4.8 Statistical Literacy

Age and Sleep

The graph below showing the relationship between age and sleep is based on a graph that appears on this web page.

What do you think?

Why might Pearson's correlation not be a good way to describe the relationship?

Scatterplot of Hours slept (y, 6 to 16) against Age (x, 0 to 20), one point per year. Sleep falls steeply from 15 hours at age 1 to about 10 hours at age 9, then levels off near 9 to 9.5 hours from age 11 through 18 before dropping to 8 at 19 and 20. The relationship is strong but distinctly curved, which is why Pearson's correlation — a measure of LINEAR relationship — describes it poorly.

Pearson's correlation measures the strength of the

linear relationship

between two variables. The relationship here is not linear. As age increases, hours slept decreases rapidly at first but then levels off.

Adapted from Online Statistics Education: A Multimedia Course of Study (onlinestatbook.com), Project Leader: David M. Lane, Rice University. Developed with NSF support. The original work is in the public domain; it is cited here at the authors' request. Changes were made: reformatted as an accessible XYZ web edition with native MathML. License: Public-Domain.