Lies , damned lies and statistics
Couldn't find the book but the journal of statistics came to my aid.
I wish I had not asked!
As a variety of popular health books in addition to Protein Power suggest that readers assess their health, at least in part, by estimating their percentage of body fat.
15 percent fat for men and 22 percent fat for women seem to be maximums for good health often quoted.
How exactly are they doing the estimating has been my quest.
These predictive equations in books and the odd website use skinfold measurements, body circumference measurements (e.g., abdominal circumference), and, some simply height and weight.
The secret equation for the determination of body fat is determined through .....multiple regression.
A group of subjects is gathered, and various body measurements and an accurate estimate of the percentage of body fat are recorded for each using water density more of that in a minute.
Then body fat estimates can be fitted to the other less wet measurements using multiple regression , giving, we have to believe, a useful predictive equation for people similar to the subjects.
The various measurements other than body fat recorded on the subjects are, ones that are easy to obtain and serve as proxies for body fat, which is not so easily obtained.
Body fat apparently can be fairly accurately recorded by an underwater weighing technique as the percentage of body fat for an individual can be estimated from body density.
As an approximation, it is assumed that the body consists of two components -- lean tissue and fat tissue.
It now gets a bit technical so go and make the tea and come back in a little while-
One method (brosek)says:
Let
D = body density,
W = body weight,
A = proportion of lean tissue,
B = proportion of fat tissue (so A + B = 1),
a = density of lean tissue, and
b = density of fat tissue,
we have
D = weight/volume
= W/[lean tissue volume + fat tissue volume]
= W/[A*W/a + B*W/b]
= 1/[(A/a) + (B/b)].
Solving for B we find
B = (1/D) * [ab/(a - b)] - [b/(a - b)].
Using the estimates a = 1.10 gm/cm^3 and b = 0.90 gm/cm^3 we come up with "Siri's equation" (Siri 1956):
Percentage of body fat (i.e., 100 * B) = 495/D - 450,
where D is in units of gm/cm^3.
This is considered accurate for "individuals in whom the body weight has been free from large, recent fluctuations."
Now wake up at the back there![/ B]
We all remember Archimedes and his bath..... well-- [B]the technique of underwater weighing "computes body volume as the difference between body weight measured in air and weight measured during water submersion . In other words, body volume is equal to the loss of weight in water with the appropriate temperature correction for the water's density" (Katch and McArdle 1977, p. 113).
Using this technique,
Body density = W/[(W - WW)/c.f. - LV],
where
W = weight in air (kg)
WW = weight in water (kg)
c.f. = water correction factor
(equal to 1 at 39.2 degrees F because one gram of
water occupies exactly one cm^3 at this temperature,
equal to .997 at 76-78 degrees F)
LV = residual lung volume (liters)
(Katch and McArdle 1977, p. 115).
So all we have to do is fit 300 people in my bathroom........
Determine
their Percent body fat using Brozek's equation
Then record
Density (gm/cm^3)
Age (yrs)
Weight (lbs)
Height (inches)
Adiposity index = Weight/Height^2 (kg/m^2)
Fat Free Weight= (1 - fraction of body fat) * Weight, using Brozek's formula (lbs)
Neck circumference (cm)
Chest circumference (cm)
Abdomen circumference (cm) "at the umbilicus and level with the iliac crest"
Hip circumference (cm)
Thigh circumference (cm)
Knee circumference (cm)
Ankle circumference (cm)
Extended biceps circumference (cm)
Forearm circumference (cm)
Wrist circumference (cm) "distal to the styloid processes"
Carry out a multiple regression analysis which I don't know how to do and then you can infer fat percentage of everybody else in the world without them getting wet by any combination of the other measures.
Now look are you still paying attention because there is a term paper in a few weeks.
Do you think that this could really be true?
Last edited by rustpot : Sat, Mar-16-02 at 11:48.
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