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=N 1 +N 2 +N 3 +…+N h Where N is the total population size N h is the size of the h th 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
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.