1. Stratified and Cluster Sampling Chapter 16

2. Stratified Sample SLIDE 16-1 A probability sample in which: The parent population is divided into mutually exclusive and exhaustive subsets A simple random sample of elements is chosen INDEPENDENTLY FROM each group or subject

3. Why used  Can produce sample statistics that are more precise or which have smaller sampling error  Allows the investigation of the characteristics of interest for particular subgroups since one can ensure adequate representation from each subgroup of interest Issues  What criteria should be used to stratify the population of interest?  How many strata should we have?  Should we use Proportionate stratified sampling, or Disproportionate stratified sampling Some Characteristics of Stratified Samples SLIDE 16-2

4. A decision as to the degree of confidence desired A point estimate of the population mean An estimate of the sampling error associated with this statistic How might you get each of these? Quantities Needed to Establish a Confidence Interval for a Population Mean With a Stratified Sample SLIDE 16-3

5. Example Calculations for Generating a Confidence Interval with a Stratified Sample SLIDE 16-4 III IIIIV n 1 = 100 x 1 =  X i1 = 3.2 n1n1 x 1 ) 2  (X i1 =.14 n1n1 s 1 2 = ^ n 3 = 100 x 3 =  X i3 = 5.8 n3n3 x 3 ) 2  (X i3 =.20 n3n3 s 3 2 = ^ n 4 = 100 x 4 =  X i4 = 7.2 n4n4 x 4 ) 2  (X i4 =.18 n4n4 s 4 2 = ^ n 2 = 100 x 2 =  X i2 = 4.6 n2n2 x 2 ) 2  (X i2 =.12 n2n2 s 2 2 = ^

6. Size of Strata in Parent Population SLIDE 16-5 N 1 = N 2 = N 3 = N 4 = N = 50000 x st = = 1/10(3.2) + 5/10(4.6) + 3/10(5.8) + 1/10(7.2) = 5.08 =.0226 NhxhNhxh N  L h=1 WhxhWhxh  L s x st =  L h=1 Whs2xhWhs2xh = NhNh N 2 (s h ) 2 nhnh ^  L h=1 2 s x st = I. II. III. IV. 5000 25000 15000 5000 () = (1/10) 2 (.14) + (5/10) 2 (.12) + (3/10) 2 (.20) 100 + (1/10) 2 (.18) =.000512 100

7. Cluster Sample SLIDE 16-6 A probability sample in which: The parent population is divided into mutually exclusive and exhaustive subsets A random sample OF subsets is chosen

8. Target Population of Companies in City SLIDE 16-7 Company Location of Company Allows Flexible Schedules ABCDEFGHIJKLMNOPQRSTABCDEFGHIJKLMNOPQRST U V W X Y Z AA BB CC DD EE FF GG HH II JJ KK LL MM NN Company Location of Company Allows Flexible Schedules West South East West North West South North East South West East North South North East West North South West East West South West East North West North South North East West North Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No

9. Statistical Efficiency SLIDE 16-8 A relative notion used to compare sampling plans. One sampling plan is more statistically efficient than another if, FOR THE SAME SIZE SAMPLE, it produces a smaller standard error of estimate.

10. Systematic Sample SLIDE 16-9 Procedure to draw: Determine the sample size n Determine the sampling fraction f = where n is the population size Determine the sampling interval i = 1/f Generate a random start between 1 and i using a random number table Use the randomly determined element and every i th element thereafter for the sample A form of cluster sampling in which every k th element in the population is designated for inclusion in the sample after a random start. nNnN

11. Area Sample SLIDE 16-10 A form of cluster sampling in which areas (for example, census tracks, blocks) serve as the primary sampling units. The population is divided into mutually exclusive and exhaustive areas using maps and a random sample of areas is selected. If: All the households in the selected areas are used in the study, it is one-stage area sampling If the areas themselves are sampled with respect to households, it is two-stage area sampling.

12. Suppose 5 blocks are to be selected and suppose a random number table indicates blocks 2, 8, 19, 31, and 39 are to be used If all of the households within these blocks are contacted, it is one-stage area sampling If a sample of households is selected from each of these blocks, it is two- stage area sampling 12345678 9 10 1112131415 16 17 18 192021222324 2526272829303132 3334353637383940 12345678 9 10 1112131415 16 17 18 192021222324 2526272829303132 3334353637383940 Illustration of Area Sample SLIDE 16-11

13. Simple  A certain proportion of second-stage units (e.g., households) is selected from each first- stage unit (e.g., block) Probability-proportional-to-size  A fixed number of second-stage units (e.g., households) is selected from each first-stage unit (e.g., block) but the probability of each first-stage unit being chosen is directly related to its size Types of Two-Stage Area Samples SLIDE 16-12