Statistical Analysis for Education and Psychology Researchers

The first question relates to determination of power (set to −9 in the programme) given
an alpha of .001, a difference in means of 0.6 (10.3–9.7), and a sample size of 828. The
missing and problematic parameter is the standard deviation of the difference scores,

This is generally not available. Not all is lost, however, provided we make an
assumption of homogeneity of variance (here similar variance in pre-and post-

intervention measures, ), then the standard deviation of the difference
scores can be estimated if we have a measure of the correlation (or an estimate of this)
between the related measures (pre- and post-intervention scores).
Using the variance sum law, the variance of the difference of two variables is equal
to the sum of the two variances minus twice the correlation between the two variables
times the product of the two standard deviations.

In notational form this is

Assuming homogeneity of variance, then by rearrangement,

Standard

deviation

difference

scores—5.3

where ρ is the correlation between the two related measures. We also require an
estimate of the pooled standard deviation. For related measures the sample size in the two
groups is equal and therefore a simplified version of equation 5.2 (pooled standard
deviation for independent samples) is:

(^) Pooled
standard
deviation
—5.4
The pooled standard deviation is 4.06 ((4.08^2 +4.042^2 )/2)0.5. Note, a value raised to the
power 0.5 is equivalent to the square root of that value, for example, 40.5=2. Using
equation 5.1 to evaluate the standard deviation of the difference between pre-and post-
intervention measures of the teachers’ psychological distress variable,
To answer the first question, the values to enter into the SAS programme are, power
=−9, alpha=0.001, diff=0.6, sd=3.676 and n=828; to answer the second question the
values to enter into the programme are, power=0.80, alpha=0.05, diff=0.8 sd = 20.715
and n=−9. Relevant sections of the SAS programme POWER3 are shown in Figure 5.7
and the SAS output from this programme is shown in Figure 5.8.
data a;
Statistical analysis for education and psychology researchers 140