Statistical Analysis for Education and Psychology Researchers

group where alcohol education was delivered in science vs. the other group where alcohol
education was not delivered in science lessons. A similar null hypothesis was tested
comparing pupils where alcohol education was delivered through PSE or not. Although
not specifically stated by the investigators, the alternative hypotheses appear to be non-
directional and therefore a two-tailed test is appropriate.
Each case was assigned a rank with the ranking done from the lowest upwards so that
the direction of difference can be determined by inspection of the mean ranks. The
investigators concluded that there was a significant difference in alcohol consumption
where it was delivered through science, the higher mean rank score indicates that
consumption is higher where alcohol education is delivered in science, U=320695,
p<0.0009.

Worked Example

Based on an investigation by Kyriacou (1992) into active learning in secondary school
mathematics, a research student designed her dissertation study to address, amongst other
issues, the following research question, ‘Is there any difference in the percentage of
active learning activities as a percentage of all mathematics learning activities.for upper
school classes and lower school classes?’
Data from this study is used to illustrate computational details of the Wilcoxon M-W
test. The investigator identified, based on classroom observation, interviews with
teachers, and exploratory group discussions, seven types of learning activity in
mathematics classes, four of which were regarded as active and three as traditional
learning. The second phase of the study sought the views of mathematics teachers
regarding the extent to which any of the four types of active learning occurred in
mathematics lessons in their school. Two independent samples of teachers were
approached, lower school maths teachers (first second and third years) and upper school
maths teachers (fourth and fifth year groups). Each teacher was asked to rate, on a scale
of 1 to 100, an indication of the expected frequency of the activity in 100 randomly
selected mathematics lessons in their school (either upper or lower school as appropriate).
This was recorded as the percentage of lessons that could be described as active learning.
The obtained results of the survey are shown in Table 7.3.

Table 7.3: Results of a survey of learning activities

in upper and lower school mathematics lessons

Maths teachers: per cent maths lessons active learning

Lower school (n 1 =10) 30 51 48 28 26 42 44 66 68 21

Upper school (n 2 =12) 30 31 54 32 34 38 40 52 65 30 40 39

The Wilcoxon M-W test is appropriate because the null hypothesis to be tested is:

H 0 : There is no difference in the distribution of active learning activities,

as a percentage of the total types of learning activities in maths lessons,

for upper-and lower-school teachers.

Inferences involving rank data 221