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Chapter 6, part II Foundations of Measurement

Chapter 6, part II Foundations of Measurement. EDUC 502 October 24, 2005. Sampling Scenario.

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Chapter 6, part II Foundations of Measurement

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  1. Chapter 6, part IIFoundations of Measurement EDUC 502 October 24, 2005

  2. 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.

  3. 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.

  4. 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).

  5. 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?

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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???

  11. 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).

  12. 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 group’s 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.

  13. 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.

  14. Final points about soup example • If properly taken, an absolutely and relatively small sample could perform well the job pollsters expect.

  15. 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 cook’s taste buds

  16. 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?

  17. The Normal Distribution • Many populations of interest are normally distributed. • See: http://www.gifted.uconn.edu/siegle/research/Normal/Normal%20DistributionShow.pps For a good demonstration/explanation of the normal distribution.

  18. Extra homework problem • Page 147 (#11).

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