Natasha Demkina, a young girl living in Saransk, Russia, began to receive a lot of media attention around the middle of last month. It started with an article in Pravda, which hailed her as the 'Girl with X-ray vision'. You see, Natasha possesses the unusual ability to peer through human flesh and spot diseases and injuries that are lurking unseen within people's bodies. Or, at least, this is what Pravda claimed. It didn't take long for more newspapers to catch onto the story. The British Sun has been the most relentless about pursuing it. They've actually flown Natasha to London and are now parading her around like some kind of weird curiosity. Does Natasha really have x-ray eyes? Well, I doubt it. But I'm sure The Sun is going to milk this for all it's worth.
Comments
The problem of the chance of Natasha correctly matching a given number of people with their correct diagnoses if she were guessing is a classic known as the 'matching problem'. For those who want a reference, Feller's An Intro. to Probability and its Applications, Chapter IV will give you the full gory details, but the essential result is on page 107. I got out my calculator and found that the chance of Natasha passing (5 or more correct) if she were guessing would be about 1 in 230, whereas the chance of her guessing 4 or more if she were guessing would be about 1 in 55. It is true that conventionally, that if a result could have occurred less frequently than 1 in 20 times by chance, Statisticians consider that there is something of interest in the data. CSIOP evidently set a higher standard of evidence than that usually required because of the implications if the claims of Nayasha are true.
Watching the programme, I was sympathetic towards Natasha, as I am sure most people were, and I noted that the investigators were in no way abusive to her. I was struck both by professional physicians in Russia at all becoming convinced of her gift (though not all have been), but I wondered about her hesitancy in the test situation and her inability to diagnose the metal plate. My personal opinion, for what it is worth, is that if Natasha has a special gift (the idea of which I am not opposed to on principle), it may be best for her to use it discreetly. It may be that such gifts do not lend themselves to this kind of investigation, and that Providence has so disposed things that deception, belief and scepticism will always be possible in this world, for to have it otherwise would fail to respect our free will adequately, and undermine the value of this world as the arena of our soul-making, which necessarily involves the coooperation of our free will.
Good luck to Natasha, whatever she does.
If she, as is claimed, can see clearly into people, then for the simple features she was looking for, she should have been 100% correct after looking for a few minutes. It's like if I claim that I can identify coins in glasses of water. If I could clearly see the coins then I'd be able to give a 100% correct answer in seconds. If it takes me four hours to look at the coins, and even then I only get 4 out of 7 correct.
The test showed that she achieved results much greater than would be achieved by random guessing. But, this is not just a black and white situation where either she's guessing randomly, or she is truly able to use x-ray vision. Alternative explanations include that she, after six years, has grown adept at guessing people's health conditions by observing their external appearance, movements, etc. This would be a good explanation of a higher than expected, but not perfect diagnosis. And, I would quote her FOUR HOUR examination of the subjects, and continual communication with others (e.g. by cell phone) as evidence that this is what she is doing.
If she can truly see fine details inside a person, then we'd expect 100% accuracy. 4/7 just does not cut it, and suggests an alternative method of diagnosis other than random chance, and other than being able to clearly see into people. Even if experiments were repeated many times, obtaining a strongly statistically significant result, this would only show that she is doing "something", not that she has paranormal powers. To show that she has paranormal powers requires an experiment that can distinguish between paranormal powers and diagnosis by observation of the external characteristics of the subject.
You ("skepps") say that the " believers" are avoiding evidence etc. but in much cases (and also in this case) I notice that the "skepps" are avoiding things!
You only respond on the "lacks" in our stories. You don't see the story as a whole and don't look at our whole experience.
That's the problem with the whole world. A lot of times we are focused too much on details. Focussing on details is oke but not at te cost of our picture of the whole. In my opinion everything would change if we would concentrate more on the whole.
If we give then thousend reasons why we believe or know that the paranormal excist, you find that reason that is the "weakest" in your opinion.
I don't say that I know everything, but I have my own reasons to believe in the paranormal. I am sure it excists. But what is evidence for me isn't nessesary evidence for another person. That's oke...but you should know that reality is in my opinion experience. What is reality without experience? In my opinion reality as we know it doesn't excist without experience. It is the experience that is our reality. What makes my reality different that yours...it that what we experience.
That is one big different between my believe and the believe of most skepps. You only take something for real if many people are experiencing the same thing in ways wich you can accept! And if you don't like it what many people say they experience, you whipe it away.
Reality has everything to do with experience. In kind of a way everything you experience is reality.
We shouldn't focus so much on whats real and what's not. That realy depends on experience. We should focus on what works and what not! What do we want...what do we want achieve in live. Do we want to help the ill people. Maybe some aura readers can help us...who knows...and if one can't help us...maybe another...maybe they experience different things and call it one and the same. Maybe one sees after-images and another sees realy a subtile energy that is connected to our health. It is really a mather of experience...and as we become better aware of what we want to achieve in live, we start to focus on how to achieve it...if some kind of meditation, visialisation, an healing ore whatever can help you achieving your live goal, why not? You dont' have to believe that these things are real. They will become real for you when they start helping you in achieving what you want. They start to be real for you if you notice they work. You can do someting with it. And maybe you will realize that the experience of that other person and his discription of what he experienced wasn't so strange at all. (smile)
If we give then thousend reasons why we believe or know that the paranormal excist, you find that reason that is the "weakest" in your opinion.
You may BELIEVE all the new-age hogwash you like, but you KNOW nothing. Evidently not even the definitions of those two words. Just because you BELIEVE something and could give even 10 billion reasons WHY you believe it, doesn't make it fact. Your weakest point, if that's even the case, probably gets debunked first and most often because it's the most obvious and therefore quickest way to move towards making a point.
Reality doesn't equal experience, or vice-versa, as your experiences as interpreted by you are subject most likely to whatever "new-age" drugs your taking to promote your inner chakra-aura-healing abilities that week. What flavor was your kool-aid by the way? If what's evidence for us isn't evidence for you that's because you don't know the meaning / definition of the word evidence. What would be more correct to say would be that just because YOU think something is evidence doesn't necessarily make it such. Look up the definition.
Everything you experience is reality. Your a major fan of LSD aren't you? Obviously we don't believe something just because a lot of other people are experiencing it or we'd be on the other side of this argument, huh? Evidence which would result in proof would make us believe. What evidence does exist on this matter serves only to debunk the claims made.
Go back to the hippie-compound and tell them all about how we are so close-minded... maybe over the "Kool-aid" induced LSD trip tonight you can all come up with some more magic to cure us all of our inability to be more gullible.
PS - You should check into DNA perfection... I bet you'd be real big on that as well. Get that done and you might then be SUPER-ENLIGHTENED! 😊 She missed the metal plate in the head after making the claims that were made??? Just that one miss and NO MORE information is required to show it's not real. I've got a $15 metal detector that could probably do just as well as she did... Come on Marlon, they're the ones who claimed small metal objects, past fractures, etc etc could be detected... not us. SHE / IT failed... get over it!
I think that if I would be super enlightened I wouldn't be a bit irritated now because some people don't agree with me. Haha... But If I annoy people with writing things as (have a good day, ore smile) I suppose I'd better not do that again.
Why do you find my discription of reality is nonsense, cause that's what it comes down on, isn't it?
In the dictionary (Dutch) stands:The discription of reality is: "The real existence of something" / " the here and know".
Know we can only inteprit reality with our senses. And our experiences has much to do with our senses. Why should the one thing we sense be reality and the other not. Is only the physical reality real? Why? That isn't the meaning of the word reality.
About Natasha...I can imagine that you don't believe in her gift because she missed the metal plate...but then your looking at a part and not at the whole.
We find your description of reality a nonsense because we have a tool called "science" which is the best tool we have for distinguishing sense from nonsense. It's by no means perfect, but it certainly beats other tools such as "superstition", "jumping to conclusions" and similar.
If I was unaware of magnetism or similar phenomena, then I would be inclined to disbelieve that a small metallic object could attract another metallic object through a barrier such as a thin sheet of glass. However, skeptical as I would be, if someone gave me a magnet, and allowed me to experiment with it, then I'd soon discover that there was some attractive force. I'd try different sheets of glass, other barriers, see that the magnet attracts other metallic objects, and eventually I'd be convinced that the magnet was able to attract some metals. Therefore I'd conclude that the claim for the existence of magnetism was sense, not nonsense. If I gave the magnet to another "magnetism skeptic" then s/he could then convince themselves of the reality of the effect. And, if magnetism was a new discovery, there would be huge numbers of cases of people demonstrating that the effect is real.
However, when I see claims for such phenomena such as the efficiacy of homeopathic remedies, all I see is that when people try to verify these claims, and do so using proper methods and experiments, the results suggest that the claim is incorrect. Hence I classify such claims as nonsense.
There is a problem in society in general that the vast majority of people simply do not have the education and "tools" required to adequately separate sense from nonsense. Arrogant as this may sound, once someone studies science properly, and undestands how it really works (including an in-depth knowledge of statistics), there is no other conclusion that can be made.
It only takes a quick read of one of any number of books, such as _Methodological Errors in Medical Research_ by Bjorn Anderson (ISBN: 0-632-02137-3) to see that even among trained medical researchers publishing in medical journals, a large proportion don't have sufficient training to design experiments adequate to separate sense from nonsense. And that explains a lot of what we see in the real world.
Cheers,
Ross-c
Some people in this thread have spoken of auras. I don't know whether you believe in auras or not, but please hear me out. Would you consider the following an adequate experiment to see whether or not people can truly see auras.
First, we'd need a number of people (lets call them 'seers') who claim to be able to see auras. Since this experiment is going to be based on consistency, the seers would have to trust each other's ability, so we'd allow them to talk to each other, do demonstrations, and establish that all of them (say 3 of them) do have this "power".
There would then be a session where the three 'seers' would agree on a number of properties of aura that differ between people, and how these are named. The three seers would be placed in separate rooms with no means of communication. New people ('subjects') whom the seers have not seen before would be shown to each of the seers in turn. The seers would describe the auras of these people in the terms previously agreed.
If the descriptions of the auras agreed to a degree such that random chance could be ruled out with 95% certainty, then it would be concluded that the seers can truly see the aura of the subjects, and hence that the aura exists.
Marion, do you think that this would be both a fair, and an accurate experiment to test for the ability of seers to see the auras, and therefore that the aura exists? Rather than just a yes/no answer, may I ask you to explain the reasoning behind your answer?
Cheers,
Ross-c
I mean, if it had, they'd have seen the impressive rate of diagnoses, rather than a weak 4/7 after four hours.
It's painfully obvious that you have drawn your conclusion without any actual EVIDENCE and that you are not going to let any EVIDENCE change your mind.
The facts are what the facts are and, unfortunately for your belief system, they don't support what you think. There comes a time when a reasonable person throws in their hand. I think you have long since passed that point. You're trying to bluff with a pair of deuces. Throw in.
Natasha claimed to have a "gift", and claimed that this gift enabled her to look inside people. Her ability or inability to look inside people is something that can be objectively tested, and the evidence is that she can't. So, if she still believes that she can see inside people, then "deluded" is a fair judgement. Given the result of the experiment, the only ways that we can describe her is "deluded" or "a fraud". Which would you prefer?
Cheers,
Ross-c
0 - 1854
1 - 1855
2 - 924
3 - 315
4 - 70
5 - 21
6 - 0
7 - 1
The probabilities associated with each score are these numbers divided by 5040. The probability of Natasha getting a score of 4 was thus 1.389%. Or 1 chance in 72 - not 1 in 50 or 1 in 55, as other people have said.
"Natasha claimed to have a "gift", and claimed that this gift enabled her to look inside people. Her ability or inability to look inside people is something that can be objectively tested, and the evidence is that she can't. So, if she still believes that she can see inside people, then "deluded" is a fair judgement. Given the result of the experiment, the only ways that we can describe her is "deluded" or "a fraud". Which would you prefer?"
Very well said, Ross. The bottom line here is that she claimed to have a "gift," she agreed to be tested, she was tested based on what she claimed she could do and she failed. End of story.
As Ross said, either she's a conscious fake or she's self-deluded. Pick one.
Cheers,
Ross-c
But I'm puzzled that Andrew Skolnick, posting here on 9 Dec 04, quotes Professor Ray Hyman responses to Puck's first (wrong) estimate of the probability:
"The second mistake this critic makes is to use the probability for getting exactly four correct matches. The number that is relevant for our test is the probability of getting four or more correct matches. Contrary to this persons assertion, the probability of getting exactly four matches in our test is .01533 and not 1/840 (.0012) as he claims. The relevant probability is the probability of getting four or more correct matches which is .01899 (rounded to .02 or 1 in 50)."
Now, by my calculations, the probability of getting exactly four matches is 70/5040 or 0.01389, not .01533. And the probability of getting four or more is 0.01818, not .01899. These are slight differences, but differences all the same. So how did they get their figures? By using a formula out of some book, it seems. What is this formula, and how was it derived?
I wondered if the original calculations were done using the binomial distribution (which would have been a silly thing to do, but I gave it a go). Those numbers are much further off. So, I have no anwer as to where their numbers came from.
I'd guess that they made a calculation error, but could be wrong.
Cheers,
Ross-c
Cheers,
Ross-c
"The problem we are dealing with is known as the matching problem. The mathematics for calculating the correct odds is not self evident. Indeed, it is very complicated. I painstakingly worked out the correct probabilities using the formulae in Frederick Mosteller's Fifty Challenging Problems in Probability With Solutions. I believe this is still available from Dover Books. The critic might find it useful to carefully follow the argument in this book. My other source was Hoel, P.G., Port, S.C., and Stone, C.J. (1971). Introduction to Probability Theory. This latter source provides some useful approximations for those who do not have the patience to calculate the exact probabilities. Richard Wiseman was able to check my probability calculations using tables provided by the Journal of the Society for Psychical Research. Our probabilities agreed."
So perhaps the figures they produced were "useful approximations" rather than "exact probabilities" for a "very complicated" problem. And the problem is indeed very complicated - or at least extremely tedious - if attempted manually. But it is quite easy to solve using a simple computer program (as you found out). This rather suggests that the probabilities were calculated using methods appropriate to a pre-computer era, and which gave approximate rather than exact answers. The 1971 book on probability cited is some 35 years old, and thus dates from an era when computers were monstrous beasts that lived in university mathematics departments, and so it was most likely written for use by people who did not have access to such computers.
I'm neither a mathematician nor a statistician, but it seems to me that people who are working with probability and statistics really ought to be able to calculate their figures with an accuracy appropriate to the era in which they live. I find myself slightly raising an eyebrow that CSMMH apparently lacks the computing skill to correctly calculate probabilities (even if in this case it is relatively inconsequential). And I find myself wondering what else they can't do.
On the page:
http://www.ds.unifi.it/VL/VL_EN/urn/urn6.html
the matching problem is discussed, and the formulae given for calculating the probabilities of matches. I wrote another program to calculate the probabilities of various matches for the 7 people on the tv show. I get ...
ross@home$ ./matching
For k=0 b is 1854
For k=1 b is 1855
For k=2 b is 924
For k=3 b is 315
For k=4 b is 70
For k=5 b is 21
For k=6 b is 0
For k=7 b is 1
ross@home$
Or, 70/5040 for k=4, and 92/5040 for k >= 4. I.e. the same as both of us got with our previous programs.
The page mentions a "Poisson approximation", but this is for very large matching problems, not 7. Also, even if the problem had been solved by hand, it wouldn't be that difficult. So, there's probably more to this than it appears.
Though, in the end, the differences in the probabilities are very small.
Cheers,
Ross-c
You said: It's painfully obvious that you have drawn your conclusion without any actual EVIDENCE and that you are not going to let any EVIDENCE change your mind.
I don't agree with what you say. If you look at her credentials you can see that she followed several studies and trainings. With some of them you can "earn" a official grade and with some of them not. Some of them are universal studies and some of them are not. When I read the credentials I understood that the grades in Atmospheric Physics, Theology and Philosophy are official.
Now, someone here told me that the universities where she got the grades in Theology and Philosophy are not regocnized in some states. He showed me some sites. I didn't really understand those sites but I think he told the truth by saying that these universities aren't regocnized by some states.
My opinion about this case is that only because a school is not regocnized by some states doesn't mean that you don't learn anything during your studie at that university. As far as I know, after reading his post, there are only a few states that don't recognize the universities. So most states DO recognize that universities. Because of that I think she has the right to say that she holds a doctorate in Philosopy an Theology. As far as I know from the most states do.
You seem quite reasonable to me. I also find it very fair that you say science isn't perfect...
About the experiment.I don't thinkt this is a fair, and an accurate experiment to test for the ability of seers to see the auras, and therefore that the aura exists.
The seers could make appointments with eachother.
For example thay can say...If the person has blond hair and wears glasses, we say that the person his aura is torned on the left side. If the person is a man and is bold, his aura is red, with a lot of grey and green. Ore they could say, if the person has brown eyes his aura is very large and bright...
And so they could make many appointments.
And if no one nows this, it seems to be that they ARE able to see aura's.
So, this test would be worhtless if you want to prove that some people can see aura's and that the aura exists.
I hope I have made my point claar about this
Marlon
First, can I apologise for getting your name wrong in one of my answers. The font I was reading this in at work wasn't that clear.
OK: About your answer concerning the experimental design. Yes, the experiment is flawed as it would permit the seers to cheat. However, it's actually much worse than that.
In the initial stages where the seers are agreeing on everything and checking out each other's abilities, there is the possibility that they could agree to cheat. But, a far more subtle problem is that the seers might adjust their decisions to be consistent without realising it. Hence, there would be no concious cheating, but an unconcious cheating. I think it's important to consider the possibility that this unconcious agreement is a potential cause for consistency.
I believe that it's problems like these that cause a lot of the problems between "scientific" and "alternative" types. Imagine this scenario: the three seers spend quite some time together, and without realising it, start to synchronise their predictions. "hmmm... both A and B say the aura is detached here, is there something that I'm missing ...". They perform the experiment, and consistency is found. Then, someone accusses them of coming to an agreement ahead of time, i.e. cheating. The seers know that they haven't (conciously) cheated, and hence their beliefs in their ability to see the aura are strengthened even further, as they're being told that they "must have cheated", but they know that they didn't. Hence they are now *really sure* that they have the power. That such implicit effects can occur seems reasonable given the research into the necessity for double blind (not just single blind) experiments.
In terms of science being imperfect. I work at a uni myself both teaching and researching. About two years ago I decided to "upgrade" my knowledge of stats and experimental design. Hence reading books such as "Methodological errors in medical research". What I'm slowing coming to understand is how poor people's abilities are in designing and interpreting experiments in quite a number of fields. Problems in medical research are better known than most, because of the importance of medical research being correct. Even then I've just been reading how hospitals have been using medicines to prevent heart attacks which the research suggests will increase the survival rate. Except that it isn't, and poor research is quoted as the most likely cause. In other sciences, there is much less pressure to ensure that research is actually accurate, and I personally believe that there are "fields" of science where much, if not most, published research is unreliable.
I'm not claiming that I'm good at stats (yet). But, in my field, I seem to be in the situation where I know that I'm not yet really good enough, but I'm better than (it seems) many other people. This is scary.
Cheers,
Ross-c
I realy don't matter you got my name wrong. That can happen to anyone.
I find the things you have written very interesting. I can learn something from you. I will read it again. Hopefully we can all learn something from eachother.
Thank you,
Marlon
"You ("skepps") say that the " believers" are avoiding evidence etc. but in much cases (and also in this case) I notice that the "skepps" are avoiding things!"
Yes, we try to avoid false statements of facts and making irrational arguments.
She says, "You only respond on the "lacks" in our stories. You don't see the story as a whole and don't look at our whole experience."
A premise based on false facts is not a true premise. A belief based on error is in error. A belief based on a lie is a lie. Marlon's solution for avoiding reality is to look past contradictory facts in order to embrace the conclusion she wants to believe.
Marlon continues: "That's the problem with the whole world. A lot of times we are focused too much on details. Focussing on details is oke but not at te cost of our picture of the whole. In my opinion everything would change if we would concentrate more on the whole."
By "details" Marlon means "facts." When facts get in their way of our beliefs, she says we should look past those troubling facts and just embrace the beliefs.
She then offers us this falsehood: "If we give then thousend reasons why we believe or know that the paranormal excist, you find that reason that is the 'weakest' in your opinion."
Marlon hasn't been listening. Skeptics have not been asking for a "thousend reasons," they've been asking for at least ONE sound piece of evidence to prove the existance of the paranormal. Not thousands. Even just one piece of evidence that can stand up to rational examination and be verified would do it. What we get instead are thousands of flimsy claims, testimonials, pseudoscientific experiments, outright fraud, covered with a myriad of excuses and obfuscations. What we want Marlon is ONE. Not thousands. Just one. Give us your best. We don't want you're "weakest." Give us one irrefutable piece of convincing evidence.
Marlon does not understand why we're asking for this, because she believes the paranormal is real. For her, belief comes first, and evidence is just the icing you put on the cake. "I am sure it excists," she says. And for her, that's all that counts.
Sorry, Marlon, that's not good enough. If we stuck with beliefs instead of facts and reason, we would still be fighting smallpox by casting out demons and burning witches instead of finding out the true cause of the illness and then eliminating it from the world.
Marlon says, "Reality has everything to do with experience. In kind of a way everything you experience is reality. We shouldn't focus so much on whats real and what's not."
I remember "Son of Sam" (David Berkowitz) who experienced voices from his neighbor's dog commanding him to shoot and kill young women and their boyfriends who were necking in their cars. Wow! I guess those voices must be real afterall. In this case, I think we need to set David Berkowitz free.
All in favor say, "Aye! I'm crazy too."
Cranky Media Guy, Marlon doesn't even have a pair of deuces in her "hand." But she believes she's holding the winning hand and, in her view of reality, a good belief will trump any real hand of cards. It is because she wishes it to be. She makes her own reality simply by believing it so. Don't you wish you could do that?
That's not what I said. I said those "universities" are non-accredited diploma mills and the degrees they offer are bogus.
And she says, "I didn't really understand those sites but I think he told the truth by saying that these universities aren't regocnized by some states."
The only reason she doesn't want to "understand those sites" (which are simply lists of schools offering bogus degrees that are posted on Michigan and Oregon state web sites) is because they contradict her "reality." Marlon is never interested in any truths if they disagree with her beliefs. And it comforts her to believe that her teacher has doctorate degrees in theology and in philosophy and that the B.A. degrees her teacher's school offers are also real. Any honest, rational person would be troubled to learn that their teacher's credentials are bogus. But Marlon is never troubled by facts, when she's got her beliefs to keep her happy.
"Cranky Media Guy, Marlon doesn't even have a pair of deuces in her "hand." But she believes she's holding the winning hand and, in her view of reality, a good belief will trump any real hand of cards. It is because she wishes it to be. She makes her own reality simply by believing it so. Don't you wish you could do that?"
Yes and no. Yeah, it's tempting at times to wish that I could believe in stuff just because I want it to be real. After all, I had 12 years of Catholic school; I was taught a LOT about things that don't have any basis in fact. I confess that there's a (small) part of me that might wish that I could just turn off the section of my brain that says, "Oh yeah? Show me!"
The thing is, though, that I just don't want to be a "mark." I see so much in contemporary life that's based on lying to the public at large. I see intelligent people actively working at suspension of belief so that they can rationalize their political convictions. It's sad and, I believe, dangerous for society to ignore reality. That way lies madness and collapse. Nazi Germany was based, in large part, on unsupportable beliefs.
Ever seen the play, "Rhinoceros?" The protagonist, whose name I forget, finds everyone around him turning into a rhino (I'm told it's supposed to be a metaphor for Nazism). Part of him wants to conform but he just doesn't have it in him to be a rhino too. I don't mean to sound pompous, but sometimes I feel like that.
My local Fox TV affiliate lead their 10 o'clock news the other night with a "story" about a local "psychic" who said that a missing woman was buried in a shallow grave in a wooded area! Uh, you know any murdered people buried in a DEEP grave in the middle of town? This is especially sad when you know that a majority of Americans say that they get all or most of their news from local TV newscasts. I just don't want to be one of the rhinos who believe in "psychics."
Cheers,
Ross-c
Ross-c and I discussed last week some of your earlier posts concerned with calculating the probablities of the matching problem. We concluded that the probabilities had been slightly miscalculated.
Are you able to state exactly how the probabilities were calculated?
In any case, the variations in numbers are small. I think it's important not to get too mired in the details and lose sight of the big picture.
Cheers,
Ross-c
I think we simply used accurate computing methods that the testers did not. It's fairly clear, from Slotnik's earlier postings, that they used another less accurate approximation to arrive at their numbers.
The only question is: what was that approximation method? And why did they use that rather than compute the figures accurately?
And I think the little details are part of the big picture.
"The problem we are dealing with is known as the matching problem. The mathematics for calculating the correct odds is not self evident. Indeed, it is very complicated. I painstakingly worked out the correct probabilities using the formulae in Frederick Mosteller's Fifty Challenging Problems in Probability With Solutions. I believe this is still available from Dover Books. The critic might find it useful to carefully follow the argument in this book. My other source was Hoel, P.G., Port, S.C., and Stone, C.J. (1971). Introduction to Probability Theory. This latter source provides some useful approximations for those who do not have the patience to calculate the exact probabilities. Richard Wiseman was able to check my probability calculations using tables provided by the Journal of the Society for Psychical Research. Our probabilities agreed."
What earthly reason are you obsessed with the minor difference between the approximate odds Profs. Hyman and Wiseman calculated using tables published in books and the more precise odds you calculated by brute force using a computer? A difference that makes no difference is no difference. Would you critize someone for using 3.14 instead of 3.141159 to calculate the circumference of his swimming pool?
If as you say the little details are part of the big picture, why should anyone trust YOUR comments. Not only did you mispell my name, you mispelled it again when correcting your error! It's Skolnick.
I only counted to e.
I wouldn't call it a 'brute force' method. It's the method outlined in your earlier postings, but dismissed as 'unwieldy' (which it is, performed manually). I think Puck upthread used a brute force method - of generating 10 million answers and scoring them - in order to arrive at answers less accurate than mine and Ross's.
But in answer to your question, I guess I'm puzzled why approximate probabilities were calculated using what appear to be 35-year-old pre-computing methods, rather than accurately calculated with a computer. Are the professors unaware of such computing solutions? It doesn't take long to write the program.
Natasha's was a high profile case, with a TV programme to go with it. Pretty big bucks, I'm sure. In those circumstances it would appear appropriate to have allocated a few bucks to get some bullet-proof mathematics - particularly for a test that principally depended upon calculating probabilities. Or put it this way: I think that an an extraordinary case demands extraordinarily accurate mathematics.
A Skolnick wrote: "A difference that makes no difference is no difference. Would you critize someone for using 3.14 instead of 3.141159 to calculate the circumference of his swimming pool?"
Well, I might criticize.
But why, if "a difference that makes no difference is no difference", did you bother to correct your slightly incorrect value for pi? If it made no difference, why correct it?
A Skolnick wrote: "If as you say the little details are part of the big picture, why should anyone trust YOUR comments."
There's no need for anyone to trust me. It's not me who's just spent thousands of bucks running a televised high profile test, without having bothered to accurately work out the fundamental probabilities involved.
It's like someone all dressed up smartly for their wedding, but with a gravy stain on their necktie. Sure, it's a minor detail. No part of the big picture. Most likely nobody, least of all the mother-in-law, will notice.
It's true that the difference in probabilities is very small, and does not affect the result. It is easy for scientists to know that the difference in probabilities is very small, but this is beyond the understanding of much of the general public. All they know is that someone is pointing out that "the scientists got it wrong" in some small detail, and this is something for proponents of pseudoscience to start working on. (Piltdown man is still quoted by creationists). Any excuse that can be pounced on to allow them to maintain their beliefs seems enough. To debunk pseudoscience, the debunking needs to be more than just "good enough" but damn near perfect.
I am concerned about the use of tables that gave an approximate result. The alternative method (I posted a link earlier on) which calculates the probabilities exactly would be easy to complete by hand by anyone using a calculator with a factorial button. Mathematically, the differences to be a non-issue, I would still like to know why tables were used. It allows people to start quibbling about details, and quibbling about details has a risk of burying the main point.
I would like to ask whether the people who designed the experiment are aware of (and the need for) such things as p-value adjustment, and the situations where bayesian statistics suggests that the confidence suggested by "standard" statistics are unreasonably high. I personally think that there is grave risk that debunking is going to be counter-productive for the following reason: No matter how good the statistical experiment, there is always a non-zero chance of the wrong result occurring by chance. Natasha could have been 100% correct by random chance. If the paranormal is tested over and over and over again, then eventually one trial will come up supporting the paranormal. And when that happens, the single result will be trumpeted far and wide by paranormalists, and the other experiments conveniently forgotten about. This can happen even with properly designed and analysed experiments.