More about Correlation

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More about Correlation
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Basketball Players

• A class of 15 students happens to include 5
  basketball players.
• True or false, and explain the relationship
  between heights and weights for this class should
  be summarized by r.

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Use the Correlation Coefficient?
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Nonlinear Association
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Exceptional Cases

• The correlation coefficient r is less useful in
  case there are outliers.
• Moreover, r measures linear association, not
  association in general.

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Ecological Correlation

• In one study, a scatter diagram was shown showing
  the relationship between the rate of smoking per
  capita and the rate of deaths from lung cancer in
  eleven countries.
• The correlation between these eleven pairs of
  rates was 0.7.
• Comment on this data.

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Ecological Correlation

• Correlations based on rates or averages can be
  misleading.
• For example in each country, there is a lot of
  spread around the averages.
• Replacing the people by the countrys average
  eliminates the spread, and gives the misleading
  impression of tight clustering.

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Example
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Suicide and Literacy

• A sociologist is studying the relationship
  between suicide and literacy in
  nineteenth-century Italy. He has data for each
  province. The correlation is 0.6.
• Does this give a fair estimate of the strength of
  the association between literacy and suicide?

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Association is not Causation

• For school children, shoe size is strongly
  correlated with reading skills.
• In the Great Depression, better educated people
  tended to have shorter spells of unemployment.
  Does education protect you against unemployment?

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Reading and the TV

• Studies have found a negative association between
  hours spent watching television and scores on
  reading tests.
• Does watching television make people less able to
  read?

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Fat in the Diet and Cancer
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True or False?

• If r -0.80, below average values of the
  dependent variable are associated with
  below-average values of the independent variable.
• If y is usually less than x, the correlation
  coefficient between x and y will be negative.

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Height and Weight, Again

• An investigator collected data on heights and
  weights of college students.
• Suppose the correlation coefficient between
  height and weight for the men was about 0.60 for
  the women, about the same.
• What happens to the correlation coefficient if
  you take the men and women together?

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Math SAT scores

• ETS computed the average score for each of the 51
  states, and the percentage of the high-school
  seniors in that state who took the test. The
  correlation between these two variables was equal
  to 0.86.
• True or false test scores tend to be lower in
  the states were a higher percentage take the test.

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Math SAT scores

• In New York, the average score was only 471 in
  Wyoming, the average was 507.
• True or false the data show that on average, the
  schools in W. are doing a better job at teaching
  math than the schools in NY.

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Verbal SAT

• ETS computed the average Verbal SAT score for
  each state, as well as the average Math SAT
  score. The correlation between these 51 pairs of
  averages was 0.97. Would the correlation between
  the Math SAT and Verbal SAT computed from the
  data on all the individual test takers be larger
  than 0.97, about 0.97, or less than 0.97?