Statistical Analysis for Education and Psychology Researchers

Test Assumptions

The test assumptions are:

• Data consists of more than two related samples.


• The response variable is measured at least at an ordinal level.


• The response variable has an underlying continuous distribution.

Statistical Inference and Null Hypothesis

The null-hypothesis tested is that the repeated measures (conditions) have been sampled
from a single population (or k-populations with the same medians), the alternative
hypothesis is that at least one of the conditions has a different median to the others. In
this situation the rank sum and the mean rank for each condition would vary.

Example from the Literature

In a study to test the hypothesis that measured level of success in the coordination of
spatial perspectives is related to the mode of response employed in their representation,
Robinson and Robinson (1983) tested twelve infants and twenty-four junior school
children (ages 5–6 years, 8–9 years and 10–11 years) on a repeated measures
representation task. Each child was presented with four tasks (modes of response
representation): matching; drawing; verbal; and making. In the matching condition a
child had to select an appropriate card from a set of eight picture cards. Each card
depicted a particular view and one matched the view of a model placed in front of the
child. In the drawing condition a child was asked to draw a particular view (that matched
the model), in the verbal condition the child was asked to describe a view and in the
making condition the child was invited to construct the particular view from cut-out and
coloured shaped cards. Binary scoring was used for each test (three tests for each
condition), a value of 1 was awarded for a correct response and 0 for an incorrect
response.
The investigators reported the average test scores for infants in each condition:
Matching 2.25; Drawing 0.42; Verbal 0.91; and Making 0.67. For infants, matching
seemed the easiest. To elucidate the descriptive findings the investigators carried out a
Friedman’s ANOVA on the rank score of performance across the four conditions
(repeated measurement factor). A significant difference among the four presentation
modes was reported. In this example the outcome variable is a count of correct responses
which can be ranked and the within-subjects factor is the four repeated measurements
corresponding to the experimental conditions of matching, drawing, verbal and making.
The investigators wanted to know whether the apparent differences in average
performance across the four tasks were large enough to indicate a statistically significant
difference in central tendency between the four modes of presentation (no specific alpha
level was mentioned). The keen reader should look carefully at the reported significance
levels in this paper.

Inferences involving rank data 241