It is possible to devise various alternative random sample designs. These alternative designs will vary in terms of precision achievable, convenience and cost. In the following subsections we discuss several basic designs. Sample designs for large surveys, e.g. national surveys may be more complex than any of these basic designs but will incorporate the same ideas: they may be made up of several stages and involve combinations of the strategies of the basic designs discussed here. The choice of sample design in a practical situation is a question
of choosing the design that gives maximum precision subject to the constraints of cost and resources (including the availability of a sampling frame).
In studying the alternative basic designs described below, you should ensure that you understand
(i) how to apply each of them
(ii) their relative advantages and disadvantages
11.2.7.1 Simple Random Sampling
Definition: Simple random sampling (s.r.s.) is a method of random selection where every
subset of the chosen sample size has the same chance of selection.
It can be proved that s.r.s. has the property that every member of the sampled population has the same chance of selection but this property is not unique to s.r.s. and therefore should not be used as a definition thereof.
The application of simple random sampling is very simple. We need a list of all members of the target population. This list is numbered serially (e.g. if the population consists of 10,000 individuals, we number them 00001, 00002, 00003 etc., up to 10,000). Suppose we need a sample of size 400. We select 400 random numbers (lying between 00001 and 10,000) from a table of random numbers using the method described in 11.2.5. above.
Simple random sampling is important for two main reasons: (i) it serves as a yardstick against which to compare other sample designs in terms of precision, convenience and cost. (ii) it is a component of other sample designs. This latter statement will become clear as we discuss these other designs.
This is not only inconvenient from the point of view of organisation of the field work; it is also costly as it inflates field costs, e.g. the travel costs of field staff if face to face interviewing is used.
S.r.s. gives more precision than cluster sampling but less than stratified sampling.
11.2.7.2 Systematic Sampling
Drawing numbers from a random number table, although more practical than picking out slips of paper from a basket can nevertheless prove tedious if the sample to be drawn is large. Given a sampling frame, it is possible to select a sample in a very practical way as follows:
Suppose we have a list of N people and it is desired to select a sample of n from it. Regard the N units as arranged in a circle. Let k be the nearest integer to N/n .We first select a random number between 1 and N. This identifies our first selection. We then select every kth individual after that first selection going round the circle until n units have been selected.
For example suppose we have a population of 2000 and we need a sample of 175. Then k=11. We select a random number (from a random number table) between 0001 and 2000. Suppose this number is 0379. Then the first selection into our sample is the 379th individual from the start of our (original) list. We then, referring to our imaginary circle, select every kth individual after that first selection going round the circle until 175 units have been selected.
If our list of individuals is not arranged in any particular order, then systematic sampling is almost (but not quite equivalent) to simple random sampling. The difference is that not all subsets are possible as in srs.(Think why). However, this is not a very serious drawback and the convenience of systematic sampling constitutes a great practical advantage.
If the list is arranged, say by age starting from the youngest, then the systematic sampling procedure spreads out the sample across age more evenly than simple random sampling would do normally. Systematic sampling in these conditions becomes almost equivalent to stratified sampling (discussed in the next subsection) with stratification according to age. The procedure, however, should be avoided if there are cyclical patterns in the list, as may happen
if there are several subgroups in the list with each subgroup ordered by age. The selections may then coincide with a particular age range thus biasing the sample.
11.2.7.3 Stratified Random Sampling
Stratified sampling consists of dividing the target population into sub groups called strata and taking a separate sample within each stratum. The sample within each stratum is usually drawn by simple random sampling.
Stratification i.e., the division of the target population into groups must be on a criterion or on criteria relevant to the survey topic. For example it is pointless to ensure representativeness in terms of religion if respondents’ answers are unlikely to be influenced by religion. But provided the stratification criterion or criteria are appropriate, the representativeness (on these criteria) achieved by stratified sampling produces greater precision than with simple random sampling. In practice this is reflected by smaller margins of error.
The data prerequisites for implementation of stratified sampling are however more demanding than for simple random sampling. We need not only a list of every member of the target population but also in respect of each such member we need information on the stratification criterion. For example, if we are stratifying by educational level, we need to know every individual’s educational level.
There are a number of options for allocating the total sample to the various strata i.e. how many to sample from each stratum. One simple option is to share the total sample among the various strata in proportion with their sizes (i.e. a stratum which has 40% of the population gets 40% of the sample, another which has 25% of the population gets 25% of the sample and so on). We refer to this as stratified sampling with proportionate allocation. This allocation has the advantage that it gives every member of the population the same chance of selection and hence eliminates the need for re weighting at the analysis stage.
possible that proportionate allocation will produce too small samples from such strata for meaningful comparisons.
11.2.7.4 Cluster Sampling
Sometimes populations occur or can be conveniently divided into groups or clusters. For example, school children are located in schools. Households in a country can be grouped into geographical clusters made of blocks of houses bounded by streets or natural boundaries. This fact provides an alternative random sampling strategy. This consists of drawing up a list of clusters that together comprise the whole population and then selecting a sample of clusters. This can be done by simple random sampling. We can then include in our sample all individuals in each selected cluster. This is referred to as sampling of whole clusters. It gives equal chance of selection to every member of the population.
The method of sampling just described has the great advantage that it does not require a list of all members of the target population. It only requires a list of the clusters and this is usually not hard to obtain. Furthermore, it concentrates the field work (think why and contrast with srs!) and this reduces field costs. However, if the clusters are of unequal size, the method provides no control over the overall sample size. Note that sample size has a direct bearing on costs. In addition, for the same size of sample, the precision with cluster sampling is less than with either srs or stratified sampling.
Instead of including every individual in the selected clusters into the sample it is possible to take only a sample from each selected cluster. This method is referred to as cluster sampling
with subsampling. Note that it requires lists of individuals but only for the selected clusters.
Various strategies are available for both the selection of clusters and the the selection of individuals within clusters.
Activity 1
Explain how you would select a random sample of students from the University of Mauritius for the purpose of eliciting their views on the University Library services
(a) by simple random sampling
(b) by stratified random sampling (choose appropriate stratification criteria and justify your choice)
(c) by cluster sampling (d) by systematic sampling