13.1 13.3 Populations, Surveys and Random Sampling

1
13.1 - 13.3 Populations, Surveys and Random
Sampling

• Kent  Mr. Simpson, how do you respond to the
  charges that petty vandalism such as graffiti is
  down eighty percent, while heavy sack-beatings
  are up a shocking 900?
• Homer  Aw, people can come up with statistics
  to prove anything, Kent.  Forty percent of all
  people know that.The Simpsons, Homer the
  Vigilante

2
So what is statistics, anyway?

• The gathering, organizing, interpreting and
  understanding of data.

3
The Population

• The complete set of individuals or objects
  about which we are seeking information is
  referred to as the population.
• A silly exampleMayor Quimby takes a poll to
  find how many Springfielders plan to vote for him
  in the next election then the population would be
  the voters of Springfield.

4
The N - value

• If it were possible to accurately count every
  member of a population we would get a number, N,
  called the N - value of the population.

5
The N - value (A Point or Two)

• This value is often difficult to make--and
  therefore can require various adjustments.For
  instance, if a scientist were studying the effect
  of genetically modified corn on the monarch
  butterfly it would be practically impossible to
  accurately calculate the N - value.

6
The N - value (A Point or Two)

• This value can change with time.
• In the case of the monarch butterfly, the
  number of actual insects will obviously be
  different from year-to-year.

7
Example U.S. Census
8
Example U.S. Census
9
Example U.S. Census
10
Surveys

• Since collecting information from large
  populations is so difficult, researchers instead
  gather data from selected subgroups and use that
  information to make inferences regarding the
  population as a whole.
• This process is what math-and-science-y types
  refer to as a survey.
• The selected subgroup is called a sample.

11
Surveys (contd)

• There are two major issues when setting up a
  survey1. You need a sample that is a good
  representative of the population being
  studied.2. You need a sample that is large
  enough to draw accurate information from, yet
  still small enough to be practical.

12
Example Literary Digest and the 1936
Presidential Election

• Literary Digest was a popular magazine that had
  accurately predicted the winner in the five
  elections prior to 1936.
• That year, the publication ambitiously decided
  to poll 10 million Americans.
• The individuals contacted came from magazine
  subscription lists and telephone directory
  listings.

13
Example Literary Digest and the 1936
Presidential Election

• When the results came in 2.4 million people had
  responded and the survey predicted that the vote
  would end Landon 57 FDR 43
• What actually happened?

14

• The actual results were FDR 61 Landon
  36.5 Other 2.5 (Landon, in fact, did not even
  carry his home state.)

15

• George Gallup, however, made an accurate
  prediction with a sample of only 50,000 people.
• Why were his results superior?

16

• George Gallup, however, made an accurate
  prediction with a sample of only 50,000 people.
• Why were his results superior? There are two
  main reasons 1. The names were taken from
  phone directories and subscription lists--the
  people surveyed were disproportionately
  wealthy. When a survey has an inherent tendency
  to exclude a segment of the population being
  studied it is said to have selection bias. 2.
  Out of 10 million people contacted only 24
  replied. This example of what is called
  nonresponse bias only magnified the first
  problem.

17
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18

• The actual result was. . . Truman 49.9 Dewey
  44.5 Others 5
• So, what went wrong this time?

19

• The actual result was. . . Truman 49.9 Dewey
  44.5 Others 5
• So, what went wrong this time?
• There are too many characteristics you could use
  for your quota.
• The methods used in 1948 did not take economic
  status into account and oversampled Republican
  voters.
• Most pollsters stopped gathering data when
  Dewey was coming in 13 ahead of Truman in some
  of the surveys.

20
Lessons to take from these occurrences. . .

• A small, well-chosen sample is better than a
  poorly-chosen large one.
• Selection bias and nonresponse bias need to be
  taken into account.
• Dont stop surveying early.
• Quota sampling is flawed.

21
Random Sampling

• Random sampling methods in which a level of
  chance is used to choose a sample
• Simple random sampling a larger scale version
  of picking names out of a hat.
• The problem with simple random sampling is one
  of practicality.

22
Random Sampling

• The solution--used in modern opinion
  polling--is stratified sampling.
• This method breaks the population down into
  strata (categories) and then randomly choose a
  sample from the strata.
• The strata are then divided into substrata and
  the process is continued

23
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25
13.1 - 13.3 Populations, Surveys and Random
Sampling

• Kent  Mr. Simpson, how do you respond to the
  charges that petty vandalism such as graffiti is
  down eighty percent, while heavy sack-beatings
  are up a shocking 900?
• Homer  Aw, people can come up with statistics
  to prove anything, Kent.  Forty percent of all
  people know that.The Simpsons, Homer the
  Vigilante

26
So what is statistics, anyway?

• The gathering, organizing, interpreting and
  understanding of data.

27
The Population

• The complete set of individuals or objects
  about which we are seeking information is
  referred to as the population.
• A silly exampleMayor Quimby takes a poll to
  find how many Springfielders plan to vote for him
  in the next election then the population would be
  the voters of Springfield.

28
The N - value

• If it were possible to accurately count every
  member of a population we would get a number, N,
  called the N - value of the population.

29
The N - value (A Point or Two)

• This value is often difficult to make--and
  therefore can require various adjustments.For
  instance, if a scientist were studying the effect
  of genetically modified corn on the monarch
  butterfly it would be practically impossible to
  accurately calculate the N - value.

30
The N - value (A Point or Two)

• This value can change with time.
• In the case of the monarch butterfly, the
  number of actual insects will obviously be
  different from year-to-year.

31
Example U.S. Census
32
Example U.S. Census
33
Example U.S. Census
34
Surveys

• Since collecting information from large
  populations is so difficult, researchers instead
  gather data from selected subgroups and use that
  information to make inferences regarding the
  population as a whole.
• This process is what math-and-science-y types
  refer to as a survey.
• The selected subgroup is called a sample.

35
Surveys (contd)

• There are two major issues when setting up a
  survey1. You need a sample that is a good
  representative of the population being
  studied.2. You need a sample that is large
  enough to draw accurate information from, yet
  still small enough to be practical.

36
Example Literary Digest and the 1936
Presidential Election

• Literary Digest was a popular magazine that had
  accurately predicted the winner in the five
  elections prior to 1936.
• That year, the publication ambitiously decided
  to poll 10 million Americans.
• The individuals contacted came from magazine
  subscription lists and telephone directory
  listings.

37
Example Literary Digest and the 1936
Presidential Election

• When the results came in 2.4 million people had
  responded and the survey predicted that the vote
  would end Landon 57 FDR 43
• What actually happened?

38

• The actual results were FDR 61 Landon
  36.5 Other 2.5 (Landon, in fact, did not even
  carry his home state.)

39

• George Gallup, however, made an accurate
  prediction with a sample of only 50,000 people.
• Why were his results superior?

40

• George Gallup, however, made an accurate
  prediction with a sample of only 50,000 people.
• Why were his results superior? There are two
  main reasons 1. The names were taken from
  phone directories and subscription lists--the
  people surveyed were disproportionately
  wealthy. When a survey has an inherent tendency
  to exclude a segment of the population being
  studied it is said to have selection bias. 2.
  Out of 10 million people contacted only 24
  replied. This example of what is called
  nonresponse bias only magnified the first
  problem.

41
(No Transcript)
42

• The actual result was. . . Truman 49.9 Dewey
  44.5 Others 5
• So, what went wrong this time?

43

• The actual result was. . . Truman 49.9 Dewey
  44.5 Others 5
• So, what went wrong this time?
• There are too many characteristics you could use
  for your quota.
• The methods used in 1948 did not take economic
  status into account and oversampled Republican
  voters.
• Most pollsters stopped gathering data when
  Dewey was coming in 13 ahead of Truman in some
  of the surveys.

44
Lessons to take from these occurrences. . .

• A small, well-chosen sample is better than a
  poorly-chosen large one.
• Selection bias and nonresponse bias need to be
  taken into account.
• Dont stop surveying early.
• Quota sampling is flawed.

45
Random Sampling

• Random sampling methods in which a level of
  chance is used to choose a sample
• Simple random sampling a larger scale version
  of picking names out of a hat.
• The problem with simple random sampling is one
  of practicality.

46
Random Sampling

• The solution--used in modern opinion
  polling--is stratified sampling.
• This method breaks the population down into
  strata (categories) and then randomly choose a
  sample from the strata.
• The strata are then divided into substrata and
  the process is continued

47
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