The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

2.3 Selecting Simple Random Samples 19

using a pseudo - random number generator on the index set for the

population.

2.3 SELECTING SIMPLE RANDOM SAMPLES

Simple random sampling can alternatively be defi ned as sampling at
random without replacement from the population. Going by our origi-
nal defi nition, a brute force way to generate a random sample would
be to enumerate and order all the possible samples from 1 to CnN and
randomly select an integer k , where 1 ≤≤kCnN.
To illustrate this method, we will look at a simple example where
N = 6 and n = 4. Then the number of possible samples is
C 46 ==×=642 65215!/[! !] /. Suppose these six elements represent
patients, and we denote them as the set {A, B, C, D, E, F}. Using this
notation, we can enumerate the 15 distinct samples any way we want
and assign integer indices from 1 to 15. A systematic enumeration
might look as follows:

1. {A, B, C, D}


2. {A, B, C, E}


3. {A, B, C, F}


4. {A, B, D, E}


5. {A, B, D, F}


6. {A, B, E, F}


7. {A, C, D, E}


8. {A, C, D, F}


9. {A, C, E, F}


10. {A, D, E, F}


11. {B, C, D, E}


12. {B, C, D, F}


13. {B, C, E, F}


14. {B, D, E, F}


15. {C, D, E, F}