The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

24 CHAPTER 2 Sampling from Populations

the fi rst column. We did this to illustrate repeat values and how they
are handled in generating the sample.
Recall that when we subdivide the interval into six equal parts, we
get:

If 0.0000 ≤ U < 0.1667 then the index is 1.

If 0.1667 ≤ U < 0.3333 then the index is 2.

If 0.3333 ≤ U < 0.5000 then the index is 3.

If 0.5000 ≤ U < 0.6667 then the index is 4.

If 0.6667 ≤ U < 0.8333 then the index is 5.

If 0.8333 ≤ U < 1.0000 then the index is 6.

Also recall the correspondence of patients to indices:

1 is A

2 is B

3 is C

4 is D

5 is E

6 is F

So the random sequence generates A, B, E, E, E, A, F. Since we didn ’ t
get a repeat among the fi rst three patients, A, B, and E are accepted.
But the fourth random number repeats E, so we reject it and take the
fi fth random number. The fi fth number repeats E again so we reject it
and look at the sixth random number in the sequence. The sixth random
number chooses A, which is also a repeated patient, so we reject it and
go to the seventh random number. This number leads to the choice of
F, which is not a repeat so we accept it. We now have four different
patients in our sample so we stop.
The rejection method can also be shown mathematically to gener-
ate a simple random sample. So we had the advantage of only doing
one partitioning, but with it came the repeats and the need to sometimes
have to generate more than four random numbers. In theory, we could
get many repeats, but a long series of repeats is not likely. In this case,
we needed seven random numbers instead of just four. The rejection