Suppose a study finds that the correlation coefficient relating family income and SAT scores is r = +0.98. Which of the following are proper conclusions?
I. Poverty causes low SAT scores
II. Wealth causes high SAT scores
III. There is a very strong association between family income and SAT scores
I only
II only
III only
I and II only
II and III only
III only. Correlation coefficients do not indicate causality, only a relationship.
Only lll
I only
The proper conclusion based on the given information is III only: "There is a very strong association between family income and SAT scores."
The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is +0.98, which indicates a very strong positive association between family income and SAT scores. A correlation coefficient of +1 indicates a perfect positive linear relationship, while a correlation coefficient of -1 indicates a perfect negative linear relationship.
However, correlation does not imply causation. Therefore, it is not proper to conclude that poverty causes low SAT scores or that wealth causes high SAT scores based solely on the correlation coefficient. Other factors could be affecting the relationship between family income and SAT scores, such as access to education resources, parental involvement, or individual student abilities and efforts.