Overview of Sampling Methods II

1. Overview of Sampling Methods II (Session 04)

2. 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.

3. 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 )

4. 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)

5. 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.

6. 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

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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

14. Some practical work follows …