There is a lot of confusion about parametric vs. non-parametric statistics and tests. Some of the literature that explains the difference gets pretty technical. Here is a layman’s description that might not be 100% technically accurate but that will let you understand the difference. Read more!
After one measures central tendency or location of a variable, the next thing to measure is often spread or dispersion. That is, how varied are the data. The best known measure of dispersion is the standard deviation, but it is hardy the only one and may not be the best one. It depends on your variable and its distribution.
In his wonderful book “A
Mathematician’s Lament” Paul Lockhart writes:
“Math isn’t a language, it’s an adventure”
But many people say math is a language. Read more!
BMI, or body mass index, is calculated by dividing by weight by height squared. Specifically, it’s weight in kilograms divided by height in meters, squared. If you prefer pounds and inches, then it’s weight in pounds *703 divided by height in inches, squared. For example, I am 5’8″ tall and weigh 179 pounds. 179*703 = 125837. 5’8″ is 68 inches, and 68^2 = 4624, finally, 125837/4624 = 27.21 and that’s my BMI. If you don’t like doing all that calculating, there are lots of online BMI calculators. According to the US Department of Health and Human Services, that BMI puts me in the category “overweight”. Their categories are:
- Underweight Below 18.5
- Normal 18.5 to 24.9
- Overweight 25-29.9
- Obese 30 and higher
Arbitrary BMI categories
The categories are arbitrary. If your BMI is 24.9 then you are “normal” and if it is 25.1 you are “overweight”. Is this sensible? That means that if I weighed 168 I would be “normal” and if I weighed 170, BOOM my BMI is over 25 and I am “overweight”, to be “normal” BMI I would have to go down to about 162 or below.
BMI ignores everything but height
Not all people who are the same height are the same dimensions, even at their ideal weight. Where is your height? Do you have (compared to other people who are your height) long legs or short legs? People with long legs will have lower BMI than people with short legs, because legs weigh less per inch than torsos. Per What is the weight of a human leg? [answer updated] each leg weighs about 10% of the total weight, and the torso about 60%. But the average person’s legs are about half his or her height and the torso about 40% of height. Thus, torsos weigh about 4.5 times as much per inch as legs. I am 68″ tall, but is that 34″ of legs and 27″ of torso (with the rest head and neck)? Or is it 30″ of leg and 31″ of torso? Or 27″ of leg and 34″ of torso? It makes a difference of about 7 pounds, which, plugged into the formula above, is a point of BMI.
Do you have a long neck or a short neck? Do you have a big head? Necks are light, heads are heavy! All these things vary. It’s hard to find data, but they make hats in sizes for men with heads from 20 ½ inches to 25 ½ inches (see hat sizes). Per the site above, the average human head weighs about 12 pounds. But a head that is 25″ in circumference will have almost double the volume of one that is 20″ … so, does your head weigh 5 or 10 pounds? That’s about another point of BMI.
In addition, people vary in how muscular they are. A very muscular person may have low body fat and still have a very high BMI. Professional body builders are obese, by this criterion. Arnold Schwarzenegger, in his prime, was 6’2 and 235 pounds that gives him a BMI of 30.2! There are running backs in American football who are 5’8″ or 5’9″ and over 200 pounds. Running backs are not fat. Heck, Michael Jordan was 6’6″ and 216 pounds – borderline obese per the above!
One more problem with BMI is that weight should be related to the cube of height, not the square – we have three dimensions, not two. People who are taller are not only taller, they tend to be broader (say, from shoulder to shoulder) and thicker (from, say, belly button to spine).
A better method than BMI
If BMI is not the right tool, what is? Well, to really accurately tell what percent of your weight is fat, you have to be weighed underwater. That’s a hassle, not the sort of thing the average person can do, certainly not on a regular basis. But, with just a tape measure, you can calculate your waist-hip ratio. Then you can use Waist to Hip Ratio to see if it’s in a healthy range. This is a much more sensible measure. For men, 0.9 (or a bit less) is close to ideal. For women, about 0.75 (or a bit less) is ideal.
I attended the 2015 meeting of the Southeast SAS Users’ Group in Savannah, Georgia from September 27 – 29.
I gave a 4 hour course entitled “Lies, damn lies and …. SAS to the rescue!” that had 13 attendees. As far as I can tell, that went well (no one fell asleep, no one left in the middle) and also gave a 50 minute talk: “Alternative methods of regression when OLS is not right” that I had given at Global Forum earlier in the year.
And I attended lots of talks.