Percentages are Often Meaningless II

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Summary: You can reduce the percentage of one item by increasing the total amount of all items.  This can give the illusion that you've reduced the amount of the item in question, but is just that ... an illusion.

That previous post on this was inspired by yet another round of Fun with Numbers, this time courtesy of David Ludwig and Dariush Mozaffarian in JAMA ... and now the NYT   (I'm beginning to see a pattern here.  NYT is the publicity outlet for all JAMA editorial nonsense, much like Time is the outlet for BMJ's Open Season on Science Heart journal.)

On Facebook I received the following response to my first post of this title:  (not on public page so shared anonymously)
As an Accountant it's always a red flag when people just give percentages or even worse when in the same document give percentages part of the time and raw numbers other times. It's an obvious sign they are presenting the information in the best way to support their position.

Whenever I get a proposal like this (it's usually to spend $) it usually takes about 5 minutes after analyzing the raw data to determine that the numbers don't support what the project paper claims and the project gets shelved.

In most of the cases there was a deliberate attempt to hide or distort the data. It's never incompetence, usually deceit.
This echos my sentiments exactly!!   Don't get me wrong, percentages are useful values but are often abused as indicated above.   When comparing pies, they must be for the same size pie!  Otherwise they are meaningless.

In promoting the notion that the real problem in America is some mythical ceiling on fat consumption the pair of Boston based "nutrition experts" resort to your typical mathematical contortions with percentage math.   (Seriously, I have a post in the works, this is beyond absurd and should not be coming from academics ... $omething is behind this and I don't think it's senility setting in.  I've come to expect this from Feinman and Harcombe and Hite and Teicholz, but these two?)

MacSmiley asked Mozaffarian on Twitter about this and this was his response:

Link to the Tweet, but don't bother, he deleted it after a couple of days.
The picture in Melanie's tweet came from this blog, and I'll include this updated version that I created specifically for the forthcoming  Ludwig & Mozaffarian piece.

Let's do the math magic for Mozaffarian's example:
His grandma eats 50 g fat/day * 9 cal/g fat = 450 calories of fat/day.  Thus 450 fat cals /1500 total *100 = 30% fat calories on the nose.  
Mozaffarian eats 75 g fat/day * 9 cal/g fat =  675 calories of fat/day.  Thus 675 fat cals/3000 total * 100 = 22.5% fat calories.
Now my first question is why is Mozaffarian authoring articles that even imply that low fat diets are dangerous if he's eating under 25% calories from fat ... but let's presume this is totally hypothetical.

Grandma Mozaffarian is eating less fat than her grandson in this scenario, not more fat.  The percentage is irrelevant and 50 grams is less than 75 grams.  But let's look at this a few other ways.

  • If Granny M doubled her caloric intake to 3000 cal/day by doubling her fat to 100 g/day, then she's still consuming 30% fat.  So we can say she's eating the same amount of fat?    ... or ...
  • If Granny M doubled her caloric intake to 3000 cal/day by eating Captain Crunch soaked in nonfat milk and drinking Fanta, but kept her fat intake at 50 g/day, she'd now be consuming 15% fat:  So she is now eating half the fat she used to?  ... or ...
  • If Granny M goes on Atkins such that she cuts her caloric intake (spontaneously of course) to 1000 cal/day but fat remains at 50 g/day, she's consuming 45% fat:   So now she's "upped the fat" in her diet?  ... or (last one) ...
  • If Granny M cuts her fat intake to 40 g/day and keeps calories at 1500 cal/day by eating 90 calories of rice instead, thereby reducing fat intake to 24% fat:   So she's eating less fat than she used to?
The answers to the above bolded questions would be -- or should be -- a head-shaking "are you serious?", and yet serious people from Tufts and Haahvaahd are telling you just this.  The only scenario where the question can be answered with "yes", is the blue bolded one.

Because absolute amounts, as in grams of fat, are always directly comparable, and 75 grams will always be more than 50 grams, and 50 grams will always be the same as 50 grams, and 40 grams will always be less than 50 grams.  Percentages always rely on context to be relevant and are useless in comparing any scenario where that "whole" changes in any way.

But as if to almost throw down the gauntlet, Mozaffarian tweeted this yesterday, screenshot right.

Alrighty then, first a quibble.  This is 2015, please include data past 2000, it's not like it's not available.

Second, a serious issue.  Why show part of the picture all the time?  Trends in energy intake among adults in the United States: findings from NHANES (note authors are affiliated with the CDC but did not write this in their official capacities)

Here is the full picture.
FIGURE 1.  Mean adjusted intakes of macronutrients among adults aged 20–74 y by NHANES study period. A: Results shown as absolute intake in grams per day. B: Results shown as percentage of energy intake. Results were adjusted for age, sex, race or ethnicity, educational status, and BMI.
One more for you, that was also brought to Mozaffarian's attention.  This one I'll embed as I don't think it will be going poof in the night.

Stop the deceit please.  It is most unbecoming.