Statistical Analysis for Education and Psychology Researchers

there were four groups of parents, but the data presented in Table 7.5 refers to only three
groups, middle-class, working-class and Asian families, and one ordinal response
variable, number of rapid reading corrections.

Table 7.5: Rapid correction reading correction

scores for three groups of families

Subjects Middle-class Working-class Asian

value rank value rank value rank

1 22 10.5 31 15 13 2

2 26 12 30 14 16 3

3 27 13 21 8 21 8

4 22 10.5 17 4.5 17 4.5

5 18 6 21 8 12 1

Sum of ranks 52 49.5 18.5

Mean of ranks^ 10.4 9.9 3.7

The null hypothesis is that there is no difference among the three groups of middle-class,
working-class and Asian families in the way that they correct reading errors using rapid
correction. The alternative hypothesis is that the three groups differ in the way they use
the rapid correction strategy to correct childrens’ reading errors. Alpha is set to 5 per
cent.
The computational steps are:

• Combine all scores into one group and assign a rank to each score representing its
  position in the single series.


• Each ranked value is then reassigned to its respective group (in this example middle-
  class, working-class or Asian) and the sum of rank values and the mean is calculated
  for each group. In this example sample numbers in each group are equal but this is not
  necessary.

The Kruskal-Wallis test statistic, H, is then calculated using the following formula:

Kruskal-

Wallis H-

test

statistic—

7.4

where k refers to the number of groups (independent samples), nj is the number of
observations in the jth group, N is the total number of observations in the combined

sample, and is the mean of the ranks in the jth group,

Statistical analysis for education and psychology researchers 234