5'1: Designing Samples

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5.1 Designing Samples
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Important Distinction

• Observational Study observe individuals and
  measure variables but do not attempt to influence
  the responses.
• Experiment deliberately impose some treatment
  on individuals in order to observe responses.

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Designing Samples

• Population entire group of individuals we want
  information about.
• Sample part of the population we actually
  examine.
• Samples are used due to constraints such as time,
  cost, and inconvenience.

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Census vs. Sampling

• Census contacting every individual in the
  entire population.
• Sampling studying a part in order to gain
  information about the whole.

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Sampling Methods

• Voluntary Response Sample people who choose
  themselves by responding to a general appeal
  (question, etc.).
• Bias - those with strong (especially negative)
  opinions are most likely to respond.
• Remember Ann Landers?
• Write-in, Call-in, and online polls are not very
  reliable!
• Convenience Sample choosing individuals who are
  easiest to reach.
• Bias Mall samples are convenient. However,
  they are more likely to include teenagers,
  retirees, and wealthier segments of the
  population.

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What is BIAS?

• Bias occurs when a sampling method systematically
  favors certain outcomes.
• Personal Choice (by a responder to a VRS or the
  interviewer of a CS) produces bias.
• The statisticians remedy?
• CHANCE!

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I. Simple Random Samples

• Simple Random Sample (SRS) every member of a
  population has an equal chance of being selected.
• Ex) Names in a hat (population) are drawn out at
  random until you get a handful (sample).
• NOTE larger random samples give more accurate
  results than smaller samples.
• Random Digits Table (Table B Back of Book)
• Each entry is equally likely to be any of the 10
  digits 0 through 9.
• Entries are independent of each other.

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Using Table B

• DPS would like to interview a sample of 5
  students to find ways to improve teacher quality.
  To avoid bias, DPS will use a SRS of size 5.
• Steps
• Label Give each student a numerical label. Two
  digits are needed in our class. For example, 01
  to 24.
• Table B Enter anywhere. Lets try line 130.
• 69051 64817 87174 09517 84534 06489 87201
  97245
• 69 05 16 48 17 87 17 40 95 17 84 53
  40 64 89 87 20 19
• Students 05, 16, 17, 20, 19 are selected
• Its good practice to start at a different row
  every time you use Table B

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If only I had my Table B
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TI Alternative

• MATH, PRB, randInt(1,24), hit ENTER five times
• ENTER again if you get repeats
• MATH, PRB, randInt(1,24,5), ENTER
• Works well unless you get repeats

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Other Sampling Methods

• Probability Sample a sample chosen by chance
• The use of chance to select the sample is the
  ESSENTIAL principle of statistical sampling.
• Stratified Random Sample -
• First, divide the population into strata (groups
  of individuals) that are similar in some way.
• Next, choose a separate SRS in each stratum and
  combine to form the full sample.
• Ex) Divide a population of high schools into
  public, Catholic, and other private schools

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Continued

• Cluster Sampling
• First, divide the population into groups, or
  clusters.
• Next, clusters are randomly selected.
• ALL individuals in the chosen clusters are
  selected for the sample.
• Ex) Do students feel they have enough time for
  AP Statistics free response questions?
• Randomly select a few schools from a
  comprehensive list featuring every school that
  administers the AP exam.
• Every student at the selected schools is asked
  about the time limits.
• The students interviewed would constitute a
  cluster sample.

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Average Number of Units in Durham Apartment
Buildings
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Take Caution

• Undercoverage occurs when some groups are left
  out of the sample selection process.
• Household surveys miss the homeless, inmates, and
  students in dormitories.
• Telephone polls miss the 8 of homes without
  residential lines.
• Nonresponse occurs when a selected individual
  cant be contacted or does not cooperate.

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More Caution

• Examples of Response Bias
• Respondents may lie if asked about illegal or
  unpopular behavior.
• In a recent poll, 72 said they voted when just
  56 actually did vote.
• An interviewers race or gender may influence
  responses regarding racism or sexism.
• Faulty memories
• Telescoping Example Have you visited a
  dentist in the last 6 months? will often elicit
  a Yes from someone who went 8 months ago.

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More Caution

• The Wording of Questions is the most important
  influence on the answers given to a sample
  survey.
• Ex) 1992 Opinion Poll by American Jewish
  Commission
• Does it seem possible or does it seem impossible
  to you that the Nazi extermination of the Jews
  never happened?
• 22 responded possible
• Does it seem possible to you that the Nazi
  extermination of Jews never happened, or do you
  feel certain that it happened?
• 1 responded possible

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Before You Trust a Poll

• Know the
• Exact questions asked
• Rate of nonresponse
• Date and method of the survey