Statistical Analysis for Education and Psychology Researchers

results reported in Christensen and Cooper’s paper as an example, the reader might like
to consider answers to the following questions:

• Are two independent sample averages being compared?


• Has an element of randomization entered the design, random sampling or randomization
  to groups?


• Are the groups independent?


• Are the assumptions of homogeneity of variance reasonable?


• Are the data distributions skewed? When a standard deviation is greater than the mean,
  this suggests the distribution may be skewed.


• Is the chosen alpha level and statistical power reasonable?

If a high level of alpha is selected, for example, 1 per cent, this increases the likelihood of
a Type I error (conclude there are differences although no true differences really exist)
but decreases the likelihood of a Type II error. That is accepting the null hypothesis when
it is false. In this particular example this would mean concluding there are no differences
at pre-test when there are differences.
As an exercise evaluate the statistical power of the t-tests in Table 8.5. You should for
example, find that for the variable Retrieval with an alpha of 1 per cent, the power equals
81 per cent.

Worked Example

The following data, abstracted from a student’s dissertation study on children’s strategies
for subtraction, is used to illustrate computation of the t-statistic for independent samples.
Twenty subjects, ten aged 6-years and ten aged 7-years were given a series of test items
that required subtraction (when both numbers were less than 10, subtraction of a single
digit from a two-digit number and subtraction when both numbers were double digits).
Correct answers were totalled for each subject and the subtraction strategy noted. The
researcher predicted that there would be a difference in both correct scores and strategy
use between the two age groups. In this example subjects’ total correct scores are
analysed. Data for the 20 subjects is shown in Table 8.6. A non-directional alternative
hypothesis is specified and a 5 per cent alpha level is chosen.

Table 8.6: Subtraction score for thirty test items

(total subtractions correct) for 6- and 7year-old

pupils

Group 1 AGE 6 Group 2 AGE 7
OBS SCORE OBS SCORE
1 17 11 16
2 13 12 20
3 17 13 24
4 6 14 17
5 13 15 25
6 20 16 20
7 6 17 22

Statistical analysis for education and psychology researchers 298