The June 4 decision affirmed a finding announced in August by the advertising industry’s investigative arm, the National Advertising Division, that a slew of Neurocore statistics and testimonials on improving migraines, sleeplessness and A.D.H.D. were based on evidence that was “insufficiently reliable to substantiate the strong health-related advertising claims.”

The company based many of its claims on assessments of patients before and after they completed 30 45-minute sessions watching a movie while connected to brain-wave mapping technology, which detects when a subject gets distracted and then stops the movie. The therapy claims to help retrain the brain to “stop spiking out of range.” The company advertised that through its treatments, patients “learn to breathe deeper and slower,” resulting in better brain and heart function.

“While the panel recognizes that Neurocore’s internal studies are relevant to the outcome claims discussed below, the panel does not believe that these studies constitute competent and reliable scientific evidence establishing the efficacy of neurofeedback in treating a wide variety of disorders,” the appeals panel wrote in its decision.

Neurocore said it would comply with the recommendations to halt its advertisements, though it would still share its outcomes.

In an interview, the company’s chief executive officer, Mark Murrison, said that the company had “great respect” for the panel, and that recommendations to improve its advertisements were “a win for everybody.”

Mr. Murrison said the company believed in its results but was “evolving.” He noted that although the panel did not challenge the accuracy of its results, the company had already discontinued some claims, such as a “25 percent reduction in reported symptoms on the autism evaluation checklists.”

“We believe in our outcomes and will present them in a way that is accurate and in a way that’s compliant with the decision,” he said. “We are proud we’re able to provide a nondrug option, and anytime you are bringing innovation into a new industry, you’ll be challenged by those who only know the status quo.”