Statistical Analysis for Education and Psychology Researchers

Significance is based on an initial alpha of 0.1 (two-tailed test) but adjusted for

the number of pairwise comparisons tests

First

group

Second

group

No. of

subjects

(gp 1)

NO. of

subjects

(gp 2)

Abs.

diff in

mean

ranks

SE of

diff.

critical

Z value

Adjusted

alpha

sig. at

adjusted

alpha

1 2 5 5 0.5 2.82843 2.12805 0.016667 no.

1 3 5 5 6.7 2.82843 2.12805 0.016667 yes

2 3 5 5 6.2 2.82843 2.12805 0.016667 yes

Figure 7.8: Post hoc pairwise multiple

comparisons for reading corrected

data in Table 7.5

Interpretation

Looking at these pairwise comparisons, Group 3, Asian, is significantly different from
the other two groups, but there is no significant difference between Group 1 (middle-
class) and Group 2 (working-class).

Large sample Chi-square approximation for Kruskal-Wallis test

When the number of observations in the independent groups exceeds 5 then the test
statistic H is approximated by the Chi-square distribution with k−1 degrees of freedom (k
is the number of independent samples or groups). SAS output would be interpreted as in
the previous example.

Use of Kruskal-Wallis Test with Data from r×k Contingency Tables

Marascuilo and Dagenais (1982) describe the use of the Kruskal-Wallis H-test with
ordered categorical data that is typically presented in the form of a contingency table.
Data collected by these authors, originally as part of an evaluation study, is presented in
Table 7.6 in the form of a contingency table.

Table 7.6: Frequency distribution of responses to a

question about perceived success of an integration

programme for six ethnic groups*

Type of Student

Isolates Integrates

Response categories to question:

(^) Asian Black White Asian Black White
Definitely YES (1) (^0 512610)
YES (2) 11 32 (^2014776)
Too soon to tell (3) (^3 5103515)
Statistical analysis for education and psychology researchers 238