Good points and there’s many contributors to variation/precision above. However, I provided 5 equations above with 4 inputs among them. So the user can at least compare the relative dispersion among the results from the 5 equations. To your point, the accuracy given the gauge/operator error is not addressed, and propagation of error is outside the scope of my post. One can run a DEXA scan/other “measurement” if they want to get some sense of accuracy. IMO almost no one would use or follow any dissertation I would write on propagation of error.
[To prove my point, let’s see how many times the link in the previous sentence gets clicked.]
In fact in my profession almost no one does this properly, and this is among trained scientists/engineers. Hence, I stay in business and business is good.
Short of killing the subject, the best we can do to get a sense of accuracy is to triangulate with DEXA, BodPod, and caliper methods + some underwater methods. Again, I save this for another time.
We all want the top left, but next best is bottom left. I can do with a number that is precise even if always off (as long as it is off consistently). My measurement tool may say I am 40% BF (which wouldn’t be accurate, I hope), but if it is precise, I can be sure that when it says 35% BF I have improved.
I’m simply giving the males on here a sense of the bottom left. They’ll have to do some more work to get a sense of the difference between bottom left and top left. Good graphic.
Here you are claiming that there is no measurement error possibilities in your % body fat models. I don’t see that as being the case. Anytime you pull out a measuring device there is the possibility of measurement error. That will decrease precision.
My point is that the person hoping to calculate his % body fat needs to take extreme care when taking measurements.
The old carpenter’s rule, “measure twice, and cut once” is a starting place. And get more meticulous from there, IMO.
Just for grins, ask them when was the DEXA last calibrated. If they say it self-calibrates, ask them when the self-calibration program was last calibrated.
Not sure how you arrived here. I’m pretty sure I never made such a claim. There are many sources of error we could investigate as per my above comments:
operator error
gauge error
Propagating these would give the user an estimate of absolute error for each measurement (height, waste, weight, neck).
From there one could propagate these estimates into the error involved for each formula. One could look up the origin of each formula and get a sense of the 95%/99% individual confidence limits for each correlation based on the data sets used to develop the correlation.
From 1-4 the user could then get a total standard error of the mean and a confidence interval (t-score*SEM) for each formula that would address accuracy.
The user could then compare the point estimate +/- confidence internal for each formula and compare across the 5 methods.
All of this is completely beyond the scope of what I shared above. All I addressed above was precision for point estimation among the 5 formulas (mean for 5 formulas +/- SD).
For me, yes I find it quite useful and comparable to DEXA/caliper/BODPOD/Inbody. But I also have lowish BF (I shared examples above).
So far I’ve had a couple people test drive it and seemed to be appreciative for its relative (if not completely absolute) utility as a tracking tool. I already stated waist-to-height ratio is plenty good enough for a nice little windsock. And calipers are another tool along with DEXA.
Best wishes to you. You’re welcome.
For those interested, there’s a companion thread that started all this:
Feel free to post your test-drive results and we’ll see how it does against DEXA for those that have that data.
Every morning is what they tell me. I understand the point you’re making and appreciate it. Even if the DEXA is somewhat imprecise, it is still going to be more precise for me than me looking in the mirror or taking my own measurements.
The accuracy of DXA to show equivalence to actual muscle and fat is difficult to perform in the field. The way to validate absolute calibration is to image whole or sectioned cadavers and then perform chemical analysis to definitively quantify composition. Accuracy validations have been performed over the years using fetal pigs and still-born infants (35, 36), adult cadavers (37), and lamb carcasses (38, 39). Overall, the agreement of DXA-measured mass with scale weight is typically within 1%. Agreement between DXA and whole-body CT fat mass has been found to be very high as well with correlations of 0.99 but with DXA underestimating whole body fat mass by as much as 5 kg on average (40). However, there is still a lack of reference phantoms that can be used in the field that assure absolute calibration.
