Statistical Analysis for Education and Psychology Researchers

Worked Example

A student’s PhD study was concerned with teacher-pupil communication skills and part
of the empirical investigation was based on Boser and Poppen’s (1978) study on student-
teacher relations. In a pilot study with ten pupils the researcher investigated pupils’
experiences of good and poor relationships with teachers. A videotape was produced and
shown to pupils to demonstrate five types of teacher behaviours, one of which was
sharing as originally described in Boser and Poppen’s study. Students were asked to
indicate, on a 5-point scale, how often a particular teacher with whom they had a poor
relationship had behaved in a manner similar to that demonstrated on the videotape
(example of sharing behaviour). Pupils also rated a teacher with whom they had good
relationships in a similar manner. In this study, a score of 5 indicates that the teacher
always behaves like this (reversed scoring to original Boser and Poppen study). Current
teachers were excluded from consideration. In this example, data or teachers sharing
behaviour is used, see Table 7.4:

Table 7.4: Teachers sharing behaviour in best and

poorest relationship situations

Subject Best Poorest |difference|* Rank difference

1 4 2 2 +5

2 3 1 2 +5

3 5 3 2 +5

4 2 2 0 −

5 3 1 2 +5

6 5 1 4 +8

7 1 1 0 −

8 4 3 1 +1.5

9 3 4 1 −1.5

10 4 2 2 +5

* Difference is (best-poor)

Observed test statistics T+=34.5; T−=1.5

The null hypothesis tested by the researcher was that teachers sharing behaviour is the
same in poorest and best relationship situations. The alternative hypothesis was non-
directional (two-tailed) and the selected alpha was 5 per cent.
The computational steps are:

1 For each pair of observations determine the absolute difference score |d|.
2 Rank these absolute differences (ignore sign of difference) and give the rank of 1 to the
smallest score. Should the absolute difference, |d| be zero that is no difference between
the original pair of observations, do not rank this difference score (drop it from the
analysis) and reduce the sample size accordingly. Should two or more difference
scores be tied, the rank assigned to each member of the tied group is the average of the
ranks which would have been assigned were the differences not equal.

Statistical analysis for education and psychology researchers 228