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Proportional quota sampling
Article in The BMJ · September 2012
DOI: 10.1136/bmj.e6336
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Philip M. Sedgwick
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STATISTICAL QUESTION
Proportional quota sampling
Philip Sedgwick reader in medical statistics and medical education
Centre for Medical and Healthcare Education, St George’s, University of London, Tooting, London, UK
Researchers assessed the psychological and behavioural reactions of Londoners to the bombings in London on 7 July 2005. A cross sectional telephone survey that used random digit dialling of all London telephone numbers was conducted.
Respondents were asked to participate in an interview about current levels of stress and travel intentions. In total, 1010 participants completed the interview. Proportional quota sampling was used to recruit respondents, with quotas based on sex, age, working status, residential location, housing tenure, and ethnicity.1
The main outcome measures were presence of substantial stress and an intention to travel less on public transport once the transport network had returned to normal. The researchers reported that the bombings resulted in substantial stress among 31% of London’s population and altered travel intentions in 32%. Muslims had disproportionately greater levels of stress than respondents from other faiths.
Which of the following does proportional quota sampling represent?
a) Non-probability sampling.
b) Non-random sampling.
c) Probability sampling.
d) Random sampling.
Answers
Proportional quota sampling is a type of non-random sampling (answerb), sometimes referred to as a non-probability sampling method (answera).
Proportional quota sampling is often used in surveys and opinion polls, where the total number of people to be surveyed is typically decided in advance. In the above example, the researchers reported that they wished to interview a minimum of 1000 adults. It was imperative that the sample was representative of London with respect to its demographic distribution. Therefore, the sample was split between distinct subgroups or strata. The strata used were sex, age, working status, residential location, housing tenure, and ethnicity. Strata are combined in a hierarchical structure. Thus firstly the sample
was stratified, for example, by sex, then within sex by age, within age groups by employment status, and so on.
Members of the survey sample were selected in the same proportions as recorded for the population of London in a census prior to the survey according to sex, age band (18-24, 25-44, 45-64, or ≥65 years), working status (working or not), residential location (inner or outer London), housing tenure (house owner, or renting or other), and ethnicity (white or other). Once the numbers of survey respondents across the combined strata had been achieved in the same proportions as for the London population, then the predefined quota had been met and no more sampling was undertaken.
The researchers reported that approximately 10% of those people who were telephoned actually completed the interview. It is not uncommon for response rates to be low in a telephone survey that uses quota sampling, not least because of the need to fill specific quotas in combined strata.
There are two types of sampling method: random sampling, sometimes referred to as probability sampling; and non-random sampling, sometimes referred to as non-probability sampling.
Random sampling involves some form of random selection from the population members. Each population member has a known and typically equal probability of being selected. Simple random sampling (sometimes referred to simply as random sampling) is the most straightforward example of random sampling. A sampling frame is constructed—that is, a list of all people belonging to the population. Constructing a sampling frame requires knowledge of exactly who is in the population. A sample of a fixed size is selected at random from this list, with all members of the population having the same probability of being selected, independently of all others. The probability that a population member will be chosen is known in advance.
Samples resulting from simple random sampling will be representative of the study population as long as they are large enough. Other examples of probability sampling include cluster sampling, described in a previous question.2
Proportional quota sampling is a type of non-random (answer b) or non-probability (answera) sampling because there is an unknown probability of being selected for the sample. In the above example, random digit dialling was used to contact people
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living in London to assess their eligibility, and therefore all people living in London (providing that they had a telephone) had an equal probability of being contacted. The proportions of people living in London in each of the combined strata were known in advance because they could be estimated from the census prior to the survey. Therefore, before the survey began it was possible to calculate the probability that members of each combined stratum would be contacted. However, as interviewing began, the stratum characteristics of the next person to be rung were not known. As the quota for each combined stratus was filled, there was no way to establish whether the next person to be telephoned would be interviewed, because the quota of London residents with their stratum characteristics may already be filled. Equally, it is possible that more than one person with different characteristics could answer the telephone call.
Therefore, it was not possible to determine in advance the probability that the next population member to be contacted would be included in the sample. Therefore, proportional quota sampling is an example of non-random sampling. Other types of non-probability sampling include snowball sampling and convenience sampling, described in previous questions.2 3
In the above example, proportional quota sampling was used instead of a random sampling method, principally because it ensured that the resulting sample was representative of the population of London. If the researchers had surveyed 1000 people by using a random sampling method, there was no guarantee that the resulting sample would have been
representative of the London population in respects of sex, age, working status, residential location, housing tenure, and ethnicity. It is possible that some strata would have been over-represented or under-represented, in comparison with the population of London.
Competing interests: None declared.
1 Rubin GJ, Brewin CR, Greenberg N, Simpson J, Wessely S. Psychological and behavioural reactions to the bombings in London on 7 July 2005: cross sectional survey of a representative sample of Londoners.BMJ2005;331:606.
2 Sedgwick P. Sampling III.BMJ2010;340:c93.
3 Sedgwick P. Sampling I.BMJ2009;339:b5512.
Cite this as:BMJ2012;345:e6336
© BMJ Publishing Group Ltd 2012
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BMJ2012;345:e6336 doi: 10.1136/bmj.e6336 (Published 26 September 2012) Page 2 of 2
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