[quote]Correct. But neither can we say that the dye does not cause hyperactivity in anyone.[/quote]
No, but that is not our goal in the first place. Doing a test on every single possible trait is economically infeasible and unreasonable; ergo, net impact is our best metric.
The benefit is "we get a new food additive to use".
The net cost is zero in terms of health impact (no more hyperactivity in the general population).
Ergo, the net benefit is a new food additive. This is very simple math here. Net benefit is what we care about in this case, as it is what we are studying. If it redistributes ailments amongst the population, then there may be even more optimal uses, but we're still looking at a benefit.
If you want to delve deeper, that's going to be a seperate experiment.
[quote]Your making the claim "no evidence to the contrary" shows that you have not read the literature, have not done a PubMed search on "ADHD, food dye", and have no familiarity with toxicity studies in general. There is always evidence to the contrary. An evaluation weighs the evidence on both sides. You can take any case where the FDA has said "There is no evidence that X", and look up the notes from the panel they held where they considered the evidence for X and decided that the evidence against X outweighed it.[/quote]
Your making the claim "evidence to the contrary" suggests that any of this is worth anything. The problem is that, unfortunately, it isn't.
If someone does a study on 20 different colors of M&Ms, then they will, on average, find that one of the M&Ms will change someone's cancer risk. The fact that their study showed that, with 95% confidence, blue M&Ms increased your odds of getting cancer, [b]is not evidence for the idea that blue M&M's cause cancer[/b].
Worse, the odds of the negative finding studies being published is considerably less than the probability of the positive finding study being published. This is known as "publication bias". Additionally, people are more likely to be biased against artificial additives than towards them, particularly "independent researchers" who very likely are researching it precisely because they harbor the belief that it does in fact have an effect.
This is very basic and is absolutely essential to understanding any sort of data of this sort. When I say that there is no evidence for it, I am saying precisely that - just because someone studied 20 colors of M&M's and found that one has a 95% chance of causing more cancer tells me nothing. It isn't evidence for anything. It is entirely possible that it DOES cause cancer, but the study has failed to provide me for evidence of that fact.
You are thinking in terms of formal logic, but that is not how science works. If you lack sufficient evidence to invalidate the null hypothesis, then you don't have evidence. And the problem is that a mere study is often insufficient to actually demonstrate it unless the effects are extremely blatant.
quote The answer is, "This is very likely." This is how studies turn out all the time, partly due to genetics. Different people have different genetics, different bacteria in their gut, different lifestyles, etc. This makes them metabolize food differently. It makes their brain chemistry different. Different people are different.[/quote]
For this to happen, you would require that the space to be very similar in size on both ends.
Is it possible for things to help one person and harm another? Absolutely.
Is it probable that something will help almost exactly as many people as it harms? No. Especially not some random genetic trait (there are genetic traits, such as sex, where this IS likely because it is an even split in the population, so you do have to be careful for that, but sex-dependence of results is pretty obvious).
The probability of equal distribution of the traits is vastly outweighed by the probability of it not being equally distributed. Ergo the result you are espousing is in fact extremely unlikely.
When I said that "making the claim "no evidence to the contrary" shows that you have not read the ...
I used to teach logic to undergraduates, and they regularly made the same simple mistake with logical quantifiers. Take the statement "For every X there is some Y such that P(X,Y)" and represent it symbolically:
∀x∃y P(x,y)
Now negate it:
!∀x∃y P(x,y)
You often don't want a negation to be outside quantifiers. My undergraduates would often just push it inside, like this:
∀x∃y !P(x,y)
If you could just move the negation inward like that, then these claims would mean the same thing:
A) Not everything is a raven: !∀x raven(x)
B) Everything is not a raven: ∀x !raven(x)
To move a negation inside quantifiers, flip each quantifier that you move it past.
!∀x∃y P(x,y) = ∃x!∃y P(x,y) = ∃x∀y !P(x,y)
Here's the findings of a 1982 article [1] from JAMA Psychiatry (formerly Archives of General Psychiatry), back in the days when the medical establishment was busy denouncing the Feingold diet:
Now pay attention; this is the part everyone gets wrong, including most of the commenters below.
The methodology used in this study, and in most studies, is as follows:
People make the error because they forget to explicitly state what quantifiers they're using. Both the t-test and the F-test work by assuming that every subject has the same response function to the intervention:
response = effect + normally distributed error
where the effect is the same for every subject. If you don't understand why that is so, read the articles about the t-test and the F-test. The null hypothesis is that the responses of all subjects in both groups were drawn from the same distribution. The one-tailed versions of the tests take a confidence level C and compute a cutoff Z such that, if the null hypothesis is false,
P(average effect(test) - average effect(control)) < Z = C
ADDED: People are making comments proving they don't understand how the F-test works. This is how it works: You are testing the hypothesis that two groups respond differently to food dye.
Suppose you measured the number of times a kid shouted or jumped, and you found that kids fed food dye shouted or jumped an average of 20 times per hour, and kids not fed food dye shouted or jumped an average of 17 times per hour. When you run your F-test, you compute that, assuming all kids respond to food dye the same way, you need a difference of 4 to conclude with 95% confidence that the two distributions (test and control) are different.
If the food dye kids had shouted/jumped 21 times per hour, the study would conclude that food dye causes hyperactivity. Because they shouted/jumped only 20 times per hour, it failed to prove that food dye affects hyperactivity. You can only conclude that food dye affects behavior with 84% confidence, rather than the 95% you desired.
Finding that food dye affects behavior with 84% confidence should not be presented as proof that food dye does not affect behavior!
If half your subjects have a genetic background that makes them resistant to the effect, the threshold for the t-test or F-test will be much too high to detect that. If 10% of kids become more hyperactive and 10% become less hyperactive after eating food coloring, such a methodology will never, ever detect it. A test done in this way can only accept or reject the hypothesis that for every subject x, the effect of the intervention is different than the effect of the placebo.
So. Rephrased to say precisely what the study found:
Converted to logic (ignoring time):
!( ∀child ( eats(child, coloring) ⇨ behaviorChange(child) ) )
Move the negation inside the quantifier:
∃child !( eats(child, coloring) ⇨ behaviorChange(child) )
Translated back into English, this study proved:
However, this is the actual final sentence of that paper:
Translated into logic:
!∃child ( eats(child, coloring) ⇨ hyperactive(child) ) )
or, equivalently,
∀child !( eats(child, coloring) ⇨ hyperactive(child) ) )
This refereed medical journal article, like many others, made the same mistake as my undergraduate logic students, moving the negation across the quantifier without changing the quantifier. I cannot recall ever seeing a medical journal article prove a negation and not make this mistake when stating its conclusions.
A lot of people are complaining that I should just interpret their statement as meaning "Food colorings do not affect the behavior of MOST school-age children."
But they didn't prove that food colorings do not affect the behavior of most school-age children. They proved that there exists at least one child whose behavior food coloring does not affect. That isn't remotely close to what they have claimed.
For the record, the conclusion is wrong. Studies that did not assume that all children were identical, such as studies that used each child as his or her own control by randomly giving them cookies containing or not containing food dye [2], or a recent study that partitioned the children according to single-nucleotide polymorphisms (SNPs) in genes related to food metabolism [3], found large, significant effects in some children or some genetically-defined groups of children. Unfortunately, reviews failed to distinguish the logically sound from the logically unsound articles, and the medical community insisted that food dyes had no influence on behavior until thirty years after their influence had been repeatedly proven.
[1] Jeffrey A. Mattes & Rachel Gittelman (1981). Effects of Artificial Food Colorings in Children With Hyperactive Symptoms: A Critical Review and Results of a Controlled Study. Archives of General Psychiatry 38(6):714-718. doi:10.1001/archpsyc.1981.01780310114012.
[2] K.S. Rowe & K.J. Rowe (1994). Synthetic food coloring and behavior: a dose response effect in a double-blind, placebo-controlled, repeated-measures study. The Journal of Pediatrics Nov;125(5 Pt 1):691-8.
[3] Stevenson, Sonuga-Barke, McCann et al. (2010). The Role of Histamine Degradation Gene Polymorphisms in Moderating the Effects of Food Additives on Children’s ADHD Symptoms. Am J Psychiatry 167:1108-1115.