Do tall students tend to have better vocabulary skills than short students? We might think so looking at a sample of students from grades 1, 6, and 12 of Lake Wobegon school district. The correlation was 0.81 between their height and their vocabulary test score: Taller students tended to have higher vocabulary test scores.
a. Is there a causal relationship, whereby being taller gives you a better vocabulary?
b. Explain how a student’s age could be a lurking variable that might be responsible for this association, being a common cause of both height and vocabulary test score.
c. Sketch a hypothetical scatter plot (as we did in Figure 3.22 for the example on crime and education), labeling points by the child’s grade (1, 6, and 12), such that overall there is a positive trend, but the slope would be about 0 when we consider only children in a given grade. How does the child’s age play a role in the association between height and test score?