
512 F.3d 858 (2008)
FEDERAL TRADE COMMISSION, Plaintiff-Appellee,
v.
QT, INC., Q-Ray Company, Bio-Metal, Inc., and Que Te Park, Defendants-Appellants.
No. 07-1662.
United States Court of Appeals, Seventh Circuit.
Argued October 31, 2007.
Decided January 3, 2008.
*859 *860 Lawrence DeMille-Wagman (argued), Imad D. Abyad, William E. Kovacic, Federal Trade Commission, Office of the General Counsel, Washington, DC, for Plaintiff-Appellee.
Helen E. Witt (argued), Wendy Netter Epstein, Kirkland & Ellis, Chicago, IL, for Defendants-Appellants.
Before EASTERBROOK, Chief Judge, and BAUER and WILLIAMS, Circuit Judges.
EASTERBROOK, Chief Judge.
WIRED Magazine recently put the Ray Ionized Bracelet on its list of the top ten Snake-Oil Gadgets. See http://blog. wired.com/gadgets/2007/11/10-awesomegadg.html.


The "Gold Deluxe" Q-Ray Ionized Bracelet
The Federal Trade Commission has an even less honorable title for the bracelet's promotional campaign: fraud. In this action under 15 U.S.C. §§ 45(a), 52, 53, a magistrate judge, presiding by the parties' consent, concluded after a bench trial that the bracelet's promotion has been thoroughly dishonest. The court enjoined the promotional claims and required defendants to disgorge some $16 million (plus interest) for the FTC to distribute to consumers who have been taken in. 448 F.Supp.2d 908 (N.D.Ill.2006), modified in part by 472 F.Supp.2d 990 (N.D.Ill.2007).
According to the district court's findings, almost everything that defendants have said about the bracelet is false. Here are some highlights:
 Defendants promoted the bracelet as a miraculous cure for chronic pain, but it has no therapeutic effect.
 Defendants told consumers that claims of "immediate, significant or complete pain relief' had been "test-proven"; they hadn't.
 The bracelet does not emit "Q-Rays" (there are no such things) and is not ionized (the bracelet is an electric conductor, and any net charge dissipates swiftly). The bracelet's chief promoter chose these labels because they are simple and easily rememberedand because Polaroid Corp. blocked him from calling the bangle "polarized".

*861  The bracelet is touted as "enhancing the flow of bio-energy" or "balancing the flow of positive and negative energies"; these empty phrases have no connection to any medical or scientific effect. Every other claim made about the mechanism of the bracelet's therapeutic effect likewise is techno-babble.
 Defendants represented that the therapeutic effect wears off in a year or two, despite knowing that the bracelet's properties do not change. This assertion is designed to lead customers to buy new bracelets. Likewise the false statement that the bracelet has a "memory cycle specific to each individual wearer" so that only the bracelet's original wearer can experience pain relief is designed to increase sales by eliminating the second-hand market and "explaining" the otherwise-embarrassing fact that the buyer's friends and neighbors can't perceive any effect.
 Even statements about the bracelet's physical composition are false. It is sold in "gold" and "silver" varieties but is made of brass.
The magistrate judge did not commit a clear error, or abuse his discretion, in concluding that the defendants set out to bilk unsophisticated persons who found them selves in pain from arthritis and other chronic conditions.
Defendants maintain that the magistrate judge subjected their statements to an excessively rigorous standard of proof. Some passages in the opinion could be read to imply that any statement about a product's therapeutic effects must be deemed false unless the claim has been verified in a placebo-controlled, double-blind study: that is, a study in which some persons are given the product whose effects are being investigated while others are given a placebo (with the allocation made at random), and neither the person who distributes the product nor the person who measures the effects knows which received the real product. Such studies are expensive, not only because of the need for placebos and keeping the experimenters in the dark, but also because they require large numbers of participants to achieve statistically significant results. Defendants observe that requiring vendors to bear such heavy costs may keep useful products off the market (this has been a problem for drugs that are subject to the FDA's testing protocols) and prevent vendors from making truthful statements that will help consumers locate products that will do them good.
Nothing in the Federal Trade Commission Act, the foundation of this litigation, requires placebo-controlled, double-blind studies. The Act forbids false and misleading statements, and a statement that is plausible but has not been tested in the most reliable way cannot be condemned out of hand. The burden is on the Commission to prove that the statements are false. (This is one way in which the Federal Trade Commission Act differs from the Food and Drug Act.) Think about the seller of an adhesive bandage treated with a disinfectant such as iodine. The seller does not need to conduct tests before asserting that this product reduces the risk of infection from cuts. The bandage keeps foreign materials out of the cuts and kills some bacteria. It may be debatable how much the risk of infection falls, but the direction of the effect would be known, and the claim could not be condemned as false. Placebo-controlled, double-blind testing is not a legal requirement for consumer products.
But how could this conclusion assist defendants? In our example the therapeutic claim is based on scientific principles. For the Q-Ray Ionized Bracelet, by contrast, *862 all statements about how the product worksQ-Rays, ionization, enhancing the flow of bio-energy, and the likeare blather. Defendants might as well have said: "Beneficent creatures from the 17th Dimension use this bracelet as a beacon to locate people who need pain relief, and whisk them off to their homeworld every night to provide help in ways unknown to our science."
Although it is true, as Arthur C. Clarke said, that "[a]ny sufficiently advanced technology is indistinguishable from magic" by those who don't understand its principles ("Profiles of the Future" (1961)), a person who promotes a product that contemporary technology does not understand must establish that this "magic" actually works. Proof is what separates an effect new to science from a swindle. Defendants themselves told customers that the bracelet's efficacy had been "test-proven"; that statement was misleading unless a reliable test had been used and statistically significant results achieved. A placebo-controlled, double-blind study is the best test; something less may do (for there is no point in spending $1 million to verify a claim worth only $10,000 if true); but defendants have no proof of the Q-Ray Ionized Bracelet's efficacy. The "tests" on which they relied were bunk. (We need not repeat the magistrate judge's exhaustive evaluation of this subject.) What remain are testimonials, which are not a form of proof because most testimonials represent a logical fallacy: post hoc ergo propter hoc. (A person who experiences a reduction in pain after donning the bracelet may have enjoyed the same reduction without it. That's why the "testimonial" of someone who keeps elephants off the streets of a large city by snapping his fingers is the basis of a joke rather than proof of cause and effect.)
To this defendants respond that one study shows that the Q-Ray Ionized Bracelet does reduce pain. This study, which the district court's opinion describes in detail, compared the effects of "active" and "inactive" bracelets (defendants told the experimenter which was which), with the "inactive" bracelet serving as a control. The study found that both "active" and "inactive" bracelets had a modestand identicaleffect on patients' reported levels of pain. In other words, the Q-Ray Ionized Bracelet exhibits the placebo effect. Like a sugar pill, it alleviates symptoms even though there is no apparent medical reason. The placebo effect is well established. See, e.g., Anne Harrington, The Placebo Effect: An Interdisciplinary Exploration (1999); Asbjorn Hrobjartsson & Peter C. Gotzsche, Is the Placebo Powerless? An Analysis of Clinical Trials Comparing Placebo with No Treatment, 344 New England J. Medicine 1594 (2001); Ted Kaptchuk, Intentional Ignorance: A History of Blind Assessment and Placebo Controls in Medicine, 72 Bulletin of the History of Medicine 389 (1998). Defendants insist that the placebo effect vindicates their claims, even though they are falseindeed, especially because they are false, as the placebo effect depends on deceit. Tell the patient that the pill contains nothing but sugar, and there is no pain relief; tell him (falsely) that it contains a powerful analgesic, and the, perceived level of pain falls. A product that confers this benefit cannot be excluded from the market, defendants insist, just because they told the lies necessary to bring the effect about.
Yet the Federal Trade Commission Act condemns material falsehoods in promoting consumer products; the statute lacks an exception for "beneficial deceit." We appreciate the possibility that a vague claimalong the lines of "this bracelet will reduce your pain without the side effects *863 of drugs"could be rendered true by the placebo effect. To this extent we are skeptical about language in FTC v. Pantron I Corp., 33 F.3d 1088 (9th Cir.1994), suggesting that placebo effects always are worthless to consumers, But our defendants advanced claims beyond those that could be supported by a placebo effect. They made statements about Q-Rays, ionization, and bio-energy that they knew to be poppycock; they stated that the bracelet remembers its first owner and won't work for anyone else; the list is extensive.
One important reason for requiring truth is so that competition in the market will lead to appropriate prices. Selling brass as gold harms consumers independent of any effect on pain. Since the placebo effect can be obtained from sugar pills, charging $200 for a device that is represented as a miracle cure but works no better than a dummy pill is a form of fraud. That's not all. A placebo is necessary when scientists are searching for the marginal effect of a new drug or device, but once the study is over a reputable professional will recommend whatever works best.
Medicine aims to do better than the placebo effect, which any medieval physician could achieve by draining off a little of the patient's blood. If no one knows how to cure or ameliorate a given condition, then a placebo is the best thing going. Far better a placebo that causes no harm (the Q-Ray Ionized Bracelet is inert) than the sort of nostrums peddled from the back of a wagon 100 years ago and based, on alcohol, opium, and wormwood. But if a condition responds to treatment, then selling a placebo as if it had therapeutic effect directly injures the consumer. See Kraft, Inc. v. FTC, 970 F.2d 311, 314 (7th Cir. 1992) (a statement violates the FTC Act "if it is likely to mislead consumers, acting reasonably under the circumstances, in a material respect").
Physicians know how to treat pain. Why pay $200 for a Q-Ray Ionized Bracelet when you can get relief from an aspirin tablet that costs It? Some painful conditions do not respond to analgesics (or the stronger drugs in the pharmacopeia) or to surgery, but it does not follow that a placebo at any price is better. Deceit such as the tall tales that defendants told about the Q-Ray Ionized Bracelet will lead some consumers to avoid treatments that cost less and do more; the lies will lead others to pay too much for pain relief or otherwise interfere with the matching of remedies to medical conditions. That's why the placebo effect cannot justify fraud in promoting a product. Doctor Dulcamara was a charlatan who harmed most of his customers even though Nemorino gets the girl at the end of Donizetti's L'elisir d'amore.
Now for the remedy. Defendants do not contest the terms of the injunction. They do, however, say that the financial award was excessive. The magistrate judge set as his goal the disgorgement of the profits that defendants made while the Q-Ray Ionized Bracelet was heavily promoted with infomercials on late-night television. Disgorging profits is an appropriate remedy. See FTC v. Febre, 128 F.3d 530, 534 (7th Cir.1997); FTC v. Amy Travel Service, Inc., 875 F.2d 564, 571-72 (7th Cir.1989). But defendants say that the record does not contain evidence about their profits. True, the FTC compiled balance sheets showing profits running in the millions every year. These should not be considered, defendants insist, because when Que Te Park (defendants' principal investor and CEO) testified about the subject, he was asked only whether he could "see" the enterprise's net income (he conceded that he could), not whether the figures *864 are correct, and the FTC's lawyer then forgot to offer the balance sheets themselves as evidence.
This is too clever by half. The FTC made estimates of profits from the Q-Ray Ionized Bracelet business and gave defendants an opportunity to respond. They chose not to do so. Park's noncommittal answers avoided any risk of prosecution for perjury but did not meet the FTC's prima facie showing. The magistrate judge was entitled to treat the evasion as an admission that the FTC's computation is in the ballpark. A monetary award often depends on estimation, for defendants may not keep (or may conceal) the data required to make an exact calculation. Defendants' business was a profitable one; that much, at least, they concede. (It is so profitable that they continue to carry it on despite the injunction that requires them to stop making most of their old claims for its efficacy. Today it is sold with testimonials and vaporous statements.) A court is entitled to proceed with the best available information; if defendants thought that their profits for these years were below $16 million, they should have produced their own figuresfor once the FTC produces a reasonable estimate, the defendants bear the burden of showing that the estimate is inaccurate. Febre, 128 F.3d at 536.
Although defendants complain that the magistrate judge failed to separate ill-got gains from legitimate profits, they offer no reason to think that any of their profits are "legitimate." Defendants' sole business is the sale of Q-Ray products.
On top of paying $16 million (plus interest) into a fund for distribution to all of their customers, defendants must refund the full purchase price of some bracelets purchased over the Internet. Defendants' infomercials promised buyers that the purchase price would be refunded any time during 30 days after the sale if the buyers were not satisfied with their bracelets. Defendants honored that promise for bracelets purchased by telephone but not for bracelets purchased from their web sites. Internet purchasers were allowed only 10 days to return their bracelets. The district court held that defendants must refund the purchase price of anyone who bought from the web sites and returned the merchandise between days 11 and 30. Defendants protest that their web sites disclosed the 10-day refund period, but this does not meet the FTC's point. The infomercials promised a 30-day return period, then suggested that customers purchase online. Anyone who followed that advice received only a 10-day return period. The disclosure of this shorter period was buried several clicks away in the web site. The district court was entitled to conclude the switch deceived reasonable persons who relied on what the infomercials told them.
Finally, Park contends that he should not have been held jointly and severally responsible for the financial aspects of the judgment. Yet he not only participated in the false promotional activities but also had the authority to control them. Either participation or control suffices. Amy Travel, 875 F.2d at 573. Park insists that he believed the representations to be accurate (or at least thought them to be such transparent prattle that they could not be false), but the district court found otherwiseand sensibly.
AFFIRMED
