Body fat percentage (BF%) is easily measured by skinfold calipers. It can be mea
ID: 3306518 • Letter: B
Question
Body fat percentage (BF%) is easily measured by skinfold calipers. It can be measured much more reliably by Dual Energy X-Ray Absorptiometry (DEXA). Body Mass Index (BMI) and waist-to-hip ratio (WH ratio) are two other measures of body composition commonly used in health assessment.
Use the following health data, which was collected from 7 college students, to establish the concurrent validity of WH ratio as a measure of body composition.
What is the correlation coefficient associated with the criterion validity of WH ratio with respect to BF% as measured by DEXA? (Answer to three decimal places)
Subject BF%DEXA BF%
skinfold BMI WH ratio 1 14.4 14.1 24.0 0.96 2 18.7 25.9 26.4 1.05 3 11.7 15.2 19.5 0.74 4 18.2 23.4 28.9 1.01 5 12.4 13.4 19.7 1.03 6 21.3 22.9 31 1.05 7 28.7 35.2 38.2 1.09
Explanation / Answer
r (correlation)=E(x-x)(y-y)/sqrtE(x-x)^2E(y-y)^2
=2.773/(209.868571)(0.0826)
=2.773/4.16
=0.666
BF% WH ratio (xi-x) (yi-y) (xi-x)^2 (yi-y)^2 (xi-x)(yi-y) DEXA 14.4 0.96 -3.514285714 -0.03 12.35020408 0.0009 0.105428571 18.7 1.05 0.785714286 0.06 0.617346939 0.0036 0.047142857 11.7 0.74 -6.214285714 -0.25 38.61734694 0.0625 1.553571429 18.2 1.01 0.285714286 0.02 0.081632653 0.0004 0.005714286 12.4 1.03 -5.514285714 0.04 30.40734694 0.0016 -0.220571429 21.3 1.05 3.385714286 0.06 11.46306122 0.0036 0.203142857 28.7 1.09 10.78571429 0.1 116.3316327 0.01 1.078571429 209.8685714 0.0826 2.773