The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

2.3 Selecting Simple Random Samples 21

7. Then referring to the systematic list, we see that the index 7 corre-
   sponds to the sample {A, C, D, E}.
   Now this method is feasible when N and n are small like 6 and 4
   above, since the number of combinations is only 15. But as N and n
   get larger, the number of combinations gets out of hand very quickly.
   So a simpler alternative is to consider the sampling without replace-
   ment approach. In this approach, the individual patients get ordered.
   One ordering that we could have is as follows:

1 is A

2 is B

3 is C

4 is D

5 is E

6 is F

Now we divide [0, 1) into six equal intervals and assign the uniform
random number as follows:

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.

Example: From a table of uniform random numbers, suppose the fi rst
number to be 00439 for 0.00439, since 0.00439 is in the interval [0,
0.1667], we choose index 1 corresponding to patient A. Now A is taken
out so we rearrange the indexing.

1 is B

2 is C

3 is D