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2 DRAWING SIMPLE RANDOM SAMPLING 1.Use random # table 2.Assign each element a # 3.Use random # table to select elements in a sample.

3 STRATIFIED SAMPLING 1.The parent population is divided into mutually exclusive and exhaustive subsets. 2.A simple random sample of elements is chosen independently from each group or subset.  Each subset is called a stratum or subpopulation  Why stratify? -To reduce sampling error -To allow investigation of particular subgroups (guarantees representation of very small subgroups)  Consideration of stratification -Establishing the correct bases for stratification. Try to partition the population according to one or more criteria that are expected to be related to the characteristic of interest. -Determining the number of strata. -look at variances in each subgroup -Proportionate v.s. Disproportionate Stratified Sample

4 A Stratified sample in which the number of observations in the total sample is allocated among the strata in proportion to the relative number of elements in each stratum in the population. PROPORTIONATE STRATIFIED SAMPLE A stratified sample in which the individual strata or subsets are sampled in relation to both their size and their variability; strata exhibiting more variability are sampled more than proportionately to their relative size, while those that are very homogenous are sampled less than proportionately. DISPROPORTIONATE STRATIFIED SAMPLE

5 CLUSTER SAMPLING  Statistical efficiency v.s. Economical efficiency Statistical efficiency- Standard error w.r.t. sample size Economical efficiency - cost / observation Cluster usually often more overall efficient than stratified 3.If use all elements in subsets chosen - one stage If probabilistically choose only certain elements in the chosen subsets - two stage 2.A random sample of the subsets is selected: 1.The parent population is divided into mutually exclusive and exhaustive subsets  Difference from stratified sampling Stratified: A sample of elements is selected from each subgroup Cluster: A sample of subgroups is chosen Stratified: Want homogeneous subgroups Cluster: Want heterogeneous subgroups

6 Cluster Sampling: Area Sampling Do not need a listing of population to draw sample One stage - Sample only primary sampling units Two stage- Simple - Probabilities Proportional to Size (PPS) Simple - certain proportion of second-stage units are selected from each first-stage unit Probabilities proportionate to size (PPS) - a fixed number of second-stage units is selected from each first-stage unit Cluster Sampling: Systematic Random Sampling Type of cluster sampling Used for simple random sampling Dangers - cycles (periodicity)

7 A probability sample distinguished by a two-step procedure in which (1) the parent population is divided into mutually exclusive and exhaustive subsets, and (2) a random sample of subsets is selected. If the investigation then uses all the population elements in the selected subsets for the sample, the procedure is one-stage cluster sampling; if a sample of elements is selected probabilistically from the subsets, the procedure is two-stage cluster sampling. CLUSTER SAMPLE A measure used to compare sampling plans; one sampling plan is said to be superior (more statistically efficient) to another if, for the same size sample, it produces a smaller standard error of estimate. STATISTICAL EFFICIENCY

8 A form of cluster sampling in which every kth element in the population is designated for inclusion in the sample after a random start. SYSTEMATIC SAMPLE A form of cluster sampling in which areas (for example, census tracts, 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 subsampled with respect to households, the procedure is two-stage area sampling. AREA SAMPLING

9 A form of cluster sampling in which certain proportion of second-stage sampling units (e.g., households) is selected from each first-stage unit (e.g., blocks). SIMPLE TWO-STAGE AREA SAMPLING A form of cluster sampling in which a fixed number of second-stage units is selected from each first-stage unit. The probabilities associated with the selection of each first-stage unit are in turn variable because they are directly related to the relative sizes of the first-stage units. PROBABILITY-PROPORTIONAL-TO-SIZE SAMPLING