Dear Renee,
The effective sample size of 20 per cell is basically derived from the theory of
statistical estimation as follows.
The tax compliance costs incurred by business taxpayers are the sum of various
component costs. For illustration, consider the costs of accountants to business
taxpayers (X). To estimate the required size per cell we use the formula
n = (z/B)2
where
n = sample size
z = 1.64 for 90% confidence interval
 = population standard deviation of X
B = error bound = 20% of population mean of X
The following table is produced using the 1994-95 data based on a survey of 8,000
business taxpayers. Population mean and standard deviation are approximated by
sample mean and standard deviation. We disaggregate data by business size (small,
medium and large), legal form (sole trader, partnership, trust, super fund and
company) and industrial classification (13 categories). Choosing 15 cells (i.e, about
10% of the total number of active cells) at random we obtain:
Sigma
680
144
943
890
250
1699
943
890
1708
3786
3556
566
823
106
354
Mean
870
833
1925
1457
419
2175
1925
1457
2250
5667
6550
1100
1241
425
1250
Error bound
174
166.6
385
291.4
83.8
435
385
291.4
450
1133.4
1310
220
248.2
85
250
Sample size
41
2
16
25
24
41
16
25
39
30
20
18
30
4
5
The total sample size required is thus 336 for 15 cells or, on average, 22 observations
per cell. This supports our request for a total sample size of 8,000 for the new
survey. (This is based on 150 active cells and a response rate of 37.5%:
8,000 = 15020/37.5%)
It is also worthwhile to mention that we have attempted to improve the response rate
and quality of data by two mail reminders and post-survey structured telephone
interviews. However, our efforts in this area are hampered by the lack of data as the
ATO could not supply us with businesses’ phone numbers. Face to face contact is
obviously not a feasible alternative.