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Goal of Sampling

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To obtain as much information as possible about the population at the least cost (money, time, other resources).

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Stratified Sample - 1

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Provides more information about the population for less cost than simple random sampling.

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Stratified Sample - 2

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(A random sample of each homogeneous subgroup (stratum) of a population form a stratified sample.).A stratified sample is obtained by separating the population into non-overlapping groups called strata. Then obtain a simple random sample from each stratum.

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Stratified Sample - 3

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The individuals within each stratum should be homogeneous (or similar) in some way. *Think political party, political polls, age brackets* (To get your random sample of each subgroup, you would take a few from each political party).

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Advantage of Stratified Sample

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It allows fewer individuals to be surveyed while obtaining the same or more information. Additionally it guarantees that each stratum is represented in the sample.

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Obtaining a Systematic Sample

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In both simple random and stratified sampling, it is necessary for a list of the individuals in the population being studied (the frame) to exist. These sampling techniques require some preliminary work before the sample is obtained. A sampling technique that does not require a frame is systematic sampling.

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Systematic Sampling

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(An individual plus every kth individual after form a systematic sample).A systematic sample is obtained by selecting every nth individual from the population. The first individual selected corresponds to a random number between 1 and n.

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Why is Systematic Sampling Useful?

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For when you can't obtain a list of the individual's in the population that you wish to study.

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Systematic Sampling Process

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Select a number n, randomly select a number between 1 and n and survey that individual then survey every nth individual thereafter.

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Systematic Sampling Example

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We might decide to survey every k = 8th individual. We randomly select a number betweekn 1 and 8 such as 5. This means we randomly survey the 5th, 5+8=13th, 13+8 = 21 and so on, individuals until we reach the desired sample size.

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Systematic Sample Book Example

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Kroger - page 31.

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Determine the value of k - Step 1

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If the size of the population, is unknown, there is no mathematical way to determine k. It must be chosen by determining a value of k that is not so large that we are unable to achieve our desired sample size but not so small that we do not obtain a sample size that is representative of the population.

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Determine the value of k - Step 2

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To determine the value of K when the size of the population, N is know is relatively straightforward. We wish to suravey a population whose size is known to be N = 20,325 and we desire a sample size of n =100.

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Determine the value of k - Step 3

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To guarantee that individuals are selected evenly from both the beginning and the end of the population (such as early and late shoppers), we compute N/n and round down tot he nearest integer. 20,325/100 = 203.25, so k = 203.

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Determine the value of k - Step 4

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Then we randomly select a number between 1 and 203.

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Book Steps for Systematic Sampling

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1- If possible, approximate the population size, N.2- Determine the sample size desired, n.3- Compute N/n and round down to the nearest integer. This value is k.4- Randomly select a number between 1 and k. Call this number p.5- The system will consist of the following individuals: p,p+k, p+2k,...., p+(n-1)k.

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Cluster Sample

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(All individuals within a randomly selected subgroup(s) or a population form a cluster sample)

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Cluster Sample Example

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All tenants on a floorCertain classrooms in a schoolRandomly one group - either all republicans, dems, or independents.

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Cluster Samples: Homogeneous vs. Heterogeneous

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Homogenous (similar individuals).Heterogeneous (dissimilar individuals). When clusters are heterogeneous, fewer clusters with more individuals in each cluster are appropriate.

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Convenience Sampling

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(A non-random, easily obtained sample is a convenience sample). A sample in which the individuals are easily obtained and not based on randomness. Examples are self-selected and voluntary response samples.

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Multistage Sampling Example: US Census

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Stage 1 - Stratified sampleStage 2 - Cluster sampleStage 3 - Stratified sampleStage 4 - Cluster sampleStage 5 - Systematic sample

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Sample Size Consideration

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Researchers must find the correct balance between the reliability of the results and the cost of obtaining the results. The more money and time the researcher has available the more accurate the results of the statistical inference will be.