Statistical Analysis for Education and Psychology Researchers

Worked Example

In a replication of Robinson and Robinson’s study (1983) a PhD research student wanted
to know whether there was a difference in successful task performance among four
presentation conditions: matching, drawing, verbal and making (repeated measures). Data
from a pilot study with 6 subjects aged 7 years is shown in Table 7.7.

Table 7.7: Task success (number correct) for four

representation conditions

Subject Matching Drawing Verbal Making

Score Rank Score Rank Score Rank Score Rank

1 5 3.5 1 2 0 1 5 3.5

2 5 4 3 3 2 2 1 1

3 3 3 2 2 4 4 0 1

4 5 4 1 1 2 2 4 3

5 5 4 0 1 3 3 1 2

6 4 4 2 2 0 1 3 3

Σ Ranks (R) 22.5 11 13 13.5

Σ Ranks squared (R)^2 506.25 121 169 182.25

In the pilot study each task had five conditions so the maximum possible score was 5,
a score of 1 was awarded for a correct response and 0 for an incorrect response. The
underlying rationale for the analysis is simply whether the number of correct responses is
higher or lower in comparing one condition with another. The least number of correct
responses receives a rank of 1 and the condition with the highest number of correct
responses receives a rank of 4 (ranked across the four conditions). Ties are assigned
average rank values (see section 7.4, Wilcoxon Mann-Whitney test for an explanation of
average ranks). Alpha was once again set to 5 per cent.
The null-hypothesis tested was that different modes of representation of spatial
perspectives do not effect measured levels of success on the tasks. The researcher should
note that what is actually tested by Friedman’s ANOVA procedure is that the distribution
of responses in each of the repeated measurement occasions come from the same
population, that is they have the same population median. The alternative hypothesis is
that at least one pair of repeated measurements (conditions) has a different central
tendency (median).
Computational steps:

1 For each subject the response variable (number correct) is ranked across the four
conditions. The smallest score is given a rank of 1.
2 The rank sum (R) and the rank sum squared (R^2 ) for each condition are evaluated.

3 Using the data presented in Table 7.7 the Friedman’s Test statistic, is calculated as
follows:

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