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Sampling. The basic problem. You want to make a general statement about a large group of people (a population ). The population size makes studying everyone impractical.

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the basic problem
The basic problem
  • You want to make a general statement about a large group of people (a population).
  • The population size makes studying everyone impractical.
  • You select a part of the group (a sample) to study. You measure numerical facts of interest (parameters) for the sample.
  • Use statistics to generalize (infer) from the sample to the population.
1936 presidential election
1936 Presidential Election

Alf Landon (Republican)

Franklin Roosevelt (Democrat)

1936 presidential election1
1936 Presidential Election
  • To predict the winner, Literary Digest magazine mailed out 10 million questionnaires to addresses from telephone books and vehicle registrations.
  • 2.4 million responded: 57% said they’d vote for Landon
  • The election result:
1936 presidential election2
1936 Presidential Election
  • To predict the winner, Literary Digest magazine mailed out 10 million questionnaires to addresses from telephone books and vehicle registrations.
  • 2.4 million responded: 57% said they’d vote for Landon
  • The election result: Roosevelt won 62%-38%.
  • (Literary Digest soon went bankrupt)
1936 presidential election3
1936 Presidential Election
  • How was the LD sample different from the population of all voters?
  • Consider what kind of people had phones and cars in 1936, and which party those kind of people tended to vote for.
  • The LD sample systematically favored wealthier people, and wealthier people tended to vote Republican.
slide7
Bias
  • Selection bias: a systematic tendency of the sampling procedure to exclude a portion of the population
    • Example: randomly choosing from a phone book
  • Non-response bias: a tendency of survey respondents to be different from those who didn’t respond.
    • Sometimes indicated by a large non-response rate
slide8
Bias
  • If a sampling procedure is biased, a larger sample size won’t help.
  • Bias can’t always be detected by looking at data. You have to ask how the sample was chosen.
  • So…did pollsters fix the bias issue?
1948 presidential election
1948 Presidential Election

Thomas Dewey (Republican)

Harry Truman (Democrat)

1948 presidential election1
1948 Presidential Election
  • Three major polls covered the election. All used large sample sizes.
  • These polls all used a different method of sampling than Literary Digest.
1948 presidential election2
1948 Presidential Election
  • Three major polls covered the election. All used large sample sizes.
  • These polls all used a different method of sampling than Literary Digest.
quota sampling
Quota Sampling
  • Goal: Create a sample which faithfully represents the target population with respect to key characteristics.
  • Implementation: Define categories of interest (e.g. residence, sex, age, race, income, etc.). Establish a fixed number of subjects to interview overall and in each category. Interviewers select freely within categories.
quota sampling1
Quota Sampling
  • Example: A Gallup poll interviewer was required to interview 13 people.
    • 6 from suburbs, 7 from city
    • 7 men, 6 women
    • Of the men (and similarly for women)
      • 3 under age 40, 4 over age 40
      • 1 black, 6 white
    • Of the white men,
      • 1 paid over $44 monthly rent, 2 paid less than $18
quota sampling2
Quota Sampling
  • The Gallup poll seems to guarantee the sample will be like the voting population in every meaningful way. What happened?
  • The interviewers were free to select within categoriesand this introduced bias.
  • In 1948, Republicans (in each category) were marginally easier to reach for interviews because they tended to be wealthier, better educated, own telephones, have addresses, etc.
quota sampling3
Quota Sampling
  • The bias in quota sampling is generally unintentional on the part of interviewers.
  • Prior to 1948, Democratic majority was so large, this bias didn’t show up. In a close race, the bias was significant.
  • Can we remove this bias from an otherwise sensible approach to sampling?
probability methods
Probability Methods
  • Interviewers have no discretion at all as to whom they interview
  • Sampling procedure intentionally involves chance variation.
  • Investigators can compute the probability that any particular individual will be selected.
  • Quota sampling fails these tests.
probability methods1
Probability Methods
  • Simple Random Sampling: Each individual is given a number. Numbers are drawn at random without replacement.
    • Each person has an equal chance of being selected
    • As sample size increases, the sample proportion for each parameter approaches the population proportion (Law of Averages)
    • Still impractical for very large populations
probability methods2
Probability Methods
  • Cluster sampling:
    • Divide population into “natural” groups.
    • Randomly choose which groups to study.
    • Randomly select individuals from the chosen groups.
    • Can be done in stages, dividing each group into subgroups several times
probability methods3
Probability Methods
  • Post-1948 Gallup Poll sampling method
do probability methods work
Do Probability Methods Work?
  • A degree of bias is inevitable in any survey.
  • Using probability introduces chance error (also called sampling error).
  • Nonetheless, improvements are noticeable.
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