Sampling
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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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Sampling

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Sampling

Sampling


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.


Sampling

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


Sampling

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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