SADC Course in Statistics General approaches to sample size determinations (Session 12)

SADC Course in Statistics

General approaches to sample size determinations

(Session 12)

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Learning ObjectivesBy the end of this session, you will be able to

• distinguish instances when a formula can, or cannot be used

• recognise the need to have a broader view when thinking about sample size issues

• appreciate the importance of paying attention to objectives, resources and data analysis when planning the size of a survey investigation

• list key considerations that are likely to enter decisions about sample size


Sample size issues in general

• It is common for survey planners to imagine there is always a formula to compute the correct sample size

• Usually however, no clear-cut method exists for producing an answer to the question “How large a sample do I need?”

• It depends on – the objectives– field data collection conditions – the planned analysis and its use– the likely behaviour of the results and – resource limitations.


When do the formulae apply

• Formulae apply only when estimation of a quantitative response is of interest.

• Formulae exist for fairly simple sampling procedures, e.g. simple random sampling, stratified random sampling.

• Typically, surveys will often be multi-stage and other considerations generally apply at the initial stages of sampling (see later).

• Formulae are likely to apply only at the final stage of sampling.


Difficulties with formulae• Knowledge of variability is needed to apply

any formula – usually this is unknown

• In a typical survey, there are many responses of interest – if formulae are applied (assuming variability known for each response), could select the largest sample size that the formulae reveal, but this may not be practically feasible

• Sometimes resources are limited and achieving this sample size is not possible.

So what can be done?


Two basic ideasAlthough statistical formulae have limited value in decisions concerning sample sizes, two basic ideas are still relevant.

(a) the larger the sample size, the more precise your results will be;

(b) the greater the variability in the population of the variable (qualitative or quantitative) of interest, the larger the sample size you need.


What results are expected?• Think through to how you might present

the survey results

• Often this is in the form of tabulations – so what sort of tables are needed?

• Draw up “dummy” tables and consider whether percentages are needed – if so, is the sample likely to be of adequate size to ensure results reported as percentages are meaningful?

• Allow for the possibility of non-response


What is known about the population?• Make use of information you have on the

population and use this in deciding on sample sizes at initial stages of a cluster or multi-stage sampling procedure.

• If results are required for different sub-groups of the population, then consider separately what sample sizes are required within each stratum.

• Build up a sampling frame at each of the stages and consider most appropriate sample size while thinking of resources.


Other issues with several stages

• How many stages should be used? Often related to administrative groupings.

• Should the same number of units be selected from each cluster, or more from the larger ones?

• Actual number of units will often be decided in accordance with resources.

• Sample size of final stage units will often be determined by amount of work that one enumerator can cope with.


Attention to objectives & resources• Think through to how you might present

the survey results

• Often this is in the form of tabulations – so what sort of tables are needed?

• Draw up “dummy” tables and consider whether percentages are needed – if so, is the sample likely to be of adequate size to ensure results reported as percentages are meaningful?

• Allow for the possibility of non-response


Questions to ask yourself• What is the minimum sample size that

would make my results believable while achieving the objectives?

• Is the sample size achievable with the available time frame and personnel to do the field work?

• Should I be less ambitious about the target population I can cover?

• Can I get worthwhile results which are of good quality?


Re-visiting objectives• Compromises may be necessary in terms of

objectives

• The objectives should point towards the target population of interest – this may need re-defining

• Don’t do the survey unless it will give useful and defensible results

• Don’t leave room for criticisms because of small sample sizes or poor quality data.

• Give adequate attention to sample size issues during the planning stage, and document carefully the procedures involved.


Practical work follows…

SADC Course in Statistics General approaches to sample size determinations (Session 12)

Documents

sample size slide

sample size issues

sample likely

sample size achievable

appropriate sample size

largest sample size

correct sample size

minimum sample size