Simple random sample
Definition taught in Studies, data, and evidence, part of Data analysis
Simple random sample
| Type | Definition |
| Taught in | Studies, data, and evidence |
| Part | Data analysis |
| Worked examples | 2 |
A simple random sample of size n from a finite population of size N is drawn without replacement so that every subset of n members is equally likely to be the sample. In particular, every member has the same probability n/N of being included.
Examples
Sampling ten villages
Worked example from Studies, data, and evidence
A population lives in 10 small villages: 5 eastern villages of 50 people and 5 western villages of 100 people, so N=750. A sample of n=100 is wanted.
Question. How would a stratified sample and a cluster sample be drawn?
Solution. Stratify by east and west, of sizes 250 and 500. The eastern share is 100\times250/750=33.3, so take a simple random sample of 33 eastern villagers and 67 western ones. That will almost certainly reach every village, which is fair and representative but means a lot of travel.
For a cluster sample, make each eastern village a cluster of 50, and split each western village into two clusters of 50, giving 15 clusters. Choosing 2 clusters at random and measuring everyone in them gives the 100 observations with at most two villages visited, but most of the variety between villages is never seen. A middle course chooses 4 clusters and takes a random half of each, 4\times25=100, at the cost of visiting up to four villages. Stratifying into east and west first and then clustering within each would guarantee both regions appear.
Randomising twenty people
Question page: Randomising twenty people
Twenty people are split at random into a test group and a control group of ten. How many different test groups are possible?
A test group is an unordered choice of 10 people from 20, so there are
\binom{20}{10}=\frac{20!}{10!\,10!}=184\,756
possible test groups. Randomisation picks one of them with equal probability, for example with sample(1:20, 10).
Used in
- Taught in Studies, data, and evidence, where the derivation and examples are.
- All 6 questions on Studies, data, and evidence
See also
Random sample · Stratified and cluster sampling · Observational study · Designed experiment · Randomised controlled trial · Confounding variable · Blinding and placebo