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5.1: Designing Samples

5.1: Designing Samples. Observational Study. vs. Experiment. Population. SAMPLE. yes. yes. yes. no. no. no. no. yes. no. no. yes. no. yes. no. no. no. yes. no. no. no. no. no. no. yes. no. yes. no. yes. no. yes. no. no. no. no. no. yes. no. yes. no. yes.

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5.1: Designing Samples

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  1. 5.1: Designing Samples

  2. Observational Study vs Experiment

  3. Population

  4. SAMPLE

  5. yes yes yes no no no no yes no no yes no yes no no no yes no no no no no no yes no yes no yes no yes no no no no no yes no yes no yes no yes yes no no no yes yes yes no no no yes no no yes yes no yes yes yes yes yes no no yes yes no no no yes yes no yes no no no no no no yes no yes no no no yes no yes no no no no no no no no no yes no yes yes no no no yes yes no yes no no yes yes yes yes CENSUS

  6. yes no no yes no no no yes Sampling

  7. The design of a sample refers to the method used to choose the sample from the population. Poor sample designs can produce misleading conclusions.

  8. Bad sampling method #1: Voluntary Response Sample

  9. A fox News Poll asks: “Who is going to win the Presidential Election? Romney! Obama! Oh…just me? Romney! Romney! We are voting but don’t care enough to respond! Romney! Romney! Romney!

  10. Bad sampling method #2:

  11. What is The Average gpa At NPHS? 3.8! 3.5! SHUT THE FRONT DOOR The average GPA at NPHS is 3.84!!!!!! 4.8! 3.6! 4.2! 4.0! 3.0! 3.7! 3.4! 4.4!

  12. Results of Poor Sampling Methods The statistician's remedy: allow chance to select the sample. Choosing a sample by chance attacks bias by giving all individuals an equal chance to be chosen.

  13. The Simplest Way to use Chance… Place all names in a hat (the population) and draw out a handful (the sample).

  14. Simple Random Sample? • Choose 5 student names out of a hat • Choose every other student from an alphabetical list of student • Choose the first 5 students to walk into a class

  15. Table B

  16. Joan’s Accounting Firm Joan’s small accounting firm serves 30 business clients. Joan wants to interview a sample of 5 clients in detail to find ways to improve client satisfaction.

  17. Label Stopping Rule Table IDSample

  18. 1. Give each client a numerical label

  19. 1. Give each client a numerical label • Assign labels using any convenient manner, such as alphabetical order. • Be certain that all labels have the same number of digits. • Use the shortest possible labels. • You can begin on any row, but don’t always start on the same row.

  20. 2. Stopping Rule • Use line 130 and continue if needed until five clients are chosen.

  21. Ignore numbers that are too high 3. Table • Enter Table B anywhere and read two digit groups. For this example lets start at line 130. 69051 64817 87174 09517 84534 06489 87201 97245 4. ID Sample

  22. Other Sampling Methods Systematic Random Sampling • Often used in exit polls: • Randomly start at the (4th) person that arrives to vote. • Then randomly choose how much to “skip” (for example: ask every 6th person) • Gives each individual, but not each sample, and equal chance of being chosen.

  23. Is there enough time on the free-response section of the AP Statistics Exam? WHS WHS NPHS SVHS TOHS Agoura Agoura MHS StBoni Buena Buena Oaks OPHS Calabasas

  24. Multistage Sampling

  25. Ventura County T.O. Newbury Park Ventura Oxnard Camarillo Reino Borchard Carob Jarome Los Vientos

  26. Problems with surveys (even when sampling methods are good) • Undercoverage • Some groups in the population are left out of the process of choosing a sample. • Nonresponse • Individual chosen for the sample can’t be contacted or does not cooperate • Response Bias • Occurs when a respondent does not give an accurate response. • Causes: poor question wording, lying, etc. • *These problems may or may not cause bias.* • Bias will result if the people left out are different, as a group, than the people included.

  27. Sampling Error and Sampling Variability • Sampling Error and Sampling Variability • Sampling Variability is a statistical reality. If we selected 50 samples from a population, each one would be somewhat different! • Sampling error: Occurs because the sample rarely reflects the population perfectly. • Can’t be avoided…we just have to account for it in our calculations (example: margin of error). • Larger sample sizes  more accurate results!

  28. Sampling • Describe an example of taking a random selection of students from our school using • Systematic Random Sampling • Stratified Sampling • Cluster Sampling • Multistage Sampling P.S. I haven’t given a quiz in a while…

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