SADC Course in Statistics

Samples and Populations

(Session 02)

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Learning Objectives

By the end of this session, you will be able to

• distinguish between a sample and a population

• distinguish between finite and infinite populations

• discuss the benefits and limitations of using a sample rather than a census

• explain what is meant by, and be able to take, a simple random sample

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Population• The population is the group of all entities

about which we want information, e.g.– All children below 16 years of age to assess

their nutritional levels– All farmers growing maize to learn about total

maize production in the country– All schools in a country to learn about

educational achievements

• Populations may be finite or infinite. • For statistical concepts discussed in this

module, we will assume infinite populations.

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Sample

• A sample is a subset of the population.

• It is chosen in an appropriate way so that it is representative of the characteristics of the population

• Procedures for choosing the sample are covered in Module H6

• In this module, we will assume simple random sampling (slide 9) so that concepts can be understood without real-life complexities

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Why do we sample?

• The whole population is rarely measurable

• An exception is the conduct of a census, e.g. population censuses are usually done once every 10 years

• A well-designed sample enables us to extrapolate our results to the population

• Statistical methods enable us to measure the reliability of our conclusions

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Sampling – the benefits• Cheaper, quicker and administratively easier

• Less prone to errors – and those that do occur are more easily identified

• A well-thought out sampling procedure can ensure proper coverage of major population characteristics

• If suitably structured, the sample survey can (i) take account of varying sizes of units, e.g. farms, and (ii) correct for under-enumeration and some sorts of non-response.

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Sampling – the limitations• Sound sample surveys require considerable

time and effort to plan and run. If tasks entailed and resources needed are under-estimated, the results will be poor

• Unless a pre-determined data analysis plan is in place at the start, data relevant to objectives may not be collected, or too much unnecessary data may be collected

• Training survey staff is crucial. Ill-phrased questions, poorly linked to objectives, can lead to non-informative and/or poor results

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A smallish exercise… In small groups, discuss, identify and write down thepopulation, and type of sampling unit needed, toestimate the

• proportion of rural people who are food insecure (<6 months food for family) in Zimbabwe

• average amount of land available for cultivation in Swaziland

• infant mortality rate, i.e. deaths <12 months of age per 1000 live births in Zambia

• total number of tobacco estates of <20 ha owned by small-holder farmers in Malawi

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Simple random sampling• Simplest form of sampling procedure

• Procedure aims to give each member in the population an equal chance of entering the sample

• Rarely done in real situations which are usually multi-stage. But some element of randomness is important at some stage.

• Often, final stage units are selected using simple random sampling

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How to do simple random sampling

• Allocate to each eligible member in the population, a number

• Pick numbers at random from a list of random numbers, discarding any that occur a second time

• Sample the required number of units without replacement

A demonstration will follow using a random numbertable, selecting 5 units from a list of 759 units…

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Random sampling using Excel

Using a list of districts in Uganda (in sheet named district in file H2_data.xls), you will be shown how a sample of 8 districts can be chosen at random from the list.

The menu sequence for this is:Tools, Data Analysis

The option to choose from the resulting dialogue is Sampling.

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References

De Veaux, R.D., Velleman, P.F. and Bock, D.E. (2006). Intro Stats. 2nd edn. Addison Wesley.

Owen, F. and Jones, R. (1990). Statistics. 3rd edn. Pitman Publishing, London, pp 480.

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Practical work follows to ensure learning objectives are

achieved…