranked and the
Kruskal-Wallis test applied. This procedure is performed by the SAS programme, Krusk-
W2 (see Figure 12, Appendix A3). Output from the SAS programme Krusk-W2, using
data from Table 7.6, is shown in Figure 7.9.
NPAR1WAY Procedure
Wilcoxon Scores (Rank Sums) for Variable Response Classified by Variable
Group
GROUP N Sum of Scores Expected Under H0 Std Dev Under H0 Mean Score
1 16 1712.0000 1976.0000 233.387792 107.000000
2 46 6000.5000 5681.0000 369.018501 130.445652
3 37 3560.0000 4569.5000 338.320436 96.216216
4 22 2623.0000 2717.0000 270.078228 119.227273
5 19 2618.5000 2346.5000 252.664342 137.815789
Inferences involving rank data 239