2Session ObjectivesTo introduce basic sampling concepts in stratified samplingDemonstrate how to select a random sample using stratified sampling design
3Stratified sampling Is yet another sampling design Divides the population into non overlapping and internally homogenous subpopulations e.g districtsEach subpopulation is called a stratumList all the units in each subpopulationSelect a sample of the required size from each subpopulation using simple random sampling/systematic sampling
4Sample Selection Procedure Divide the population into h strataN=N1+N2+N3+…+NhWhere N is the total population sizeNh is the size of the hth stratumList all the units/elements in each stratum (subpopulation)Take a random sample independently for each strata using simple random sampling and/or systematic sampling
5Advantages and Disadvantages of Stratification In comparison to simple random sampling and other sampling designs, stratification can leads to a gain in precisionMay be desired for administrative convenienceIncreases 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
6Advantages and Disadvantages of stratification Stratification may be more effective if there are extreme values in the population which can be segregated into separate strataDifferent 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 urbanDisadvantagesCostly because it requires selecting a sample from each subpopulation
7Stratified Sampling : Practical example Module 3Session 6(b)
8Session Objectives revisited To introduce basic sampling concepts in stratified samplingDemonstrate how to select a random sample using stratified sampling design
9Practical ExampleSuppose 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
10Practical ExampleAnd 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 variableHow do we proceed?It is easy!!!
11Sample 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,…,305And also list all the 306 farmers from sub county B from 001, 002, …,306
12Sample Selection Procedure Since were are required to select a sample of 28 farmers from the two sub countiesHow 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
13Sample Selection Procedure The other method is to allocate the sample proportionatelyIn other words take a larger sample from the larger stratum and vice versaThis is called proportional allocationIn our example, it works out to the same thing, since we have an almost equal number of farmers in each sub county
14Sample Selection Procedure There are 305 farmers in sub county A and 306 farmers in sub county BSo 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 samplingRecall what we did under simple random samplingWe used random number tables to select the sampleYou could as well use any other random mechanism e.g. computer random number
15The sampleSuppose the yields of maize reported by the 14 selected farmers in each sub county were as follows:
16Estimation of means How do we estimate the means and totals? This will be handled later.