Example 5.2: Estimating Sample Size for Difference in Proportions
(Independent)A review of the reading recovery (RR) programme literature suggests that between 5–7
per cent of children who enter RR programmes are not significantly helped (Clay, 1990).
The RR programme is an intervention programme designed for children who show
difficulties in reading and writing. Pupils are screened on six subtests, and those that
score in the bottom 20 per cent of their class are considered to be ‘poor’ readers and
eligible for entry into a RR programme. Programme success is defined as the percentage
of children who after 20 weeks individualized RR intervention are reading at ‘average’
levels for their class or school,
A study is planned to compare poor readers’ response to a reading programme
intervention in terms of ‘success’ or ‘failure’. A group of poor readers is to be randomly
allocated to one of two intervention programmes. One group will receive a ‘usual’
remedial help reading programme (comparison group) and the other group will receive
the RR programme. The anticipated percentage of children in the comparison
group who are expected to fail is 12 per cent and this is compared to an expected 6 per
cent of failures in the RR programme.
How many children will be required in each group (comparison group
and RR group) to detect a significant difference in the proportions of
‘failure’ of 0.06 (0.12–0.06) with a two-sided test, a Type I error (alpha)
of 0.05 per cent and 80 per cent power?Two-proportions independent-groups design
To estimate the number of children in each group, the SAS programme POWER1 is
used. The SAS programme calculates sample size and power for the difference between
two proportions with independent groups (see Appendix A3, Figure 2). The required
power is 0.80, alpha is 0.05, pie1 is the smaller proportion, 0.06 (RR proportion) and pie2
is the larger proportion 0.12 (usual remedial programme), the parameter to be estimated
is sample size and this is entered as −9. The output from this programme is shown in
Figure 5.2. From this it can be seen that 354 children per group would be required.
Comparison of Two Proportions (independent groups)
(^) Finding number of subjects (n)
Power alpha pie1 pie2 Calculated value of N (per group)
0.8 0.05 0.06 0.12 354
Figure 5.2: Output from SAS programme POWER1
The programme POWER1 allows a number of ‘what...if’ power and sample size
calculations to be performed. For example, an investigator may ask what would be the
required sample size if the anticipated percentage of failures in the remedial teaching
group increased from 12 per cent to25 per cent Intuitively a larger effect size (that is
Choosing a statistical test 135