Statistical Analysis for Education and Psychology Researchers

magnitude of difference) would suggest a smaller sample size is required. The following
two lines of ‘data’ are entered in the programme POWER1:

0.80 0.05 0.06 0.12 -9

0.80 0.05 0.06 0.25 -9

Notice the first line of data input is the same as the previous example but in the second
line of data 0.25 represents the increased failure rate of 25 per cent. The output for these
sample size estimates is shown in Figure 5.3.
Comparison of Two Proportions (independent groups)

(^) Finding number of subjects (n)
Power alpha pie1 pie2 calculated of N (per group)
0.8 0.05 0.06 0.12 354
0.8 0.05 0.06 0.25 54

Figure 5.3: Sample size estimates for two different

proportions

From Figure 5.3 it is evident that to detect a larger difference in proportions requires a
considerably smaller sample size, given the same alpha and power.
The number of subjects in a design is related to the level of measurement and
summary statistics being used. In general, when data can be appropriately summarized by
means, (rather than binomial, percentage of ‘failures’ and ‘successes’) then smaller
samples are required.

Proportions in a Two-group Two-period Cross-over Design (Related

Measures)

In a two-group two-period cross-over design subjects receive both interventions, for
example, A and B in a randomized order. This is an appropriate design when the
intervention in the first period does not effect the intervention in the second period. In
many educational interventions a carry-over effect, learning, is precisely what is intended
and a cross-over design would therefore be unsuitable. However, in some psychological
experiments and clinical settings the cross-over design is desirable because it eliminates
subject variability and has the practical advantage of needing fewer subjects than a
comparable independent groups design. Paired difference between treatments for each
subject are calculated and the comparison of interest is either the average difference (the
mean of the difference scores for normal data) or a count of those subjects who have a
‘difference’ and those who have ‘no-difference’ between treatments (for count data).

Example 5.3: Estimating Sample Size for Difference in Proportions

with a Two-group Two-period Cross-over Design (Related Measures)

Johnston Rugg and Scott (1987) have demonstrated that poor readers tend to rely on

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