Overview of Sampling Methods I

1. Overview of Sampling Methods I (Session 03)

2. Learning Objectives By the end of this session, you will be able to • describe what is meant by a simple random sample and a stratified random sample • discuss the benefits and limitations of simple random sampling • take a simple random sample using a table of random numbers • explain how strata may be chosen, why this is a useful consideration, and how a stratified sample may be taken

3. Introduction to “statistical sampling” • Underlying mathematics is mostly about estimation of one numerical quantity – a population characteristic. • Sample size formulae generally relate to this objective but are applicable only to very simple scenarios • Some ideas are more broadly useful than that… • In this session, we will discuss just two approaches to sampling…

4. 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

5. How do we take a simple random sample? • The procedure is to: • Allocate a number to each member in the sampling frame consisting of all eligible population members • Pick numbers at random from this list, discarding any that occur twice • Sample the required number of members without replacement

6. Using a random number table The handout accompanying this session explains the process involved in using a random number table. The process involved will be discussed in class with an example of selecting 6 units from a sampling frame of 743 members. You will then be asked, in discussion with your neighbour, to select a sample of 7 members assuming you have a sampling frame with 490 members.

7. Benefits of simple random sampling • At any sample size, sampling objectively should avoid biases of subjective methods (…but at smaller sample sizes there is always a chance of a disconcerting sample coming up) • Provides estimate of accuracy – e.g. the standard deviation of an estimate • Claim to “represent” the whole population holds if sample is of adequate size.

8. Some challenges to SRS • Often there is no adequate sampling frame • Generally have non-homogeneous population • Geographical spread means travel costs may be excessive • Not useful if information is needed at various levels, e.g. district based estimates as well as estimates for the country as a whole

9. Generalities about stratification • If sections of the population are known to be internally relatively homogeneous with respect to key feature observed – these are good strata • Sampling separately within each stratum gives relatively accurate information for less effort …

10. Two-stratum island • Separate small samples from wet- & dry-zones more effective than an uncontrolled mixture sample:- Wet   Dry

11. Stratified sampling • Segment entire population into subsets = strata. These should not overlap. Note: may be unclear which stratification is best. • Sampling within strata is generally done at random. • Effective if members of most strata are similar to each other in studied characteristics : even a small sample yields good understanding. • Post-stratification can also be useful

12. Ineffective stratification • e.g. if all villages contain a mixture of farmers, traders, artisans, and livelihoods differ mainly by occupation, then occupation is an effective stratification variable, while village is not. • The village becomes a miniature of the population itself if %’s in different occupations are about the same in all villages

13. How to select a random sample Discussion and demonstration using Excel

14. Some practical work follows …