Question

question 10 (5 points)
describe the error in the stated conclusion.
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 individual sat scores and family income.

Explanation:

The given data is about average SAT scores of schools and average district income (group - level data). The conclusion jumps to individual SAT scores and family income (individual - level data). This is an ecological fallacy, where a correlation at the group level is incorrectly assumed to apply at the individual level. Just because school averages and district averages are correlated doesn't mean individual scores and individual family incomes have the same correlation.

Answer:

The error is an ecological fallacy. The conclusion incorrectly infers a correlation at the individual level (individual SAT scores and family income) from a correlation at the group level (average school SAT scores and average district income). A significant linear correlation between group - level variables does not necessarily imply the same correlation exists between the corresponding individual - level variables.