Sampling strategies

ObjectivesAfter this session you will be able to:• Distinguish between probability and non-

probability approaches to sampling• Describe the implications of using non-probability

sampling for external validity• Select from a taxonomy of quantitative and

qualitative sampling schemes• Integrate quantitative and qualitative sampling

approaches into a mixed methods sampling design• Sample hard to reach populations• Know when to continue sampling and when to stop

Samples and populationsA population is any group that shares a common set of traits, e.g.:• All heart disease patients in a city• All hearing impaired pupils under the age of 15 in a region

• All female directors in FTSE 500 companies in a country

Using populations is usually too expensive and logistically impractical, so we use sampling

What is a sample?• A sample is selected on the basis that it is representative of the population

• Samples are selected from a sampling frame, a list of population elements, e.g. organisation human resource database, list of electors, etc.

Sampling frame

Sample

Population

Sampling: two very different approaches

Quantitative• Large samples• Probability sampling (random selection)

• Purpose: generalisation

Qualitative• Small samples• Non-probability sampling (purposive selection)

• Purpose: rich and deep levels of understanding

Simple random sampling:             •   •             •       • •                   •            •                                  •          •                   •                      •     •                                                                 •       •           •   •   • •      •         •                       •                                                                                  •                   •         •                      •                 •        •                                                                                                                        •                           •    •             •             •                •                             •    •                           •                  •   •                 •     •

Say we wanted to interview 40 pupils in a school of 400 pupils. In the grid, each square represents one of the pupils; each 25 square block, a class.Simple random selection (using random number generator) might yield the selection in the grid opposite.BUT note that the distribution is uneven.

Hence, to avoid this under-sampling and over-sampling, we might adopt:• Systematic sampling• Stratified random sampling

Systematic random sampling    •                 •              •                   •                •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •                  •                   •              

In systematic sampling every kth element of a sampling frame is chosen for the sample. So, if the intention was to select a sample of 40 from a list of 400, every 10th element would be chosen. K is called the sampling interval, with the first element being chosen randomly. So, if the first randomly selected number was 3, we would then take this and then the 13th unit from the list, then the 23rd, etc. until we have our 40 randomly selected elements from the list

Stratified random sampling

•                  •                 

                                   •            •       •   •         •          •             •                        •                     •         •                    •                    •           •                   •              • •             •                                        •       • •  •                       •                      •     •                 •                                  •         •    •     •           •             •    •                                                  •           •                                •                  •           •                     •          •   •                 • •       •                  •     •                •                                    

Sampling error is reduced by increasing the size of the sample and by increasing the homogeneity of elements within the sample. Stratified random sampling, then, consists of taking a random sample from various strata. Taking our school example again, each of the 16 classes in the school represents a stratum and we randomly select three pupils from each strata (class)

Cluster sampling                                                                                                                                                                                             • • • • •                              • • • • •                              • • • • •                              • • • • •                              • • • • •                                                            • • • • •                              • • • • •                              • • • • •                              • • • • •                              • • • • •          • • • • •                              • • • • •                              • • • • •                              • • • • •                              • • • • •                    

Cluster sampling acknowledges the difficulty in sampling a population as a whole, especially when convenient sampling frames are not available. For example, in an educational study, you might not be granted access to a college’s enrolment list. Instead, you could obtain a list of all the classes in the college and randomly select a percentage of them. You would use all the students from these classes as your sample (this is the cluster element of cluster sampling).

Non-probability sampling• Quota• Purposive• Convenience

Non-probability sampling: Quota

Seniormanagement

Middle management

Juniormanagement

STRATA

Quota sampling is similar to random stratified sampling in that both select units from the strata chosen. However, in the case of random stratified sampling this is done (as the name suggests) randomly. In quota sampling researchers use non-random sampling methods to gather data from a stratum until the required quota, fixed in advance by the researcher is fulfilled.

Respondent

Non-probability sampling: Purposive

Used when particular people, events or settings are chosen because they are known to provide important information that could not be gained from other sampling designs. The researcher exercises a degree of judgement about who will provide the best perspectives on the phenomenon of interest. Includes:• Typical case sampling• Extreme or deviant case sampling (outlier sampling)• Maximum variation sampling• Homogenous sampling• Stratified purposeful sampling• Random purposeful sampling• Snowball sampling

Non-probability sampling: Convenience

Involves gaining access to the most easily accessible subjects such as fellow students, neighbours or people responding to a newspaper or internet invitation to complete a survey. • Cheap and quick BUT• Low credibility

Mixed methods samplingDimension Mixed methods samplingOverall purpose of sampling

To generate a sample that will address all research questions

Intended outcomes For some strands/research questions intended outcome is: external validity; for other strands intended outcome is: transferability

Rationale for selecting cases/units

For some strands the focus is on representativeness; for other strands, the focus is on information-rich cases

Sample size For some stands there will be a large number of cases/units; for other strands, there may be one case or a few cases

Depth/breadth of information per case/unit

Focus on both breadth and depth of information across all research strands

When the sample is selected

For quantitative-type strands, the sample is selected prior to the study; for more qualitative strands, sampling can occur both before and during the study

Sampling frame Both formal and informal are usedForm of data generated Both numeric and narrative data are

generated

Sampling hard to reach populations

Include marginalised groups including homeless people, prostitutes, drug addicts and individuals who are incarcerated, institutionalised or cognitively impairedAccessed through:• Gatekeepers (institutions, agencies)• Snowball samplingNote ethical issues paramount in researching vulnerable or marginalised groups

Sampling: Top tip• Ensure that the sampling strategy adopted, including its limitations, is fully described in research proposals and the outputs emanating from the research. Be clear about whose perspectives may have been excluded from the research, based on the sampling decisions taken. Also include information on the barriers and problems encountered during sampling and how these were addressed.

Non-random sampling and external validity

External validity is the extent to which it is possible to generalize from the relationships found in the data within the sample’s subjects to a larger population or setting.

Selecting random samplesUse:• Random numbers table• Web-based random numbers generator

Calculating sample sizePopulation size

Sample sizeContinuous data (margin of error = .03)

Categorical data (margin of error = .05)

alpha = .10t = 1.65

alpha = .05t = 1.96

alpha = .01t = 2.58

alpha = .50t = 1.65

alpha = .50t = 1.96

alpha = .50t = 2.58

100 46 55 68 74 80 87200 59 75 102 116 132 154300 65 85 123 143 169 207400 69 92 137 162 196 250500 72 96 147 176 218 286600 73 100 155 187 235 316700 75 102 161 196 249 341800 76 104 166 203 260 363900 76 105 170 209 270 3821000 77 106 173 213 278 3991500 79 110 183 230 306 4612000 83 112 189 239 323 4994000 83 119 198 254 351 5706000 83 119 209 259 362 5988000 83 119 209 262 367 61310000 83 119 209 264 370 623

We can see that as the population increases, so does the required sample, but at a diminishing rate

Summary• In quantitative research sampling primarily involves the use of

probability sampling techniques which involve the selection of a relatively large number of units from the population

• Probability sampling includes random, stratified, cluster sampling and sampling using multiple probability techniques

• In qualitative research sampling primary involves non-probability samples, the aim of which is to select respondents and data that are likely to generate robust, rich and deep levels of understanding

• Non-probability sampling includes purposive, convenience and mixed-methods sampling approaches

• Hard to reach populations are often accessed using snowball sampling approaches often via gatekeepers such as institutions or agencies

• The limitations of the sampling strategy adopted should be acknowledged in research proposals and outputs emanating from the research, including whose perspectives may have been excluded from the research