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Stratified Sampling

Stratified Sampling. Module 3 Session 6. Session Objectives. To introduce basic sampling concepts in stratified sampling Demonstrate how to select a random sample using stratified sampling design. Stratified sampling. Is yet another sampling design

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Stratified Sampling

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  1. Stratified Sampling Module 3 Session 6

  2. Session Objectives • To introduce basic sampling concepts in stratified sampling • Demonstrate how to select a random sample using stratified sampling design

  3. Stratified sampling • Is yet another sampling design • Divides the population into non overlapping and internally homogenous subpopulations e.g districts • Each subpopulation is called a stratum • List all the units in each subpopulation • Select a sample of the required size from each subpopulation using simple random sampling/systematic sampling

  4. Sample Selection Procedure • Divide the population into h strata • N=N1+N2+N3+…+Nh • Where N is the total population size • Nh is the size of the hth stratum • List all the units/elements in each stratum (subpopulation) • Take a random sample independently for each strata using simple random sampling and/or systematic sampling

  5. Advantages and Disadvantages of Stratification • Advantages: • In comparison to simple random sampling and other sampling designs, stratification can leads to a gain in precision • May be desired for administrative convenience • Increases representativeness of the sample to the population since the entire cross section of the population is included in the sample – each subpopulation is represented in the sample

  6. Advantages and Disadvantages of stratification • Stratification may be more effective if there are extreme values in the population which can be segregated into separate strata • Different sampling techniques may be used in each of the stratum. Which may be desirable especially if the strata correspond to different characteristics e.g. rural versus urban • Disadvantages • Costly because it requires selecting a sample from each subpopulation

  7. Stratified Sampling: Practical example Module 3 Session 6(b)

  8. Session Objectives revisited • To introduce basic sampling concepts in stratified sampling • Demonstrate how to select a random sample using stratified sampling design

  9. Practical Example • Suppose our interest is to estimate the average yield of maize per farmer and the total yield of maize in two sub counties. • The total population in the two sub counties consists of 611 farmers. • Suppose there were 305 farmers in sub county A and 306 farmers in sub county B

  10. Practical Example • And our interest is to select a sample of 28 farmers from the two sub counties using stratified sampling- taking the sub county as our stratification variable • How do we proceed? • It is easy!!!

  11. Sample Selection Procedure • Start by dividing/stratifying the population by sub county (sub county A and Sub county B) • List all the farmers in each sub county (construct a sampling frame) • In our case we shall list all the 305 farmers in sub county A from 001,002,…,305 • And also list all the 306 farmers from sub county B from 001, 002, …,306

  12. Sample Selection Procedure • Since were are required to select a sample of 28 farmers from the two sub counties • How do we decide on the number of farmers to select from each sub county? • It is easy!!! • One alternative is to select half of the sample from each sub county. • In other words choose a sample of 14 farmers from each sub county

  13. Sample Selection Procedure • The other method is to allocate the sample proportionately • In other words take a larger sample from the larger stratum and vice versa • This is called proportional allocation • In our example, it works out to the same thing, since we have an almost equal number of farmers in each sub county

  14. Sample Selection Procedure • There are 305 farmers in sub county A and 306 farmers in sub county B • So how do we select the 14 farmers from each sub county? • Using random numbers or any other random mechanism, select the sample of 14 farmers from each sub county independently using simple random sampling • Recall what we did under simple random sampling • We used random number tables to select the sample • You could as well use any other random mechanism e.g. computer random number

  15. The sample • Suppose the yields of maize reported by the 14 selected farmers in each sub county were as follows:

  16. Estimation of means • How do we estimate the means and totals? • This will be handled later.

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