Stratified and Cluster Sampling Chapter 16 Stratified Sample

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Stratified and Cluster Sampling Chapter 16

Stratified and Cluster Sampling Chapter 16

Stratified Sample A probability sample in which: • The parent population is divided into

Stratified Sample 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 SLIDE 16 -1

Some Characteristics of Stratified Samples • Why used ØCan produce sample statistics that are

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

Quantities Needed to Establish a Confidence Interval for a Population Mean With a Stratified

Quantities Needed to Establish a Confidence Interval for a Population Mean With a Stratified Sample • 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? SLIDE 16 -3

Example Calculations for Generating a Confidence Interval with a Stratified Sample I II n

Example Calculations for Generating a Confidence Interval with a Stratified Sample I II n 1 = 100 x 1 = ^s 12 = Xi 1 n 2 = 100 = 3. 2 x 2 = (Xi 1 x 1 )2 =. 14 n 1 -1 ^s 22 = n 1 III ^s 32 = n 2 = 4. 6 (Xi 2 x 2 )2 =. 12 n 2 -1 IV n 4 = 100 n 3 = 100 x 3 = Xi 2 = 5. 8 x 4 = Xi 4 = 7. 2 n 4 (Xi 3 x 3 )2 =. 20 n 3 -1 ^s 42 = (Xi 4 x 4 )2 =. 18 n 4 -1 Xi 3 n 3 SLIDE 16 -4

Size of Strata in Parent Population I. N 1 = 5000 II. N 2

Size of Strata in Parent Population I. N 1 = 5000 II. N 2 = 25000 III. N 3 = 15000 IV. N 4 = 5000 N = 50000 L xst h=1 = W h xh Nh xh h=1 L = N = 1/10(3. 2) + 5/10(4. 6) + 3/10(5. 8) + 1/10(7. 2) = 5. 08 L sx 2 st = h=1 Wh s 2 L xh = h=1 ( ) = (1/10)2 (. 14) + (5/10)2 (. 12) + (3/10)2 (. 20) 100 100 2 Nh ^ )2 (s h N nh + (1/10)2 (. 18) =. 000512 100 sxst =. 0226 SLIDE 16 -5

Cluster Sample A probability sample in which: • The parent population is divided into

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

Target Population of Companies in City Company A B C D E F G

Target Population of Companies in City Company A B C D E F G H I J K L M N O P Q R S T Location of Allows Flexible Company Schedules Yes West No South Yes East Yes West No North No West Yes South Yes North No East Yes South No West Yes East No North No South No North No East Company U V W X Y Z AA BB CC DD EE FF GG HH II JJ KK LL MM NN Location of Allows Flexible Company Schedules Yes West No North No South Yes West Yes East No West No South Yes West Yes East No North No West No North No South No North Yes East No West Yes West No North SLIDE 16 -7

Statistical Efficiency A relative notion used to compare sampling plans. One sampling plan is

Statistical Efficiency 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. SLIDE 16 -8

Systematic Sample A form of cluster sampling in which every kth element in the

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

Area Sample A form of cluster sampling in which areas (for example, census tracks,

Area Sample 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. SLIDE 16 -10

Illustration of Area Sample • Suppose 5 blocks are to be selected and suppose

Illustration of Area Sample • 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 twostage area sampling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 SLIDE 16 -11

Types of Two-Stage Area Samples • Simple Ø A certain proportion of second-stage units

Types of Two-Stage Area Samples • Simple Ø A certain proportion of second-stage units (e. g. , households) is selected from each firststage unit (e. g. , block) • Probability-proportional-to-size Ø 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 SLIDE 16 -12