n 11 =8 n 12 =3 n 13 =1
n 21 =4 n 22 =8 n 23 =0
then pie1=n 11 /(n 11 +n 12 )=0.727 and pie2=n 21 /(n 21 +n 22 )=0.333.When these values are entered into the SAS programme POWER1 the number of
subjects required per treatment sequence group is 22. If this value is inflated by 5 per
cent, i.e., 1 additional subject, then in total 46 subjects would be required.
Example 5.4: Estimating Power for Difference in Means
(Independent Groups)In the evaluation of a classroom management programme for use in teacher education,
Martin and Norwich (1991), report a significant difference, p<0.01 between a treatment
group and a control group of teachers with respect to effective classroom management.
The treatment group, n=12, mean score on a effective classroom management question
was 1.25 (sd=0.45) and the control group, n=12, comparable mean score was 1.92
(sd=1.17). The control group consisted of teachers who had not
received training with the classroom management programme but were similar in other
respects with the treatment group in terms of sex, location of school, class taught, and
length of teaching experience. While acknowledging a number of evaluation design
limitations, the authors claim that the study showed how research-based concepts and
principles of classroom management are amenable to translation into practice via a well
planned inservice programme.
What is the power of the significant difference in means between the
intervention and control groups reported by the authors?Difference between Two Means, Independent Groups
To estimate the statistical power of the reported difference in means the SAS
programme POWER2 is used, power and sample size for comparison of two means with
independent groups (see Appendix A3, Figure 3). From the author’s paper, the reported
alpha is 0.01, the difference in means is 0.67 (1.92−1.25), the pooled standard deviation
is 0.88. (using equation 5.2), and the sample size in each group is 12. The power is
estimated to be 24 per cent. The SAS output is shown in Figure 5.5. If sample sizes are
unequal the harmonic mean, n′, of n 1 and n 2 should be used. This is evaluated as 2(n 1
n 2 )/(n 1 +n 2 ). Alternatively, two power estimates can be determined, one for each n.
Comparison of Two Means (unpaired data)
(^) Finding the power
alpha diff sd n Calculated value of power
0.01 0.67 0.88 12 0.24
Figure 5.5: Output from SAS programme
POWER2: Estimated power for difference between
Statistical analysis for education and psychology researchers 138