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Methodology Glossary Tier 2 Sampling Tier 1 showed that sampling is extremely useful when you want to find out information about a large group of people but do not have time/resources to speak to each person individually. We will now look at some sampling techniques in more detail. Simple Random Sampling Theoretically, simple random sampling is the ideal method to use as it gives an equal probability of being selected to every unit in the population. Obtaining a simple random sample is relatively straightforward. A unique number is assigned to each unit and a random number generator is then used to choose which data will be included in the sample. For example, assume a researcher has 10 individual measurements for height. The researcher wishes to choose 5 for his experiment so he assigns them all a number from 1 – 10, with each measurement having a 10% chance of being included in the sample. Person A B C D E F G H I J Height(cm) 175 165 150 178 173 155 169 180 153 172 Number 0 1 2 3 4 5 6 7 8 9 Computer programs such as Excel can generate a list of random numbers e.g. 5,9,6,4,1,2,3,5,7,8,6,4,0. This means that person F will be chosen first, followed by Persons J, G, E and B. In practice, however, simple random sampling can be time-consuming and may not return a sample which contains the specific members of interest, therefore other methods are often used. Stratified Random Sampling It is common for people who are conducting statistical analysis to want to obtain information about key subsections of a population. Stratified random sampling is a technique which involves dividing a population or sampling frame into several, non-overlapping ‘strata’ (subgroups) according to a particular characteristic which reflects the variables of interest. Once the population or sampling frame is divided appropriately, simple random samples would then be selected from within each stratum. This is more preferable than simple random sampling when selecting samples for strata. Examples of usual stratification characteristics are age-group, gender, income bracket and ethnic origin. For instance, one may be particularly interested in survey responses by the ages of the respondents. If simple random sampling was used to select the sample, it would be possible that one/some groups may be over-represented and one/some may be under-represented. To ensure that adequate numbers Methodology Glossary Tier 2 of people from each age group are included in the sample, it would be necessary to conduct stratified sampling, with each age-group forming one stratum. The advantages of stratified random sampling are that it ensures better, more representative coverage of the population of interest and enables the important subgroups to be properly accounted for. Stratification will allow greater precision than simple random sampling so long as (i) members of the same stratum are as similar as possible to one another in relation to the stratification characteristic; and (ii) the differences between each separate stratum are as big as possible. This technique can also make the sampling strategy more efficient. Without stratification it may be necessary, and therefore more costly, to have a very large sample in order to ensure that each subgroup of the population is included in the analysis. By stratifying and ensuring that each group will have sufficient representation in the sample, it is possible to achieve more precise and reliable results. However, a disadvantage of stratified random sampling is that it can take longer to prepare and develop samples, due to difficulties in identifying appropriate strata and the analysis can be quite complex. Furthermore, a good knowledge of the population is required. Proportionate Allocation Normally sample sizes are proportionate to the size of the stratum which means that each stratum has the same sampling fraction. The proportionate allocation method of stratification is used to ensure that sample sizes for strata are of their expected size in relation to the population. Example A company employs 180 people and wishes to conduct an employee satisfaction survey on a sample of 40. The company is made up of staff as shown in the table below. Type of Staff Number of Staff male, full time 90 male, part time 18 female, full time 9 female, part time 63 It would make sense for the company to select a stratified random sample to ensure that they are able to capture members of staff from each of the distinct subgroups. To do this, they first need to establish the percentage of staff who are in each stratum. The table below shows that 50% of the company’s staff are male and full time. This means that in the sample of 40 employees, 20 respondents (50%) should be full time males. Similarly, the Methodology Glossary Tier 2 sample should contain 4 part time males (10%), 2 full time females (5%) and 14 part time females (35%). No. Staff % of Total No. Staff No. in Sample Male, full time 90 50 20 Male, part time 18 10 4 Female, full time 9 5 2 Female, part time 63 35 14 Total 180 100 40 The sampling frame in this example was the same for each of the strata – the sample sizes for each stratum were of their expected size in relation to the population. The sampling frame is calculated by dividing the number of people from each stratum in the sample by the total number of people in that stratum. Calculation Sampling Fraction male, full time 20/90 0.22 male, part time 4/18 0.22 female, full time 2/9 0.22 female, part time 14/63 0.22 Disproportionate Allocation With disproportionate stratification, the sampling fraction will vary from one stratum to another. This method is often used in cases when there is one (or more) minority group(s) within the population which are likely to be particularly under-represented or omitted from a simple random sample, unless specific attention is paid to them. It therefore gives larger than proportionate sample sizes for one or more strata to ensure that separate analyses by sub-group will be possible Example Suppose a local magazine has 2000 readers, of whom 100 are female and 1900 are male, and that it wishes to survey a sample of these. If we were to select a simple random sample of 100 readers we would expect by chance alone to get 5 females and 95 males. In order that both groups of readers be represented within our sample we may decide to split the membership list into two strata (male and female) and select separate samples per strata. It is decided to sample 50 male readers and 50 female readers. This means that the sampling fraction to be applied to the male stratum would be 1 in 38 (50/1900) and the sampling fraction to be applied to the female stratum would be 1 in 2 (50/100). Clearly, each stratum contains a different sampling fraction – they are disproportionate. By adopting this approach we have ensured that the minority group (females) have been more fully represented in the sample survey than they otherwise would have been. Methodology Glossary Tier 2 In order to ensure that inferences made from the survey are representative of the whole population, it is necessary for the survey estimates to be weighted. Calculating sample weights is quite straightforward – the sample weight is simply the inverse of the sampling fraction that was applied to the stratum. So for the ‘male’ stratum, where the sampling fraction was 1 in 38, all males would be given a weight of 38. Similarly, for the ‘female’ stratum, where the sampling fraction was 1 in 2, all females would be given a weight of 2. This ensures that any analysis carried out using survey estimates is representative of the entire population. Further information about weighting can be found at: http://www2.napier.ac.uk/depts/fhls/peas/theoryweighting.asp. Cluster Sampling The main reason for the development of the cluster sampling technique was to increase the efficiency of survey administration by reducing things like cost and travel time. A sample derived through simple random sampling can result in sample units which are widely dispersed geographically, meaning that interviewers must travel great distances to conduct a survey. This means that expensive travel costs are incurred and it will take longer to complete all the interviews required. Cluster sampling involves splitting the population of interest into clusters. These could be geographical areas (eg. towns, postcode sectors or local authorities) or they could be natural clusters (eg. industries, schools or hospitals). After the population is divided, several clusters are chosen at random to form the sampling frame. Ideally, the chosen clusters should be dissimilar from one another to ensure that the sample is as representative of the population as possible. Clusters provide a more localised way of conducting the survey and, whilst some may be in different geographical locations, there will be less widespread dispersion and it would be possible to assign one interviewer to each cluster. Two forms of cluster sampling are described below: One-stage Cluster Sampling This involves splitting the population into suitable clusters, then randomly selecting (via simple random sampling) a proportion of those to be included for further analysis. All units contained within the sample clusters would then be chosen to participate in the survey. For example, the Scottish Government wishes to find out information about the diets of primary one pupils. Clearly we must create a sample, as it would be expensive and time consuming to survey all primary one pupils in Scotland. We may decide that each school in Scotland represents one cluster and then select a random sample of 30 schools. In one-stage cluster sampling, we would now visit each of the 30 schools (clusters) and interview all of the primary one pupils in each. Methodology Glossary Tier 2 Two-stage cluster sampling This involves splitting the population into suitable clusters and, once more, selecting a proportion of those to be included for further analysis. However, in this method, the units within each sample cluster would be subject to a further round of simple random sampling so that only a proportion of units in each cluster would actually be surveyed. For example, the Government now wishes to find out information on the sleep patterns of all primary school pupils which will require one to one interviews with school pupils and their parents/guardians. Obviously it is not feasible to survey pupils in all schools or even to study all the students in a sample of schools. Instead, we would select a sample of clusters and then select a random sample of pupils from those schools to participate in the study. In all cases, we expect the sampled units to represent the population as a whole whether the method used is one-stage or two-stage cluster sampling. We have established that the main and overriding advantage of using cluster sampling is that it saves travel time and reduces costs. However, there are a number of disadvantages which mean that this technique should be approached with a degree of caution. For example, units which are quite close (geographically) to one another may be relatively similar and therefore less likely to represent the wider population. Furthermore, cluster sampling is generally less precise than simple/stratified random sampling and produces a larger standard error than these methods. Despite its disadvantages, clustering usually enables the selection of larger samples than simple/stratified random sampling. Consequently, if it is possible to target a large enough sample that offsets the loss of precision, then cluster sampling may be the most appropriate choice of sampling method. The selection process effectively comes down to a trade off between two factors – precision and cost. If you require a very accurate and precise sample, then simple/stratified random sampling is more appropriate whereas, if cost and time are the more important factors in your considerations, then cluster sampling is likely to be more suitable, so long as the sample is large enough to offset the loss of precision. Note: The difference between Strata and Clusters All strata are represented in a sample but only a subset of clusters are included. With stratified sampling, the best survey results occur when units within strata are internally homogeneous (i.e. members of one strata are similar to one another). However, with cluster sampling, the best results occur when units within clusters are internally heterogeneous (i.e. members of a cluster are dissimilar). Further Information Tier 1 Sampling | Social Survey Design

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