Endgames Statistical Question

# Sampling II

BMJ 2010; 340 doi: http://dx.doi.org/10.1136/bmj.b5677 (Published 07 January 2010) Cite this as: BMJ 2010;340:b5677
1. Philip Sedgwick, senior lecturer in medical statistics
1. 1Centre for Medical and Healthcare Education, St George’s, University of London, Tooting, London SW17 0RE
1. p.sedgwick{at}sgul.ac.uk

Using a cross-sectional survey, researchers investigated the body weight patterns of adults living in Tirana City, Albania.1 To obtain a representative sample, the city was divided into 256 zones on the basis of map divisions, of which 58 were randomly selected. In each of the selected zones, 12 households with two or more inhabitants aged 25 years or over were randomly selected. Two adults from each household were invited to participate.

Which of the following terms best describes the sampling method used in the above study?

• a) Cluster sampling

• b) Multistage sampling

• c) Convenience sampling

• d) Proportional quota sampling

b—Multistage sampling entails several stages of random sampling based on the hierarchical structure of natural clusters of individuals within the population. Examples of natural clusters include towns and cities, schools, general practices, streets, and households. A different type of cluster is sampled at each stage, with the clusters nested within each other at successive stages. The final stage of sampling involves choosing a random sample of individuals in the clusters selected at the penultimate stage.

In the above study, a random sample of zones within Tirana City was obtained, followed by a random sample of households within each selected zone. The zones represent the first stage units and households the second stage units. Although the selection of individuals within each selected household was not random, it is reasonable to infer that individuals were the third stage units and that, overall, sampling was a three stage process in this case.

Multistage sampling is used if the population is geographically diverse, making simple random sampling impractical or too expensive. Simple random sampling was described in last week’s statistical question.2 It is not necessary to construct a sampling frame for the entire population in multistage sampling, only a list of the clusters sampled; therefore, resources may be concentrated in fewer places.

Answer a is false. Cluster sampling involves taking a random sample of natural clusters or groups of individuals from the population. All individuals in the selected clusters would then be sampled. Although in the above study the zones in the city were randomly selected, not all individuals within each zone were then sampled.

Answer c is false. Convenience sampling entails selecting individuals using a non-random approach. Individuals are sampled simply by the virtue that they are readily available and convenient to the researcher. Little attempt, if any, is made to ensure the sample is representative of the population. An example of convenience sampling would be consecutive patients in a clinic. In such a case, caution must be applied if generalising the results outside the clinic and to the wider population of patients with a similar condition. Convenience sampling was described in last week’s statistical question.2

Answer d is false. Proportional quota sampling is often used in opinion polls where the total number of people to be sampled is decided in advance. The sample is then split between a number of distinct subgroups, or strata, in proportions equalling that in the population. For example, a total sample size of 1000 might be required. If the population consisted of 40% women and 60% men, then sampling would continue until 400 women and 600 men were obtained and the overall sample quota met. Proportional quota sampling does not use random sampling because individuals are recruited consecutively. Other strata that quotas may be set to fill include age, working status, and ethnicity. Given that proportional quota sampling is not random, there is no guarantee that the opinions of the resulting sample will be representative of the population with respect to the topic under study. A similar method of sampling is non-proportionate quota sampling, where a fixed number of individuals per strata are sampled regardless of the proportion the strata constitute in the population.

## Notes

Cite this as: BMJ 2010;340:b5677

## Footnotes

• Competing interests: The author has completed the Unified Competing Interest form at www.icmje.org/coi_disclosure.pdf (available on request from the corresponding author) and declares (1) No financial support for the submitted work from anyone other than his employer; (2) No financial relationships with commercial entities that might have an interest in the submitted work; (3) No spouses, partners, or children with relationships with commercial entities that might have an interest in the submitted work; (4) No non-financial interests that may be relevant to the submitted work.

## References

View Abstract