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Chapter 12

Chapter 12. Sample Surveys. Vocabulary. Population- all exp. units that you want to make a conclusion about Sampling frame – list of individuals from whom the sample is drawn. Not always the population of interest.

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Chapter 12

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  1. Chapter 12 Sample Surveys

  2. Vocabulary • Population- all exp. units that you want to make a conclusion about • Sampling frame – list of individuals from whom the sample is drawn. Not always the population of interest. • Examples: phone book, registered voter list, list of tax returns, school roster, etc. • Sample- small group of the population that you do an experiment/study on.

  3. ◦Parameter -Describes the population -Fixed Value -Often Unknown ◦Statistic -Describes the sample of a population -Changes from sample to sample -Use the statistics from repeated samples to estimate the value of the parameter

  4. Sample is said to be representative if the statistics accurately reflect the population parameters

  5. EXAMPLE 1: A polling agency takes a sample of 1500 American citizens from a list of tax returns and asks them if they are lactose intolerant. 12% say yes. This is interesting, since it has been shown that 15% of the population is lactose intolerant. 12% = _________ 15% = __________ Population? Sampling frame? Sample?

  6. EXAMPLE 2: A random sample of 1000 people who signed a card saying they intended to quit smoking were contacted a year after they signed the card. It turned out that 210 (21%) of the sampled individuals had not smoked over the past six months. 21% = _________ Population = Sampling frame= Sample = Parameter of interest =

  7. EXAMPLE 3: On Tuesday, the bottles of tomato ketchup filled in a plant were supposed to contain an average of 14 ounces of ketchup. Quality control inspectors sampled 50 bottles at random from the day’s production. These bottles contained an average of 13.8 ounces of ketchup. 14 = _________ 13.8 = __________ Population? Sample? Sampling frame?

  8. EXAMPLE 4: A researcher wants to find out which of two pain relievers works better. He takes 100 volunteers and randomly gives half of them medicine #1 and the other half medicine #2. 17% of people taking medicine 1 report improvement in their pain and 20% of people taking medicine #2 report improvement in their pain. 17% = _________ 20% = __________ Population? Sampling frame? Sample?

  9. Some more vocab…. Bias vs. Variability: * Bias- consistent, repeated measurements that are not close to the population parameter * Variability- basically like reliability * We want to keep both of these low! * To reduce bias… use random sampling * To reduce variability… use larger samples!

  10. Bias vs Variability • Bias is the accuracy of a statistic • Variability is the reliability of a statistic

  11. SAMPLING VARIABILITY * Different samples give us different results * Different size samples give us different results * Bigger samples are better!! * Sampling distribution: If we take lots of samples of the same size and make a graph True parameter

  12. * Variability = spread/width of graph Larger samples give smaller variability: Lots of samples of size 100 Lots of samples of size 1000 True parameter True parameter

  13. Label each as high or low for bias and variability True parameter True parameter

  14. True parameter Label each as high or low for bias and variability True parameter

  15. True parameter Another vocab word… • Unbiased Estimator: - When the center of a sampling distribution (histogram) is equal to the true parameter. True parameter

  16. SAMPLING DESIGNS (HOW to sample a population)

  17. GOOD Sampling Designs: 1) Simple Random Sample (SRS) - Every experimental unit has the same chance of being picked for the sample and every possible sample has the same chance of being selected • Give every subject in the population a number • Use the table of random digits and read across to select your sample • Ignore repeats

  18. EXAMPLE: Take an SRS of 5 from the following list. Start at line 31 in the table. Smith Jones Holloway DeNizzo David Adams Schaefer Gray Capito Meyers Gingrich Card Dietrich Moreland Hall Walsh Whitter Jordan

  19. EXAMPLE: Take an SRS of 4 from the following list. Start at line 18 in the table. McGloneMcCuen Wilson SzarkoBellavanceWoodring Stotler Kelly Wheeles Timmins Arden McNelis Gemgnani O’Brien Robinson Lorenz Lake Bainbridge

  20. 2) Stratified Random Sample- (not SRS) * Divide population into groups with something in common (called STRATA) Example: gender, age, etc. * Take separate SRS in each strata and combine these to make the full sample - can sometimes be a % of each strata

  21. Example: We want to take an accurate sample of CB South students. There are 540 sophomores, 585 juniors, and 530 seniors. Take a stratified random sample.

  22. 3) Systematic Random Sample – The first exp. unit is selected at random. Each additional exp. unit is selected at a predetermined interval. Examples: • Surveying every 5th person that walks thru the back door of CB South. • Selecting a random person to start with (like person #4) and then taking every 10th person on the list after that (person #14, person #24, person #34, etc.)

  23. 4) Cluster Sample – Population is broken into groups. All members in one or more groups are taken as the sample. 5) Multistage Sample -   Used for large populations Example: sampling the population of the USA

  24. Example: The government wants to survey the entire population. However they cannot just give every person a number and do an SRS. So they follow this process: * Randomly select 5 counties from each state * In each of those counties, randomly select 6 towns/cities * In each town/city, randomly select 4 streets * On each street, select 3 houses, and interview the head of the household.

  25. BIASED SAMPLING METHODS: • 1) Voluntary Response Samples • Chooses itself by responding to a general appeal. • Call-in, write-in, etc. • 2) Convenience Samples • Selecting individuals that are the easiest to reach/contact

  26. JUST CHECKING We need to survey a random sample of 30 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below: • Pick every 10th passenger that boards • From the boarding list, randomly choose 5 people flying first class, and 25 of the other passengers • Randomly generate 30 seat numbers and survey the passengers who sit there • Randomly select a seat position (right window, left window, right aisle, etc.) and survey all people in those seats

  27. Complete the Sampling Rectangles activity

  28. HW answers: 8) (a) population = all Americans? (b) parameter = true percent of people who want marijuana legalized for medicinal reasons (c) sampling frame = people who visit the website (d) sample = all people who responded to the question on the website (e) method = voluntary response sample (f) biases = voluntary response bias undercoverage- not everyone visits the site and sees the question

  29. 10) (a) population = all voters (b) parameter = issues that voters are interested in (c) sampling frame = blocks in the city’s election districts (d) sample = all residents that the staff members can find that day (e) method = stratified, then convenience within each strata (f) biases = voluntary response bias nonresponse bias

  30. 12) (a) population = all cars on the road (b) parameter = (10%) true % of cars without updated registration, insurance, and safety inspection (c) sampling frame = cars that pass thru the roadblock (d) sample = the cars they stop (e) method = convenience sample (f) biases = not random time of day and location may not be representative of all cars on the road.

  31. 14) (a) population = all dairy farms (b) parameter = % with contaminants in them (c) sampling frame = all dairy farms? (d) sample = the farms visited by inspectors (e) method = ? SRS? Or multistage? (f) biases = none, as long as farms are randomly selected and so is the milk that is tested at each farm.

  32. Last vocab… types of BIAS in samples • Undercoverage- Sampling in a way that leaves out a certain portion of the population that should be in your sample Example: Telephone polls, registered voter list, etc. • Non-response-Bias introduced when a large amount of those sampled do not respond. Example: people don’t answer phone, don’t mail back questionnaires, refuse to answer questions

  33. Response Bias- Anything in the survey design that influences the responses. Examples: * respondents lying * responses trying to please the interviewer * unwillingness to reveal personal facts or info * leading or confusing questions

  34. Book examples: p. 289 #15, 16, 17, 20, 22, 23 25

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