means (independent groups)
We can use the same SAS programme to determine the required sample size to
achieve 80 per cent power, other parameters remaining the same. The number of subjects
required in each group is 41 (see Figure 5.6)
Comparison of Tow Means (unpaired data)
(^) Finding number of subjects (n) per group
power alpha diff sd calculated value of n per group
0.8 0.01 0.67 0.88 41
Figure 5.6: Output from SAS programme
POWER2: Estimated sample size for power set to
80 per cent
Example 5.5: Estimating Sample Size for Difference in Means
(Related Groups)In a paper by Hart, Wearing, and Conn (1995) which reported on the evaluation studies
that were conducted as part of a programme on a Whole School Approach to
Discipline and Student Welfare (WSADSW-Statewide Australian Programme), changes
in teachers’ stress, discipline skills and aspects of school organizational climate were
analyzed. Data abstracted from the paper include:
Variable n rBefore WSADSW After WSADSWp-values paired
M† SD M SD t-test
Teachers’ Psychological Distress 828 .59 10.3 4.08 9.7 4.04 <.001
Student Misbehaviour 812 .37 24.7 19.55 23.9 17.29 >.10
r is a Pearson correlation coefficient; † M represents the mean.
A five-point rating scale, the General Strain Index, was used to assess teachers’
psychological distress. Student Misbehaviour was measured using a single self-report
scale. Teachers’ rated on a 100-point scale their perceptions, related to one class, of the
amount of time they spent dealing with student misbehaviour in that class.
What is the power of these t-tests used to detect the change in teachers
psychological distress following the programme? What minimum sample
size would be required to detect a change of 0.8 (24.7–23.9) in teachers’
perceptions of student misbehaviour, assuming 80 per cent power, and 5
per cent alpha (two-sided test)?Differences between Two Means, Related Samples (Groups)
To answer these questions the SAS programme POWER3 is used (see Appendix A3,
Figure 4). Five parameters are required, power, alpha level, difference to be detected,
standard deviation of the difference scores and sample size.
Choosing a statistical test 139