Statistical Analysis for Education and Psychology Researchers

similarly on spelling and reading, while the less skilled readers show a clear advantage of
spelling over reading.
Although not stated by the authors, this is likely to be a two-tailed test, the null
hypothesis being that there is no population difference in mean reading and spelling
scores. It is important not to set the alpha level after a test statistic has been evaluated and
it is presumed that the authors decided a priori on a 1 per cent level of significance.
Significant results of exploratory analyses, that is significance tests which were not
defined a priori with alpha levels and power considerations, should be interpreted
cautiously until other studies confirm similar findings. In the absence of any
distributional information about the sample distribution of difference scores the reader
should also assume that these are approximately normal. The reader should recall,
however, that percentages are often skewed and particular care is needed when checking
assumptions for the paired t-test that the difference in percentage correct scores is not
severely skewed.

Worked Example

In an example of the paired t-test we can consider data from a study on primary school
childrens referential communication skills, the study referred to in the worked example
(p. 264) on simple linear regression. Researchers were interested in the stability of one of
their measures, speaker scores, in particular. They wanted to know whether there was any
carry-over effect of testing (whether testing itself influenced scores on the referential
communication test). The data presented in Table 8.7 represents a few cases abstracted
from the test-retest analysis of the referential communication study which is intended to
show whether there is any change in speaker scores over a three-month period.

Table 8.7: Comparison of test-retest scores for

speaker (5-year-old pupils)

OBS (OCCASION 1) (OCCASION 2) DIFFERENCE (D)

1 14 17 3

2 26 13 − 13

3 37 17 − 20

4 0 6 6

5 13 13 0

6 0 20 20

7 0 6 6

8 5 19 14

9 0 12 12

10 0 9 9

Mean difference

Computation of the paired t-statistic involves three steps, 1) calculation of the mean
difference; 2) calculation of the standard deviation of the difference scores; and 3)
calculation of the standard error of the difference scores. The t-statistic is evaluated once

Inferences involving continuous data 305