By Irene Hukkelhoven, Zachary Sanicola, Natalie Thoni

# Author Archives: Irene

# Exploring Relationships in Body Dimensions

Irene Hukkelhoven, Zachary Sanicola, Natalie Thoni

For years, the Body Mass Index (BMI) has been used to quantify obesity. Recently, questions have been raised concerning the appropriateness of using this index to define someone’s healthy weight range. A particularly daunting concern stems from the medical insurance company practice of using an applicant’s BMI as one of the terms to compute and justify that person’s insurance premium. Moreover, some researchers insist that the “BMI is bogus” [1]. Our goal is to investigate the validity of this concern by redefining a healthy weight range and to determine if the BMI falsely labels a person as obese. Although de-emphasized, we will also discuss the applications of skeletal measurements in gender determination and define size-ranges for manufacturers of retail and ergonomic goods.

The dataset [2] is comprised of 507 total individuals. Specifically, our sample population contains 247 men and 260 women, all of whom complete several hours of exercise a week. The majority of the subjects were in their twenties and early thirties at the time of sampling, though the dataset also contains a handful of older men and women. To concentrate on a more specific demographic, we will eliminate those men and women over a certain age. As such, we define the population as all physically active young adults.

Several questions we will attempt to address are as follows:

1. Is height a good indicator of weight? How accurately does the BMI assign under- or overweight statuses?

2. What skeletal bone is the best indicator of gender?

3. How many units of each shirt size should a clothing retail store order to ensure they will not be overstocked? How big should an airline make their seats to accommodate the smaller 95% of the population?

Studies have already shown that height is a poor indicator of weight, so we predict that our linear regression correlation will not be near an absolute value of 1. We will show that there are other body measurements with improved correlation values that can be used to better predict a subject’s “scale weight”. To justify the higher accuracy of using other body measurements, we will use hypothesis testing on a randomly selected group within our sample population (two for each individual; H_0: u = x; H_A: u =/ x, where u is the scale weight and x is the weight determined by (1) solely height and (2) other body measurements) and calculate and compare respective p-values. Furthermore, we will attempt to define a more rigorous equation (than BMI) for determining whether an individual is within a healthy weight range, thus answering questions about the value of the obesity index for individuals whose body build is atypical for their height.

Contrary to popular belief, pelvic measurements are not the most reliable data for determining the gender of skeletal remains. Using histograms, we will uncover which skeletal measurement best evidences a male or female body. Specifically, we will seek to identify those body parts whose normal distribution curves for male versus female subjects overlap the least. Such information can be useful in forensic science and anthropological studies (i.e. identifying remains of a missing person, or shedding light on ancient cultural burial rituals)

To figure out what quantity of each shirt size a buyer for a clothing store should order, we will calculate five two-sided confidence intervals to relate weight to shirt size (XS, S, M, L, XL). Then, we can use a probability density function to determine how many units of each shirt size a buyer should order without fear of being overstocked. In a similar manner, confidence intervals can be employed to calculate the size of an airplane seat suitable for the smallest 95% of the population (this will be a one-sided interval, since a seat big enough to fit the largest people will automatically also fit the smallest people).

In conclusion, our project will primarily highlight the topic of health, obesity, and BMI. As a secondary focus, we will look into the applications of skeletal measurements for gender determination as used in forensic and anthropological research. Lastly, we will address how our data can be used to provide useful information to clothing and furniture manufacturers.

References:

1. Devlin, Keith. "Top 10 Reasons Why the BMI Is Bogus." *Npr.org*. National Public Radio, 4 July 2009. Web. 25 Mar. 2012. <http://www.npr.org/templates/story/story.php?storyId=106268439>.

2. Heinz, Grete, Louis J. Peterson, Roger W. Johnson, and Carter J. Kerk. "Exploring Relationships in Body Dimensions." *Journal of Statistics Education* 11.2 (2003).*Amstat*. Web. 25 Mar. 2012. <www.amstat.org/publications/jse/v11n2/datasets.heinz.html>.