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**Overview of Sampling Methods II**

SADC Course in Statistics Overview of Sampling Methods II (Session 04)

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**Learning Objectives By 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.

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**Pre-statistical sampling**

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 )

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**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)

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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.

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Systematic sampling This 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

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**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.

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**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.

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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 sessions 13 and 14.

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**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.

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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.

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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.

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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 X

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**Some practical work follows …**

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