The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

2.3 Selecting Simple Random Samples 23

we pick at random between B, D, and F. The indices are chosen as
follows:

1 is B

2 is D

3 is F

To divide [0, 1) into three equal parts we get:

If 0.0000 ≤ U < 0.3333 then the index is 1.

If 0.3333 ≤ U < 0.6667 then the index is 2.

If 0.6667 ≤ U < 1.0000, then the index is 3.

The fi nal random number from the table is 68381. So U = 0.68381.
We see that 0.6667 ≤ U < 1.0000. So the index for the last patient
is 3, corresponding to patient F. The random sample of size 4 that we
chose is {A, C, E, F}. This approach seems a little more awkward, but
it does generate a simple random sample using only four random
numbers. Although it is awkward, it avoids enumerating all 15 combi-
nations and therefore remains a feasible approach as N and n get large.
A simpler approach that also generates a simple random sample is
the rejection method. In the rejection method, we do not repartition the
interval [0, 1) after choosing each patient. We stay with the original
partition. This saves some calculations, but could lead to a longer string
of numbers. We simply start with the approach that we previously used
in sampling without replacement, but since we do not change the parti-
tion or assignment of indices, it is now possible to repeat an index (for
bootstrap sampling, this will be perfectly fi ne). But since a simple
random sample cannot repeat an element (a patient in our hypothetical
example), we cannot include a repeat. So whenever a patient repeats,
we reject the duplicate sample and pick another random sample. This
continues until we have a complete sample of size n ( n = 4 in our
example).
Using the same table and running down the fi rst column, the
sequence of numbers is 00439, 29676, 69386, 68381, 69158, 00858,
and 86972. In the previous examples, we ran across the fi rst row and
then the second. In this case, we get a different sequence by going down