Given: Each school in a state reports the average SAT score of its students. There is a significant linear correlation between the average SAT score of a school and the average annual income in the district in which the school is located. Conclusion: There is a significant linear correlation between the individual SAT scores and family income.
Given: The linear correlation coefficient between scores on a math test and scores on a test of athletic ability is negative and close to zero.
Conclusion: People who score high on the math test tend to score lower on the test of athletic ability.
Given: There is no significant linear correlation between scores on the math test and scores on the verbal test.
Conclusion: There is no relationship between the scores on the math test and the scores on the verbal test.
Given: There is significant linear correlation between the number of homicides in a town and the number of movie theaters in a town.
Conclusion: Building more movie theaters will cause the homicide rate to rise. Errors
Error: A lack of significant linear correlation does not imply that no relationship at all exists between the two variables.
Error: Significant correlation does not imply causality.
Error: The linear correlation coefficient is probably not significant, so no conclusion can be reached about the relationship between the two variables.
Error: Averages suppress individual variation and tend to inflate