SYSTEMATIC SAMPLING
The "technique" of systematic sampling proposed by Abramson in his "Survey
Methods in Community Medicine" (page 59 of the second edition) is unsound. To
see this, consider taking a sample of size 7 from a population of size 52. According
to Abramsom the sampling ratio is 1 in 7.43 and this value is rounded off to the
nearest whole number 7 which is what he calls the sampling interval. He would then
make a random selection from the first 7 items in the list, and select every 7th
thereafter. Items 50 through 53 may, or may not be eligible for the sample. If the
first selected item is any of 1 through 4, then one of items 50 through 54 will also
be selected; if however the first selected item is one of 5, 6 or 7, the last four
members of the population can not be included. Thus this breaks the basic rule that
every member of the population shall have an equal chance of being included in the
sample.
The correct procedure is not to round off to the nearest whole number until the last
stage of the enumeration of the sampling, both in the sampling fraction and selection
of the first item decimal places should be retained.
Thus, in the sample above, n = 7.43. Adopt Abramson's sampling procedure from
Table 1 (page 65) we require a three digit-number in the range 001 to 743 (to be
divided by 100) starting in row 4. The second triplet is 162 and so the start point is
1.62. Then we add n (not k) to this start point to get seven numbers, as follows:
1.62, 9.05, 16.48, 23.91, 31.33, 38.76, and 46.19
Note that if we had continued the procedure we would have got the ineligible
number 53.62 which is, of course, 1.62 units beyond the end of the listed
population.
It is only now that we round to the nearest whole number to identify the items in
the sample, as follows:
2, 9, 16, 24, 31, 39, and 46.
FDKL
1983.01.13