Chapter 6, part II Foundations of Measurement

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Chapter 6, part IIFoundations of Measurement

• EDUC 502
• October 24, 2005

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Sampling Scenario

• Early in 2004, the British government launched a
  formal investigation into the death of Princess
  Diana. On this side of the Atlantic, Americans
  were asked about the cause of this death. Large
  majorities of Americans do not think either the
  British government or the British royal family
  was involved in the death of Princess Diana.

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Sampling Scenario

• Fifty-eight percent of Americans believe that the
  car crash that killed Princess Diana was an
  accident as opposed to only 26 who say it was
  probably planned. Moreover, 76 of them say we
  may never find out what really happened.

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Sampling Scenario

• This poll was conducted among a nationwide random
  sample of 1024 adults, interviewed by telephone
  from March 30 to April 1, 2004. The error due to
  sampling could be plus or minus 3 percentage
  points. (CBS Public Opinion Polls, 2004).

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Questions about scenario

• Do you trust the results of this poll? Why or why
  not?
• Sampling error is mentioned in the excerpt. Might
  there also be sampling bias in this study?

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Sampling scenario II

• A candidate hires one polling organization to
  take a random sample of 1500 voters in a small
  city (with only 50,000 voters) and another sample
  of 1500 voters in a very large city (with 500,000
  voters) to estimate the percentage of the voters
  in the two cities who would support him.

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Sampling scenario II

• Suppose that the polling organization uses the
  same techniques in the two polls and the
  political attitudes of the voters in the two
  cities are roughly identical. Comment on the
  quality of the samples and hence the accuracy of
  the findings of the two polls in the two cities.

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Sampling task

• Group 1 task Cook chicken soup for 4 guests
  using a small pot.
• Group 2 task Cook chicken soup for 14 guests
  using a large pot.
• Group 3 task Cook chicken soup for 40 guests
  using a very large pot.

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Sampling task

• Working in separation, each group should decide
  how they would do the following
• Taste the soup before serving the guests to make
  sure that it is tastefully cooked
• Follow the usual ways chefs use to take soup out
  to taste
• Decide how much soup to take out to taste.
• Report out on how you performed the task.

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Sampling task solutions

• All three groups can generally agree on these
  points
• The soup must be thoroughly stirred before a
  small amount of soup is taken out to taste.
• Only a small amount of soup is taken out to taste
  and this amount is about a tablespoon (or at
  least some amount less than an entire bowl).
• What any of this have to do with sampling in
  educational research???

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Points about sampling theory

• A tablespoon of soup could help the chef to
  ascertain the quality of the soup if he/she stirs
  the soup thoroughly to assure that it is well
  mixed and as a result, a tablespoon of soup will
  faithfully reflect the overall quality of soup in
  the pot (but not only the fatty part on the
  surface for example, if he/she does not stir the
  soup thoroughly).

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Points about sampling theory

• It is unnecessary (and more expensive) to take
  out a large amount of soup to taste when a
  tablespoon can do the job.
• Taken in a proper manner, the third groups
  tablespoon of soup is as good as that of the
  first group in representing the soup in the pot,
  despite the difference in size of the amount of
  soup they have to cook.

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Final points about the soup example

• Sample size must be viewed in two different
  perspectives the absolute size (a tablespoon of
  soup) and the relative size (the ratio between a
  tablespoon of soup and the whole soup in the
  pot).
• It is the absolute sample size that matters the
  most in determining the accuracy of the findings
  of the poll, not the relative sample size.

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Final points about soup example

• If properly taken, an absolutely and relatively
  small sample could perform well the job pollsters
  expect.

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Homework Discussion question

• Map the soup metaphor over to an educational
  research situation. Explain what each of the
  following elements represent in the educational
  research context
• The soup in the teaspoon
• The entire pot of soup
• Stirring the soup
• Tasting the soup
• The teaspoon, the cooks taste buds

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Probability vs. Non-probability sampling

• The soup metaphor illustrated probability
  sampling. However, there are some questions about
  the soup that are not answered well by this type
  of sampling
• Is there anything baked onto the bottom of the
  pot? If so, what is it and how did it get there?
• What kind of chicken makes good soup?
• What situations might these correspond to in
  educational research?

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The Normal Distribution

• Many populations of interest are normally
  distributed.
• See http//www.gifted.uconn.edu/siegle/research/N
  ormal/Normal20DistributionShow.pps
• For a good demonstration/explanation of the
  normal distribution.

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Extra homework problem

• Page 147 (11).