phonological decoding when processing unfamiliar written words. Phonological decoding
of unfamiliar written words is when a reader uses letter-sound mappings in order to create
a familiar phonological representation (word sound) which is recognizable.
A PhD researcher based part of her thesis on this work and in planning the study she
decided to use a two-group two-period cross-over design. One of the experimental tasks
is to ask a sample of 9-year-old poor readers to sort written sentences presented to them
as either correct or incorrect (meaningless). Treatment A will include twenty sentences in
which 10 have a word replaced by a homophone, for example, ‘She blue up the balloon’,
blue is the homophone. Treatment B will include twenty sentences in which 10 have a
word replaced by non-homophonic non-word, for example, ‘He tain the ball’, tain is the
non-word. Homophones and non-words will be equivalent in visual similarity and
pronounceability, and sentence length will be held constant across both sets of sentences.
The number of correct sentences will be counted after presentation of each treatment. The
cross-over design is illustrated in Figure 5.4.
Treatment Difference between treatment No difference between
ncorrect on A >n ncorrect on B >n n correct on A =n correct on B
A−B n 11 n 12 n 13
B−A n 21 n 22 n 23Figure 5.4: How to determine estimates of pie1 and
pie2 for a 2×2 cross-over design
From Figure 5.4 estimates of pie1 and pie2 can be derived as follows:
where n is the number of cases in that cell. Subjects with no difference between
treatments are excluded from subsequent sample size calculations.
Once pie1 and pie2 have been estimated, the sample size analysis proceeds as in the
comparison of independent proportions using the SAS programme POWER1 (see
Appendix A3, Figure 2). However, the estimated sample size will have to be increased by
a small factor, perhaps 5 per cent, to allow for those subjects who show no difference
(cells n 13 and n 23 ). Unfortunately, there is no rule of thumb inflation factor and either
previous studies should be consulted or a range of possible factors should be tried.
What sample size would be required to detect a significant difference in
proportions between treatment A (P=n 11 /(n 11 +n 12 ) and treatment B
(P=n 21 /(n 21 + n 22 ), given 80 per cent power and 5 per cent alpha?Typically estimates of pie1 and pie2 are unknown in 2×2 cross-over designs. The
researcher often has to complete a pilot study to determine these estimates for use in
subsequent power analysis calculations. In a small pilot study with 12 children in each
treatment sequence the following values were determined:
Choosing a statistical test 137