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SADC Course in Statistics

Overview of Sampling Methods II

(Session 04)

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Learning ObjectivesBy the end of this session, you will be able to

• describe accessibility sampling, quota samples, purposive sampling

• explain what is meant by a systematic sample, cluster sample, a multistage sample

• take a sample according to one of the above sampling schemes

• explain the difference between probability and non-probability samples.


• Accessibility sampling – sample only the most convenient sampling units – sometimes called convenience sampling (not advised)

• Purposive sampling – sampling a given number of ‘typical’ or ‘representative’ sampling units

• Quota sampling - a particular form of purposing sampling where choice of actual sample is left to the enumerator’s discretion– enumerator asked to fill a pre-specified quota (a

fixed sample size for each sample segment )

Pre-statistical sampling


Difficulties with above schemes

• Accessibility samples will usually be highly biased – not an advisable approach

• Purposive sampling often done at initial stages of sampling to ensure good coverage – with good reason sometimes – more on this later

• Quota sampling (often done in opinion polls, market surveys, etc) has the advantage of being cheap and quick and not requiring the existence of a sampling frame. However, it can lead to an very biased sample if interviewer convenience has a big effect (often NOT the case for telephone polling)


Probability sampling• These are samples where every individual

in the population has a known non-zero probability of entering the sample.

• Such schemes allow the sampling error to be quantified and the chance of bias reduced.

• Simple and stratified random sampling discussed in the previous session are examples of probability based sampling procedures – others outlined below.

• In practice, partial deviations from prob-ability sampling occur with good reason.


Systematic samplingThis method requires a well-established sampling frame, i.e. list of all population members.

The procedure involves selecting one element at random from the first k elements in the list, then selecting every kth unit thereafter, progressing through the list in a systematic way.

This leads to approximately (1/k)*100% of the population entering the sample


Remarks about systematic sampling

• The process is simple, and is useful where a list of units already exists, e.g. telephone directory, list of customers in a bank

• It can also be useful in studies requiring a good geographical spread, by imposing a grid on a map of the region.

• It assumes that the original list from which the sample is drawn is itself organised in a “random” manner which is independent of the key variables of interest in the study.


Limitations of systematic sampling

• The assumption that the original list is random may not be true.

• The theory is less well developed. Hence analysis of the data relies on assuming that the sample is like a simple random sample.

• Requires the availability of a good sampling frame and knowledge of the size of the target population.


Cluster sampling

• Taking a simple random sample can be administratively difficult.

• More convenient to divide the population into non-overlapping groups (clusters)

• Then sample a few clusters at random

• Then enumerate all members in the chosen clusters

This process is referred to as cluster sampling.More discussion on this will follow in sessions13 and 14.


Cluster sampling – further notes

• In the initial division of the population, aim to make each cluster as heterogeneous as possible.

• The sampling frame is required only for the chosen clusters, so useful when a sampling frame does not exist for the whole population

• The division of the population into clusters is different from that used in identifying strata. Here, the aim is to have high within- cluster variation.


Multi-stage sampling• Consider again the population divided into a

number of clusters.

• But now, instead of including all units in the cluster, take a random sample of units within each cluster.

• Above would be called a two-stage sampling design

• This may be extended to more than two-stages– e.g. may select districts, then enumerations

areas within districts, then household within enumeration areas, to give a 3-stage design.


Multi-stage sampling• Most large-scale surveys are conducted

using a multi-stage sampling procedure.

• Can be used in combination with stratification, e.g. – first divide population into strata– continue the sampling within each

stratum according to a multi-stage sampling procedure

• There will be more discussion concerning multi-stage sampling procedures in sessions 13 and 14.


References

• Moser, C.A. and Kalton, G. (1971) Survey Methods in Social Investigations. Gower Publishing Company Limited.

• Scheaffer, R.L., Mendenhall, W., Ott, L. (1990) Elementary survey sampling, (4th Edition). PWS-Kent Publishing Company, pp. 390.

• Woodward, M. and Francis, L.M.A. (1988) Statistics for Health Management and Research (see Chapter 10 for an overview). Edward Arnold, London. ISBN 0-340-42009-X


Some practical work follows …