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**Other Sampling Techniques**

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**What are 3 important ideas to remember when a statistician takes a sample?**

Randomize – use a system to choose subjects to eliminate bias Sample Size – use a large enough sample so that your data is valuable Sample should be representative of the population!

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**Sampling Techniques Simple Random Sample (SRS) Stratified Sampling**

Cluster Sampling Systematic Sampling Multistage Sampling

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**Simple Random Sample (SRS)**

Every subject has an equal opportunity to be selected. SRS is done by numbering your Sample Frame and choosing your sample by generating random numbers. Not always representative of the population!

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**Stratified Sampling (Blocking)**

Group Individuals by common characteristics (homogenous groups) before choosing your sample, then do a SRS for each subgroup Example: If a sample was desired for Rocklin High School, you could stratify (Block) the students first into grade level and then generate samples of grade level.

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Example #1 A firm wishes to survey a sample of a large company’s employees. The company has 100 managers, 1000 laborers, and 300 engineers. Design a method to generate a sample that is representative of the company’s employees.

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Cluster Sampling Cluster sampling is done by grouping the population into similar small groups, randomly choosing a few small groups and then doing a census of the chosen small groups. Example: Surveying 15 1st period classes at RHS.

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Systematic Sampling Done when the statistician does not think the order matters. The sample is chosen by picking the nth person. There is a method of choosing subjects, but it is not necessarily random. Example: Survey the 3rd person that enters Save-Mart.

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Multistage Sampling Sampling methods that combine several methods.

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**Example #2: Determine which sampling method is used in each example.**

Pick every 10th passenger boarding a plane. Randomly choose 5 1st class passengers and 25 economy class passengers. Randomly generate 30 seat numbers and survey them. Randomly select a seat position (center, window, aisle) and survey all passengers in those seats.

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**What can go wrong when choosing samples?**

Volunteer Response Bias: Subjects that respond generally feel strongly one way or the other causing some sort of bias. Convenience Sampling: Sampling done because subjects are easily available. These samples are not usually representative of the population.

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**What can go wrong when choosing samples?**

Undercoverage: Not including some portion of the population in the sample. Bad Sampling Frame: Individuals surveyed may differ significantly than those not in the sampling frame.

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**What can go wrong when choosing samples?**

Response Bias: Either the responses are influenced by questions or the responses are not true.

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Example #3 The U.S. Fish and Wildlife Service plans to study the kinds of fish being taken out of Saginaw Bay. To do that, they decide to randomly select 5 fishing boats at the end of a randomly chosen fishing day and to count the numbers and types of all the fish on those boats. What kind of design have they used? What could go wrong with the design that they proposed?

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