Re: BMI/waist-to-height/waist-to-hips

[Guest guest]

Hi folks:

Well, I have seen data which persuaded me that, notwithstanding the

relationships we can all agree on regarding cubes and volume, in the

practical sense the relationship between weight and height in humans

is nowhere close to even approaching that of the cube.

It isn't precisely related to the square either, but it is closer to

the square than the cube. I also saw a very brief note recently

(from a source which OUGHT to have known what it was talking about!)

which supplied no data but suggested that there are data that

indicate the power of 1 is better than the square. I am skeptical

about that. But offer it here as a thought.

In addition it seems to me that there are at least two reasons to

expect women to have a *higher* BMI. One is that they have to cram

in the same number of kidneys, livers, hearts, lungs, (brains? lol)

in their frame as everyone else. (Does the size of these organs

diminish at the same rate as height?). Second, women have much more

fat than men. So that also should suggest a higher BMI for women.

But I am open minded to empirical evidence to the contrary. Which is

really what we need if this discussion is going to be resolved!

Rodney.

>

> >Maco,

> >

> >Your argument proposing deceptively low BMIs for shorter people is

> >flawed. BMI is proportional to 1/height SQUARED. So greater height

> >reduces BMI by the square of the height. Therefore a 7 foot tall

> >person will have a deceptively low BMI.

>

> Because mass/weight will increase as a cube of any one dimension,

the fact

> that BMI only corrects for a square of an increase yields excessive

numbers

> for taller people. Weight in kg/(height in meters, squared) is the

formula,

> I think.

>

> If you compare a person of a certain physique who is 60 inches tall

with

> someone who is 10% (6 inches) taller, you would expect that taller

person's

> weight to be (1.1) X (1.1) X (1.1) that of the shorter person. If

you only

> correct for the square of the height, the expectation, given

> proportionality, is that the taller person's BMI is going to be an

> overestimate relative to the shorter person by the ratio between

the

> heights of the two similarly proportioned people, so that in this

case, the

> BMI for the 5' 6 " person will be 1.1 that of the shorter person

because the

> height-corrective factor is a square rather than some flavor of

cube.

>

> Comparing your averagish 5' 4 " woman with a man who's 6' 3 "

(roughly 10%

> taller) will give people of equal proportions (unlikely, that, but

to make

> the point . . .) BMIs so that a 24 on the part of the woman will

correspond

> with a 26.4 on the part of the man.

>

> Of course, you were saying that a woman should " shoot for " a lower

BMI,

> which is true (because that lower BMI will correspond to a higher

BMI for

> taller people, anyway); I'm just pointing out (confusingly, sorry)

that for

> a given body " situation, " the shorter person is already going to

have a

> lower number, which should psychologically generate the same

conclusion you

> were initially supporting without any additional effort on the part

of the

> shorter (statistically more likely to be female) person.

>

> Waist to height at least compares a one-dimensional measurement (h)

with

> another (2-pi-r) as does waist to hips. Waist to hips is probably

better,

> but I think its easier to consistently measure waist and height

than them

> pesky hips.

> ;-)

>

> Maco

>

[Guest guest]

I originally took this offlist because I thought many of you weren't

interested in the math arguments, but given what Rodney just said, I

wanted to pipe in that I agree!

Below I have some replies to Maco's comments:

Maco mstewart@...> wrote:

> Because mass/weight will increase as a cube of any

one dimension, the fact

> that BMI only corrects for a square of an increase

yields excessive numbers

> for taller people.

> If you compare a person of a certain physique who is

60 inches tall with

> someone who is 10% (6 inches) taller, you would

expect that taller person's

> weight to be (1.1) X (1.1) X (1.1) that of the

shorter person. If you only

> correct for the square of the height, the

expectation, given

> proportionality, is that the taller person's BMI is

going to be an

> overestimate relative to the shorter person by the

ratio between the

> heights of the two similarly proportioned people, so

that in this case, the

> BMI for the 5' 6 " person will be 1.1 that of the

shorter person because the

> height-corrective factor is a square rather than

some flavor of cube.

I think the idea behind using height squared for BMI

is that cubing the height grossly exaggerates the

relative volumes of people of different height. As

you pointed out, measuring hips is difficult.

Measuring body volume is worse! Especially if someone

has a fat tummy and skinny legs. Height squared

approximates the body surface area, which roughly

correlates to body size and is less wildly sensitive

to height variation.

> Comparing your averagish 5' 4 " woman with a man

who's 6' 3 " (roughly 10%

> taller) will give people of equal proportions

(unlikely, that, but to make

> the point . . .) BMIs so that a 24 on the part of

the woman will correspond

> with a 26.4 on the part of the man.

Could you explain how you arrived at these numbers?

You're saying that 6' 3 " is 10% taller than 5' 4 " .

A BMI=24 for a 5'4 " person corresponds to 140 lbs.

A BMI-26.4 for a 6'3 " person corresponds to 211 lbs.

That's a 50% difference in weight.

By your previous argument, to

get the same BMI for the taller person, his weight

should be (1.1)^3 = 1.33 x 140 = 186. That weight

corresponds to a BMI of 23.2 for the tall person. So

his BMI is still lower than the short person's, even

though his weight is 1.1*1.1*1.1 higher.

> Of course, you were saying that a woman should

" shoot for " a lower BMI,

> which is true (because that lower BMI will

correspond to a higher BMI for

> taller people, anyway); I'm just pointing out

(confusingly, sorry) that for

> a given body " situation, " the shorter person is

already going to have a

> lower number, which should psychologically generate

the same conclusion you

> were initially supporting without any additional

effort on the part of the

> shorter (statistically more likely to be female)

person.

Thanks for saying this. However, what I was

really saying was that since women have smaller bones

and more body fat, we should shoot for lower BMIs. A

woman and man of the same height would appear very

different at the same BMI. The woman would look much

fatter.

> Waist to height at least compares a one-dimensional

measurement (h) with

> another (2-pi-r) as does waist to hips. Waist to

hips is probably better,

> but I think its easier to consistently measure waist

and height than them

> pesky hips.

> ;-)

Nevertheless, the waist-to-height measurement runs up

against the " DC level " of the lower limit of waist

circumference --due to the volume taken up by the

organs, etc. Thus, it discriminates against short

people!

Diane

[Guest guest]

Have any of you seen this web site?

http://members.nuvox.net/~on.jwclymer/bmi.html

He's collected a number of formulas that can be applied to height,

weight and other body measurements. My favorite one is for estimating

body fat based on:

(1) weight (lbs),

(2) height (inches), and

(3) waist circumference (inches)

For Males: 100*(-98.42 + 4.15*waist - 0.082*weight)/weight

For Females: 100*(-76.76 + 4.15*waist - 0.082*weight)/weight

I'm not sure where these come from, but my suspicion is that they are

empirically derived. The body fat numbers I get from this formula make

sense, unlike the numbers I get from my Tanita scale, which is

probably sniffing ketamine when I'm not looking.

[Guest guest]

Hi :

Those are interesting equations. Thank you. It gives a sensible

number for me. But what I find is that it kind-of assumes that all

your fat is in your waist ........

According to that formula, if my weight stays the same and my waist

measurement falls my body fat drops significantly.

But if my weight drops and my waist stays the same then my body fat

RISES! According to the calculation.

A bit counter-intuitive. But I am not saying it is wrong.

Rodney.

>

> Have any of you seen this web site?

>

> http://members.nuvox.net/~on.jwclymer/bmi.html

>

> He's collected a number of formulas that can be applied to height,

> weight and other body measurements. My favorite one is for

estimating

> body fat based on:

>

> (1) weight (lbs),

> (2) height (inches), and

> (3) waist circumference (inches)

>

> For Males: 100*(-98.42 + 4.15*waist - 0.082*weight)/weight

> For Females: 100*(-76.76 + 4.15*waist - 0.082*weight)/weight

>

> I'm not sure where these come from, but my suspicion is that they

are

> empirically derived. The body fat numbers I get from this formula

make

> sense, unlike the numbers I get from my Tanita scale, which is

> probably sniffing ketamine when I'm not looking.

>

[Guest guest]

Hi :

Those are interesting equations. Thank you. It gives a sensible

number for me. But what I find is that it kind-of assumes that all

your fat is in your waist ........

According to that formula, if my weight stays the same and my waist

measurement falls my body fat drops significantly.

Sure. Muscle replacing fat.

But if my weight drops and my

waist stays the same then my body fat

RISES! According to the calculation.

Sure. Abdominal fat stays while the rest of you wastes (as opposed to

waists) away. Percentage body fat will increase.

A bit counter-intuitive. But I

am not saying it is wrong.

Makes sense to me.

Also, interestingly to me, from that site:

Willoughby Athlete Weight and

Waist

The Willoughby athlete weight is calculated by dividing

the cube of the height (in inches) by 1906 [Thanks to Konrad Balcerak for

spotting a mistake in the text prior to August 2006]. The Willoughby

athlete waist is calculated by multiplying the height by

0.4584.

P Willoughby, who was a champion body builder in the early twentieth

century, performed extensive anthropometrics measurements on

highly-conditioned (male) athletes and found a direct proportionality

between waist and height. His ideal form had a WHtR of 45.8%. Willoughby

also tabulated data for the morbidly obese, and found the same

proportionality between waist and height, but with a WHtR of

57.7%.

Interestingly, although in the Metropolitan Life Tables the weight values

are proportional to the square of the height (in accordance with the

calculation of Quetelet's Index or BMI), in Willoughby's data the weights

are proportional to the cube of the height (in accordance with Rohrer's

Index).

The Willoughby athlete weight is then the average ideal weight for male

athletes; strength-trainers may weigh more, while endurance athletes will

weigh less. Are you a Willoughby athlete? A check on this is to compare

your waist measurement to the Willoughby athlete waist

calculation.

Maco

[Guest guest]

Hi :

Revised comment:

I see, reading the fine print, he says:

===================================================================

***** " waist is normally measured one inch above the navel. " *****

===================================================================

Well my circumference one inch above the navel is a full inch larger

than my smallest circumference, which I usually use to measure my

waist.

So the result is that, using the 'one inch above navel' definition, I

get a calculated body fat that is about three units higher than I had

been expecting. Which is appreciable.

fwiw

Rodney.

>

> Have any of you seen this web site?

>

> http://members.nuvox.net/~on.jwclymer/bmi.html

>

> He's collected a number of formulas that can be applied to height,

> weight and other body measurements. My favorite one is for

estimating

> body fat based on:

>

> (1) weight (lbs),

> (2) height (inches), and

> (3) waist circumference (inches)

>

> For Males: 100*(-98.42 + 4.15*waist - 0.082*weight)/weight

> For Females: 100*(-76.76 + 4.15*waist - 0.082*weight)/weight

>

> I'm not sure where these come from, but my suspicion is that they

are

> empirically derived. The body fat numbers I get from this formula

make

> sense, unlike the numbers I get from my Tanita scale, which is

> probably sniffing ketamine when I'm not looking.

>

[Guest guest]

Hi folks:

He also says:

" As your weight changes, you can expect to lose about 1 " from your

waistline for each 6-8 lbs of weight loss. "

From this, using his equation, I can calculate that, if his data are

correct, for my body fat to drop to 10% my weight would have to drop

to 126 pounds.

Gosh! At 173 pounds people told me I didn't need to lose any

weight. Including my doctor! I am going to be a little cautious

about accepting this. Perhaps instead, I will go get my BF% properly

measured.

Rodney.

> >

> > Have any of you seen this web site?

> >

> > http://members.nuvox.net/~on.jwclymer/bmi.html

> >

> > He's collected a number of formulas that can be applied to

height,

> > weight and other body measurements. My favorite one is for

> estimating

> > body fat based on:

> >

> > (1) weight (lbs),

> > (2) height (inches), and

> > (3) waist circumference (inches)

> >

> > For Males: 100*(-98.42 + 4.15*waist - 0.082*weight)/weight

> > For Females: 100*(-76.76 + 4.15*waist - 0.082*weight)/weight

> >

> > I'm not sure where these come from, but my suspicion is that

they

> are

> > empirically derived. The body fat numbers I get from this

formula

> make

> > sense, unlike the numbers I get from my Tanita scale, which is

> > probably sniffing ketamine when I'm not looking.

> >

>