For each of the following hypothetical studies, identify the primary caution each researcher should have when drawing conclusions about the relationship he or she found.

Sarah wants to determine the relationship between height and weight for high school students in the United States. She collects data on height, in inches, and weight, in pounds, for 75 randomly selected high school students in each state. She averages the values by state and performs a linear regression on the 50 state-level values. She finds a high positive linear correlation between height and weight

Sarah should be careful about the use of an ecological correlation. An ecological correlation describes two variables that are group means, as opposed to a correlation between two variables that describe individuals. In this case, Sarah did pick 75 random students in each state. However, she then obtained the height and weight means for each state, and proceeded to compare these. Therefore, Sarah is not comparing individual values, but means. It is important to notice this, because correlations at a group level can be much higher than those at the individual level.