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=== Reino Unido ===
En enero de 2004, tabloide británico''[[The Sun]]'' Demkina traído a Inglaterra. Ella dio una serie de manifestaciones y sus diagnósticos se compararon con el diagnóstico médico profesional. Un documental de Discovery Channel en Demkina menciona los informes de Demkina haber identificado con éxito todas las [[fractura ósea|fracturas]] y [[Pins (productos sanitarios)|patillas de metal]] en una mujer que recientemente había sido víctima de un accidente de coche. <ref name=Discovery /> ''The Guardian''informó de que impresionó a la acogida del programa de televisión durante el día [[This Morning (Serie de TV)|''This Morning'']] mediante la detección de que había un tobillo durante una entrevista.<ref name ="Guardian" /><ref name ="skolnick" />
Initially, Demkina's demonstrations were well received. However, after she had left the United Kingdom, it emerged that she had made errors among her diagnoses. In one incident she told television-physician Dr. [[Christopher Steele]] that he was suffering from a number of medical conditions, including [[kidney stones]], an ailment of the [[gall bladder]], and an enlarged [[liver]] and [[pancreas]]. Later medical evaluation determined that he was in good health and was not suffering from any of the ailments she had identified.<ref name=NDWeb1 /><ref name=Discovery /><ref name="Guardian" />
=== New York ===
In May 2004 she was brought to [[New York City]] by the [[Discovery Channel]] to appear on a documentary titled ''The Girl with X-Ray Eyes'',<ref name="Discovery">The Discovery Channel, 2004, [http://discoverychannel.co.in/human_files/girl_with_xray_eyes/index.shtml ''The Girl with X-Ray Eyes''], [http://web.archive.org/web/20060505051445/http://discoverychannel.co.in/human_files/girl_with_xray_eyes/index.shtml (Wayback Machine)]</ref> and to be tested by skeptical researchers from the [[Committee for Skeptical Inquiry]] (CSI) under partially controlled conditions.
As a demonstration for the documentary, Demkina was shown wearing her vision-hat and giving diagnoses to people who had previously given descriptions of their specific medical conditions. Most of the people given these readings felt that Demkina had accurately identified their conditions. The researchers, however, were not similarly impressed. CSI researcher [[Richard Wiseman]] said, "When I saw her do her usual readings, I couldn't believe the discrepancy between what I was hearing and how impressed the individuals were... I thought they were going to walk away saying it was embarrassing, but time and again, they said it was amazing. Before each reading, I asked the people what was the main medical problem and Natasha never got one of those right." Wiseman compared the belief of people in Demkina's diagnoses to the belief of people in fortune tellers, and said that people focus only on those portions of Demkina's comments that they believe.<ref name ="Guardian" />
Then CSI researchers [[Ray Hyman]] and Wiseman, and Andrew Skolnick of the now defunct [[Commission for Scientific Medicine and Mental Health]] (CSMMH) conducted their test of Demkina. <!-- I think we don't need this here: CSI is an organization dedicated to debunking paranormalist claims, and CSMMH was an affiliated organization. --> In the test, Demkina was asked to correctly match six specified anatomical anomalies to seven volunteer subjects.<ref name="skolnick" /><ref name ="hyman-SI">Hyman R, ''[[Skeptical Inquirer]]'', May 2005, [http://www.csicop.org/si/2005-05/natasha.html "Testing Natasha"]</ref> The cases in question included six specified anatomical anomalies resulting from surgery and one "normal" control subject. The researchers said that, because of limitation in time and resources, the preliminary test was designed to look only for a strongly demonstrated ability.<ref name ="hyman-SI" /> The researchers explained that while evidence of a weak or erratic ability may be of theoretical interest, it would be useless for providing medical diagnoses. In addition, the researchers said that the influence of non-paranormal observations could not be ruled out under the lax conditions of the test.<ref name ="hyman-SI" /> Demkina and the investigators had agreed that in order to warrant further testing, she needed to correctly match at least five of the seven conditions.<ref name ="hyman-SI" /> In the 4-hour-long test, Demkina correctly matched conditions to four volunteers, including the control subject. The researchers concluded that she had not demonstrated evidence of an ability that would warrant their further study.<ref name="skolnick">Skolnick AA, ''[[Skeptical Inquirer]]'', May 2005, [http://www.csicop.org/si/2005-05/demkina.html "Testing Natasha: The Girl with Normal Eyes"]</ref><ref name="hyman">Hyman R, [[Committee for the Scientific Investigation of Claims of the Paranormal|CSICOP]], [http://www.csicop.org/specialarticles/natasha2.html "Statistics and the Test of Natasha"]</ref>
Subsequently, the design and conclusions of this experiment were subjects of considerable dispute between Demkina's supporters and those of the investigators.
==== Demkina's criticism ====
After completing experiments in New York, Demkina made several complaints in regards to the conditions under which they were conducted, and about the way in which she and her diagnoses were treated. She argued that she had required more time to see a metal plate in one subject's skull, that surgical scars interfered with her ability to see the resected [[esophagus]] in another, and that she had been presented with two patients who had undergone abdominal procedure, but that she had only one abdominal condition on her list of potential diagnoses, leaving her confused as to which one matched the listed condition.
She also complained that she was unable to see that one volunteer had had their appendix removed because, in her opinion, appendixes sometimes grow back. She said she was not able to compare her own diagnosis to an independent medical diagnosis after key experiments had been conducted, preventing her from being able to see if she was diagnosing genuine conditions that were unknown to those conducting the experiments, and which were thus being listed against her in the overall results despite them being valid (as a result of this complaint, all volunteers in the Tokyo experiments were required to bring medical certificates with them prior to diagnosis).
In response to these complaints, the research team stated that Demkina should have been able to find the plate without extrasensory abilities, because its outline could be seen beneath the subject's scalp, and questioned why the presence of scar tissue in a patient's throat had not alerted her to them having an esophagus condition. Additionally, they noted that it remains clinically impossible for an appendix to spontaneously regrow.<ref name=NDWeb1 /><ref name=Discovery /><ref name=skolnick />
==== Brian Josephson's criticism ====
In a self-published commentary regarding the New York testing performed by [[Committee for Skeptical Inquiry|CSICOP]] and CSMMH, [[Brian Josephson]], a Nobel Prize-winning physicist and the director of [[University of Cambridge]]'s Mind-Matter Unification project, criticized the test and evaluation methods used by Hyman and questioned the researchers' motives, leveling the accusation that the experiment had the appearance of being "some kind of plot to discredit the teenage claimed psychic."
Stating that the results should have been deemed "inconclusive", Josephson argued the odds of Demkina achieving four matches out of seven by chance alone were 1 in 50, or less than 2% - making her success rate a statistically significant result. He also argued that Hyman used a [[Bayesian inference|Bayes factor]] that was statistically unjustifiable because it greatly increased the risk of the experiment falsely recording a moderate correlation as being no correlation.<ref name="josephson">
{{cita web
| apellido = Josephson
| nombre = Brian
| enlaceautor = Brian Josephson
| título = Scientists' unethical use of media for propaganda purposes
| editorial =
| fecha =
| url = http://www.tcm.phy.cam.ac.uk/%7Ebdj10/propaganda/
| formato =
| fechaacceso = 31-08-2006 }}</ref><ref name="thes">{{cita web
| url = http://www.tcm.phy.cam.ac.uk/%7Ebdj10/propaganda/THES1.html
| título = Scientists fail to see eye to eye over girl's 'X-ray vision'
| enlaceautor = Phil Baty
| editorial = Times Higher Education Supplement
| fecha = 10 de diciembre de 2004 }}</ref>
Hyman responded that the high benchmark used in the testing was necessary due to the higher levels of statistical significance required when testing paranormal claims (extraordinary claims requiring extraordinary proof),<ref name="hyman" /><ref name="hyman2">{{cita web
| apellido = Hyman
| nombre = Ray
| enlaceautor = Ray Hyman
| título = Statistics and the Test of Natasha
| editorial = CSICOP
| fecha =
| url = http://www.csicop.org/specialarticles/show/statistics_and_the_test_of_natasha/
| formato =
| fechaacceso = 05-02-2010 }}</ref>
and that a high Bayes factor was necessary to compensate for the fact that "Demkina was not blindly guessing", but instead "had a great number of [[Cold reading|normal sensory clues]] that could have helped increase her number of correct matches".<ref>Commission for Scientific Medicine and Mental Health (CSMMH), [http://web.archive.org/web/20050204152650/http://www.csmmh.org/demkina/answerstocritics.html "Answer to Critics"]</ref>
Bayes factors are used to compensate for variables that cannot be calculated through conventional statistics;<ref name=bayesian>Mathworld [http://mathworld.wolfram.com/BayesianAnalysis.html Bayesian Analysis]</ref><ref>{{cita web
| url = http://www.abelard.org/briefings/bayes.htm#testing_for_rare_conditions
| título = Cause, Chance and Bayesian Statistics: A Briefing Document
| fechaacceso = 11-09-2006 }}</ref> in this case, the variable created by the visual clues that Demkina might gather from observing a patient.<ref name="hyman2" /> The Bayes factors used by Hyman were calculated by professors [[Persi Diaconis]] and Susan Holmes of the Department of Statistics at Stanford University.<ref name=hyman2 /><ref name=hyman-stat-response>{{cita web|apellido=Hyman|nombre=Ray|enlaceautor=Ray Hyman|título=Statistics of the Natasha test: response to concerns and questions|editorial=Skeptical Inquirer|fecha=Sept/October 2005|url=http://www.findarticles.com/p/articles/mi_m2843/is_5_29/ai_n15622949|fechaacceso=02-02-2007}}</ref>
If some sensory cues remain despite attempts to exclude them, the possibility that correct diagnoses have been made by non-psychical means can never be completely ruled out. The question would remain as how many persons other than Natasha Demkina would be able to achieve such a success level, under the same conditions.
=== Tokyo ===
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