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Finding evidence for the paranormal is easier if you believe it exists. Believers are happy to accept this, but to sceptics it smacks of chicanery. Is this parapsychology's final battleground, asks John McCrone
IF YOU have ever had that creepy sensation of being stared at from behind, then you know what some of the subjects in Richard Wiseman's lab are feeling right now. Sitting in a soundproofed room with their skin wired up to an arousal monitor, they know that for some of the time someone may be staring at them via a CCTV link. The question is: are the subjects subconsciously aware of when they are being watched?
Wiseman, a psychologist at the University of Hertfordshire in Hatfield, UK, doesn't think they do. He's been doing experiments like this for years and he always gets nish, nada. But his co-worker, parapsychologist Marilyn Schlitz of the Institute of Noetic Sciences in Petaluma, California, begs to differ. When she does the experiment, she usually gets a slight, but significant, positive result. And so the two have set out to resolve the discrepancy in a head-to-head showdown.
It sounds like just another investigation into the paranormal, but the Wiseman-Schlitz study represents something of a watershed. The sceptic-versus-believer experiment is designed to nail down one of parapsychology's longest-standing controversies, the "experimenter effect". This is the curious phenomenon whereby the outcome of an experiment hinges upon the beliefs of the person running it. Believers tend to get positive results. Sceptics don't.
The results will be available later in the year. But arguably it's not so much the outcome that matters as the fact that the study is taking place at all. The experimenter effect is the skeleton in parapsychology's cupboard. Parapsychologists once saw nothing wrong in using it as an excuse for ignoring inconvenient experimental results. Some even argued that the fact some experimenters got results and others didn't was proof that psychic powers (or "psi") existed. But about 20 years ago, parapsychology researchers agreed to stop invoking the experimenter effect, aware that it was undermining their attempts to prove the existence of the paranormal. It simply made it too easy to dismiss studies that didn't get results, and concentrate on the ones that did.
Yet parapsychologists are increasingly bringing the experimenter effect back into the debate. The inescapable fact, they say, is that it is there in the data. Whatever kind of experiment you run, whether into extrasensory perception or telekinesis, believers get results and sceptics don't. "In my opinion, the strongest predictor of ESP results generally is the identity of the experimenter," wrote parapsychologist John Palmer of the Rhine Research Center in Durham, North Carolina, in a recent special issue of The Journal of Consciousness Studies (vol 10, p 57).
The experimenter effect itself is now an object of intense research. As well as the flagship study of Wiseman and Schlitz, almost every other parapsychology researcher is conducting some kind of test. There are also new explanations of the experimenter effect on the table. Some parapsychologists claim that it arises not through the experimenter's influence over mind or matter, but because they use their extrasensory powers to pick the right moments to sample a fluctuating process and catch any fluky, but natural, departures from randomness.
The return of the experimenter effect is leading some sceptics to claim that parapsychology has been unable to produce convincing data and so is regressing back into the pseudoscientific dark ages. But supporters of parapsychology turn that reasoning on its head: there is an experimenter effect, they say, and the imperative is now to explain it. So after a period of uneasy accord during which the two sides have worked together under mutually acceptable rules, a new schism is developing.
Until about 20 years ago, the experimenter effect was an integral part of parapsychology, along with a number of other slippery concepts that seemed to capture the weak and erratic nature of the phenomena. A run of good results seemed to be followed by a run of bad, almost as if the odds wanted to right themselves, an effect parapsychologists dubbed "psi decline". Then there was what is known as "psi missing", where post hoc analysis of results revealed that the subject kept missing the target by a slender margin. For example, in an ESP test in which the subject had to guess the suit of the card that the experimenter was looking at, they would consistently say "heart" on the turn just before or just after a heart turned up. And then finally there was the experimenter effect - the feeling that belief matters in getting positive outcomes. Some parapsychologists even complained that having a doubter visiting the building seemed to spoil their day's work.
In the 1970s, parapsychologists such as Adrian Parker, now at the University of Gothenburg in Sweden, began running studies to see if the experimenter effect might be genuine. For example, he recruited students as experimenters and then briefed them to expect either positive or negative results from a test. "It seemed completely logical to us that if psychic powers existed, then there must be the possibility of an experimenter effect. So it was obviously something we needed to get a handle on," Parker says.
But in the 1980s the field changed tack. After years of rancour in which sceptics and believers stood on opposite sides of a divide, it was agreed that the only way forward was to establish some mutually acceptable standards. Sceptics agreed to ditch their presumption of artefact or fraud whenever a positive result came in; in return, parapsychologists agreed to drop all forms of special pleading, and concentrate on getting replicable results. No single experiment could be trumpeted as proving the existence of psychic powers. And the same experiment would have to keep producing results no matter who was running the show - sceptic or believer.
This, of course, meant sacrificing the experimenter effect. Parapsychologists had to rely on the fact that if the experimental designs were sufficiently robust and enough different experimenters were involved in their replication, they wouldn't need the experimenter effect to get positive results. The presence of doubters might water them down, but should not eliminate them.
Parapsychologists took other healthy steps. Led by the example of the Koestler Parapsychology Unit at the University of Edinburgh, UK, there was a broadening of the remit to take in the "psychology" of parapsychology in general - normal, rational psychological explanations for why people might believe in the paranormal, or be fooled into believing in it. In this way, parapsychologists could come to be their own best critics, able to separate what might be true from what was mere wishful thinking. Psychologist Matthew Smith at Liverpool Hope University College in Liverpool, UK, says this mixed approach has made parapsychology more academically acceptable in the UK and Europe over the past decade, and a routine part of many psychology departments. "It has become a popular option for third-year students," Smith says. "Because issues like statistical artefact are such a concern, they can learn a lot about what is needed to do science rigorously."
So what has all this rigour done for the status of parapsychology? As usual there is no consensus. Believers claim the results show there is an effect, sceptics say they don't. The major battles have revolved around meta-analyses that blend all the studies. Wiseman and Julie Milton, then of the University of Edinburgh, did one on an ESP technique called ganzfeld (see "What is psi?") that showed no significance for some 30 combined studies, run by both believers and sceptics (Psychological Bulletin, vol 125, p 387). But the believers came back at them, saying they omitted a couple of recent, highly significant studies they knew about but left out by setting the cut-off date conveniently just before them. So it is now a matter of whose meta-analyses you want to believe.
What everyone agrees, however, is that there is an experimenter effect in the pattern of results. Believers are somehow making their experiments work - the question is how.
This is where the Wiseman-Schlitz experiment comes in. While they are not happy to see it portrayed as a battle between sceptic and believer - Wiseman says they are merely two experimenters with different track records - others see it as a test case for the idea that belief alters results. The experiment itself is simple. Subjects sit in an isolated room hooked up to electrodes which measure their arousal levels through slight changes in the sweatiness of their hands. In another room, the experimenter can see the subject on a CCTV. The experimenter's job is either to stare at the subject, or look away, according to a random 16-minute schedule divided into 30-second blocks. The hypothesis is that if the subjects know they are being stared at, they should show a detectable shift in physiological arousal during the times they are under surveillance.
Schlitz and other parapsychologists have been claiming small but statistically significant results from this experiment for more than a decade. In the mid-1990s, Wiseman - who was a professional magician before becoming a psychologist - thought he would have a crack at the same experiment. He says the set-up was attractively simple and the claimed results sounded clear-cut. But when he ran the experiment in his own lab, he got nothing.
The story might have ended there had Wiseman and Schlitz not met and found they liked each other enough - and trusted each other enough - to carry out a joint study. And so for the past eight years, Wiseman the sceptic and Schlitz the believer have been doing the remote-staring experiment while swapping labs and sharing subject pools. "Richard probably wanted to find the ways I was cheating or whatever," Schlitz laughs. "But I think he was genuinely curious also."
First Schlitz came to Wiseman's lab in Hertfordshire. Each tested 16 subjects, mostly undergraduate psychology students. Wiseman got results that were flat chance; Schlitz reported a positive outcome, though these were on "the very knife-edge of significance", as Wiseman puts it. Then Wiseman flew over to Schlitz's lab in Petaluma to repeat the experiment, this time with subjects who were using the institute as a New Age retreat. The result was the same - nothing for Wiseman and knife-edge significance for Schlitz.
Statistical power
Which brings us to the present day. It was clear the study ought to be repeated with a much larger number of subjects so as to give it real statistical power. But just as importantly, Wiseman and Schlitz needed to separate two possible sources of any putative experimenter effect. Does it come from the experimenter's psychic ability, or is there another explanation?
As even the proponents of psychic powers point out, non-psi factors could bias the running of the experiment. Faced with a cold and sceptical experimenter, apparently doubting that the study is going to produce any results, perhaps subjects are inhibited in some way. Conversely, a "psi-conducive" experimenter could be one who conveys the necessary warmth and belief to allow shy psychic abilities to flower in a laboratory setting. "These experiments can be long and tedious, so it's quite plausible that even if I tried to conceal my feelings, my boredom might still show through and affect the attitudes of subjects," Wiseman admits. "Marilyn is naturally much more enthusiastic and positive in her interactions with the subjects."
So in the latest study, due for completion this spring, the duo are splitting the "meet-and-greet" from the experimental phase. On some trials one will do both the introductions and the remote staring. On others, they will divide the jobs between them. As a further measure, the interactions between experimenters and subjects will be video-recorded, then later independently rated for factors such as warmth. With this careful crossover design, and more than 100 subjects involved, the source of any experimenter effect should become clearer.
Of course, the two possible sources of the experimenter effect rely on the existence of paranormal powers. But it's hard to know where else to turn: even Wiseman accepts that there is an unexplained experimenter effect in the results to date. Naturally the sceptical camp is hoping the new study simply finds no sign of an experimenter effect. Or perhaps that some statistical artefact will be unearthed to explain it.
Another "out" for sceptics is always going to be fraud. Some minor concerns about the statistical analysis and security precautions in the earlier Wiseman-Schlitz studies have been addressed in their latest experiment. However, Wiseman stresses that none of the concerns were major issues.
"It is a basic misunderstanding that I'm here as the sceptic to be the policeman watching Marilyn," he says. "It doesn't work like that. We take reasonable precautions in the experiment, but nothing extraordinary." Wiseman says the answer to all concerns must, as always, lie in replication. "If it is only us that gets this weird result, then it is uninteresting," he says. "Other pairs of sceptics and believers would have to work together and find the same thing happening before we could get too excited."
Whatever the outcome of the experiment, the resurgence of the experimenter effect is contributing to a new schism in parapsychology. On one side are those like Wiseman who feel that what has been proved is that psychic powers do not exist - or more accurately that, because you can't prove a negative, the null hypothesis still holds. He says every time a new kind of experimental design comes along, at first it gets good results, invigorating the field, and then these results fade away. Wiseman says either the procedures get tightened up, ruling out artefacts, or perhaps the first results are just an honest statistical fluke that cannot be repeated - a kind of "file drawer" effect in which experimenters have a go at a great many different parapsychology tests, but only report the ones where chance guessing seems to produce a significant result.
But on the other side are those like Parker who argue that psychic powers are real and the experimenter effect is part of them. Parker feels it may well be time to leave the doubters behind, take the existence of psychic powers as sufficiently proved and turn scientific attention to the finer details of how they work.
So, as usual, there are no black-and-white answers in prospect. In many ways, it is the sceptical community that is on the back foot, unable to explain away the results in terms of cheating, artefact or fluke. They are back to making suspicious noises about why believers get results. But there are downsides for the parapsychologists, too. By turning the spotlight back on the individual experimenter, they are again inviting the old accusations of methodological incompetence and fraud.
Ultimately, the real loser is the delicate accord that was struck some 20 years ago, when sceptics and parapsychologists agreed how the field should be run. That agreement at least gave us some hope of a definitive answer. Without it, one way or the other, the world again becomes divided by a question of belief.

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What is psi?
Paranormal powers can be divided into two types. One is extrasensory perception (ESP, also known as telepathy), which is the ability of two minds to communicate through an unknown channel. The other is telekinesis, the ability of minds to affect matter. Attempts to prove that these powers exist usually use one of three basic experimental designs.
Micro-PK is a test of telekinesis - PK stands for psychokinesis. Early studies focused on moving large physical objects, such as a suspended metal strip. Most experiments now concentrate on microscopic events such as the random white noise produced by a diode transistor, or the diffraction patterns of beams of photons. Subjects view the output of the particular random event generator on a computer terminal and try to "bend" the flow of events away from chance.
Results: Many experimenters fail to show an effect. Those that do typically report only the smallest deviations from chance - but because millions of events are involved, the results are claimed to be statistically significant.
GANZFELD - German for "whole field" - is a test of ESP. A subject sits in a state of isolated sensory deprivation, eyes covered, white noise playing in headphones, in the hope of maximising sensitivity to any psychic signal. In another room, a sender views one of four randomly chosen video clips played repeatedly for 30 minutes. Afterwards, the subject views all four possible clips and picks the one closest to any mental imagery experienced during sensory deprivation.
Results: The subject has a 1-in-4 chance of guessing right, so should average a "hit rate" of 25 per cent. The latest meta-analysis of 40 studies claims an overall 30 per cent hit rate - a significant result. But other meta-analyses conclude that the results are within the bounds of chance.
DIRECT MENTAL INTERACTION WITH LIVING SYSTEMS (DMILS) investigates both ESP and telekinesis. It is a general term for attempts to use a mental connection to influence a distant biological system. This could be causing changes in the physiology of another person, as in remote-staring experiments, or affecting the growth rates of seedlings and yeast cultures. Statistics are used to contrast effort versus no-effort trials. Proof would be taken as evidence for psychic healing.
Results: Latest survey of 40 remote-staring studies reports a small, yet significant deviation from chance. But when only the seven "highest quality" studies are considered, the positive effect disappears.

SCEPTICS and believers alike have been struggling for more than 100 years to show whether or not psychic powers exist. Yet still there is nothing even approaching a definitive answer. You might have imagined that a century of work would have led somewhere, so why don't we know?
One obvious conclusion is that there is simply nothing to find. Yet that does a disservice to the parapsychologists and their results. Over the past 20 years, they have made real efforts to meet the sceptics' criticisms, designing carefully controlled experiments, carried out under conditions acceptable to scientists (see "What is psi?"), in a genuine attempt to resolve the issue. And many of their experiments have produced results that, on the surface at least, look impressive.
Yet still there is no progress. Yes, there are positive results - but there are negative ones too. Overall, it's hard not to conclude that this mixed bag of data has had little effect other than to fan the flames of debate.
One of the thorniest issues is that of replicability. The ability to repeat an experiment would seem to be a reasonable thing to demand of a field that aspires to scientific respectability. But even replicability has proved a slippery and controversial concept.
Many sceptics argue that only "replication on demand" can provide conclusive proof of the paranormal. Parapsychologists, however, have successfully argued that "statistical replication" is good enough - that the effect should be replicable more often than you would expect by chance, as revealed by a "meta-analysis" of all the available data.
In practice, however, meta-analysis has failed to produce a consensus, largely because its methods contain so much room for manoeuvre. Take a widely used experimental technique in ESP research called ganzfeld, for example. Between 1995 and 1999, approximately 30 ganzfeld studies were carried out. The results from these studies have been subject to four different meta-analyses. Two conclude that the findings are significant; two that they are not.
Why the discrepancy? There are many minor differences between the four analyses, but one stands out above others: whether or not to include a hugely successful study carried out in 1997 by Kathy Dalton of the University of Edinburgh in the UK. Two meta-analyses left it out on the grounds that its results were so much better than any others that the study should be discounted as an outlier - an acceptable practice in meta-analyses. The other two included it on the grounds that meta-analyses must use all the data - again, an acceptable practice. No prizes for guessing which analyses came to which conclusions.
Another typical episode concerns the work of Robert Jahn of the Princeton Engineering Anomalies Research group at Princeton University. For more than 20 years he has been carrying out research into "micro psychokinesis", where subjects attempt to influence the output of a random event generator to produce statistically significant deviations from the expected output.
Jahn's analysis of his entire data pool for the past 12 years is difficult to argue with. Subjects seem genuinely to succeed in nudging the random number generator in the desired direction. Jahn concludes that the probability of getting the same results by chance are less than 0.00007 - a hugely significant result. And critics struggle to find holes in the methodology or the data.
But attempts to replicate the results have failed. Physicist Stanley Jeffers of York University in Canada tried to do so using a different type of random event generator and got nothing. Jahn himself, in collaboration with German researchers, has tried and failed to replicate the results.
So where do we go from here? Many parapsychologists believe their discipline as presently practised has reached an impasse. They claim that the failure of replication should be taken as a positive result because it confirms what they knew all along: paranormal phenomena are inherently elusive and you can not expect to pin them down in the lab. And increasingly they are reviving pseudo-scientific concepts to explain their data. As a result, the delicate accord of the past 20 years is feeling the strain, as John McCrone discusses on page 34.
Other observers argue that what has been proved is that the debate over parapsychology is inherently intractable. Gathering yet more data will only lead to more controversy, and so is pointless. But there is something positive to be taken from this conclusion, as Robert Matthews argues on page 38: the past 20 years of "scientific parapsychology" have taught us about the limits of science itself.

Opposites detract

Strong scientific results are supposed to build consensus, but the maths of belief is perversely paradoxical. The better the evidence for ESP gets, the harder opponents dig in their heels, argues Robert Matthews

SO, YOU think you are rational, dispassionate and swayed only by hard evidence? Then try this little test. Last September two teams of respected scientists unveiled the outcome of research to prove the effectiveness of two very different agents. One team reported a powerful effect, much larger than expected by chance alone; the other could only muster an indifferent result with borderline significance. Which of these do you find the more convincing proof?
Most of us would view this as a no-brainer, and cite the first. But you probably sense a trap and would like to know more before deciding.
The weak result came from an international team of medical scientists studying a new drug aimed at reducing the chances of recurrent heart attacks. They found that the odds of another heart attack fell by just a few per cent, barely better than the reduction expected by chance alone. The far stronger finding came from a team at the Koestler Parapsychology Unit at the University of Edinburgh, UK, and seems to support the existence of extrasensory perception (ESP).
Still feel happy to put your trust in hard data? Or do you find yourself reaching for all kinds of reasons why, in this case, the experimental results alone just aren't enough to assess the merits of a scientific finding?
If so, you're in good company. For years, well-designed studies carried out by researchers at respected institutions have produced evidence for the reality of ESP. The results are often more impressive than the outcome of clinical drug trials because they show a more pronounced effect and have greater statistical significance. What's more, ESP experiments have been replicated and their results are as consistent as many medical trials - and even more so in some cases (see Chart). In short, by all the normal rules for assessing scientific evidence, the case for ESP has been made. And yet most scientists still refuse to believe the findings, maintaining that ESP simply does not exist.
Despite this relentless rejection of their work, parapsychologists such as those at the Koestler unit have ploughed on in search of clinching evidence they hope will convince the scientific community. Some believe it is a waste of time because the reality of ESP has now been put beyond reasonable doubt. Sceptics agree it is fruitless, but on the grounds that since ESP cannot exist, all positive results must be spurious. How has such a split arisen? After all, scientific evidence is supposed to drive everyone towards a single view of reality.
Over the years, sociologists and historians have often pointed out the glaring disparity between how science is supposed to work and what really happens. While scientists routinely dismiss these qualms as anecdotal, subjective or plain incomprehensible, the suspicion that there is something wrong with the scientific process itself is well founded. The proof comes from a rigorous mathematical analysis of how evidence alters our belief in a scientific theory. And it is not so easy to write off.
Its starting point is a profound result derived independently by the mathematicians Frank Ramsey and Bruno de Finetti in the 1930s. They showed that you can assign a number to the touchy-feely concept of belief using ideas drawn from probability theory. In particular, they proved that your faith in a theory can be quantified objectively on a scale ranging from near 0 for disbelief to near 1 for certainty. They also showed that scientific reasoning is logical provided your beliefs follow a rule known as Bayes's theorem.
Widely used in probability theory, Bayes's theorem shows how the chances of an event happening change in light of developments, such as the odds of a horse winning a race given that it won its last one. Ramsey and de Finetti showed that exactly the same rule applies to updating belief in a theory as new evidence comes in. The good news is that their rule is very simple: just take your original level of belief and multiply it by the strength of the new evidence, as captured by the so-called likelihood ratio. This gives the relative probabilities of getting such evidence if the theory is true, compared to if it were false. The likelihood ratio is large if the findings are consistent with theory, thereby boosting your level of belief in it.
But there is a nasty surprise lurking in the Ramsey-de Finetti analysis. How do you arrive at that original level of belief? In many scientific studies, there is a wealth of insight and evidence on which people can base their prior level of belief. But in novel or controversial areas of research, such as the paranormal, there isn't. And in those cases, it can only be based on gut feeling, instinct and educated guesses. In other words, it is entirely subjective.
This disturbing conclusion seems utterly at odds with the conventional view of science. Every week, research journals publish hard evidence supporting a host of theories, backed by statistical arguments for taking it seriously. Bayes's theorem implies that this whole process is nothing more than an elaborate attempt to dodge the subjectivity at the root of every scientific result.
While this prompts outrage among defenders of the scientific faith, many working scientists acknowledge that subjectivity plays a big role in their day-to-day thinking. Behind closed doors they routinely dismiss claims for, say, some new link between cancer and diet, simply because they find it implausible.
Nor is such prejudice the preserve of the life sciences. Even theoretical physicists routinely resort to subjective arguments to see off awkward results. Hearing that his new theory of special relativity had lost out to rival theories in its first experimental test, Albert Einstein simply brushed the evidence aside, arguing that the other theories were less probable.
Whether they realise it or not, scientists' thinking is influenced by Bayesian reasoning, and nowhere is this more apparent than in attitudes towards ESP research. By the standards of conventional science, the weight of evidence is now very impressive, but the scientific community refuses to accept the reality of ESP. Instead, they insist that extraordinary claims demand extraordinary evidence.
This is the perfect example of Bayesian reasoning. But who decides when an "extraordinary" level of evidence has been reached? It is something that can, and clearly does, mean different things to different people. Ultimately, it is not strength of evidence, or lack of it, that has been at the heart of the controversy over ESP. Yet the response of sceptics has been the same: whatever was responsible for the positive findings, it cannot be ESP. Something else must have happened: some flaw in the experiment, say, or a slip-up in the data analysis. Perhaps even fraud.
It is a response that provokes understandable resentment among parapsychologists. They complain that exactly the same approach could be used to reject unwelcome findings in any other field of science. It is too easy, they argue, for critics to dream up endless ways to explain positive ESP findings. Sceptics, meanwhile, insist it is only right to eliminate every alternative explanation before reaching a final conclusion.
Bayes's theorem shows that both camps are right. But it also reveals another disturbing fact: wrangling over alternative explanations can never be ended objectively. The reason is that every attempt to test a scientific theory involves a slew of "auxiliary hypotheses" - assumptions made about the design of experiment, the data analysis, and even the mindset of the researchers. For instance, medics confronted with the results of a clinical trial they find implausible routinely check the researchers' affiliations to see if they have a reasons to show the results in a particular light. And perhaps this is justified, given that academic studies funded by industry are more prone to producing positive findings (New Scientist, 1 February 2003, p 8). If the medics do suspect that the research findings are skewed, they will water down their faith in the results no matter how statistically significant they may be.
Never the twain shall meet
In the case of ESP research, the mindset of researchers has become a key issue (see "The power of belief"). Some studies suggest believers are more likely to get positive results than sceptics. For sceptics, this is proof of the auxiliary hypothesis that they insist explains all evidence for ESP: slipshod or dishonest practice by true believers hell-bent on proving their case. Others, however, see it as just another case of an intriguing effect that has been observed in many other areas of research.
Even so, it is only after all these alternative explanations have been dismissed that researchers can claim their results have been vindicated. Once again, the Ramsey-de Finetti analysis provides a mathematical rule for deciding when it is safe to say that evidence best matches the theory under test, rather than some auxiliary hypothesis. The bad news is that the rule demands estimates for the plausibility of competing explanations, which is again subjective.
The worst suspicions of parapsychologists are thus entirely justified. It is impossible to find evidence for ESP that will win round the sceptics. But those who see this as final proof of the futility of parapsychology should ponder this: exactly the same holds true for all scientific research. There are always auxiliary hypotheses, and deciding whether the evidence backs them or the theory being tested is just a matter of judgement.
The famous criterion of "falsifiability", the notion that scientific theories can never be proved, only disproved, is therefore a comforting myth. In reality, scientists can (and do) dream up ways to explain away awkward findings. The only difference with parapsychology is that scientists have no qualms about invoking everything from incompetence to grand conspiracy to explain the results.
It therefore seems that all that parapsychologists can do is collect ever more evidence, in the hope of gradually persuading more scientists of the reality of ESP. In this, they are appealing to one of the central tenets of the scientific process: that as more evidence builds up, the case for a theory becomes ever stronger. Yet the mathematics of scientific inference reveals even this to be a myth.
Bayes's theorem shows that belief in a theory increases with the strength of evidence. Mathematically, this is captured by the likelihood ratio (LR) - the likelihood of getting such evidence if the theory is true, compared to if it were false. So, for example, if the evidence is 10 times as likely to emerge if the theory is true rather than false, the LR is 10, and belief in the theory increases tenfold. If, however, the evidence is twice as likely to emerge if the theory is false, then the LR is 0.5, and the level of belief is halved.
All of this is perfectly reasonable - except how do you convert raw data into the all-important LR? The answer is, there is no hard and fast rule. It is yet another occasion for judgement, opinion and educated guesswork. Subjectivity has once more reared its head, and this time it undermines the most cherished principle of the scientific process: that, in the end, the accumulation of evidence ensures the truth will come out.
Once again, parapsychology provides an important lesson. Over and over again, reputable researchers have found strong evidence for the existence of ESP in tightly controlled experiments. Many would conclude the evidence is more consistent with the existence of ESP than any other explanation, such as sloppy methodology or fraud. As such, the LR is a large number, and should greatly increase belief in the existence of ESP - or so the parapsychologists would argue.
Sceptics, on the other hand, claim that pretty much any explanation for the evidence is more plausible than ESP, so the LR is far less than 1. So any fresh evidence actually reduces their belief in ESP.
The upshot could hardly be more different from the standard view of the scientific process. Both camps can look at precisely the same raw data and legitimately reach utterly different conclusions, because they have radically different models for the cause of the data. One camp insists that the results are more plausibly caused by of ESP than anything else; the other camp simply does not agree.
It gets worse. As the evidence accumulates, the two camps will not only fail to reach consensus but actually be driven further apart - propelled by their different views about the LR. And worst of all, there is no prospect of such a consensus unless the two sides can agree about the cause of the data.
Does the evidence accumulated over all these years prove the existence of ESP? By now, it should be clear that there is no objective answer. It should also be clear this is not the fault of parapsychologists. It simply reflects the fact that science alone cannot give us what we seek: an objective view of reality.
More than any other scientific discipline, parapsychology pushes the scientific process to its limits, and reveals where its faults lie. In particular, it has highlighted that, contrary to the insistence of many scientists, data alone can never settle this or any other issue.
This does not bode well for parapsychologists hoping to amass enough evidence to convince even hardened sceptics of the reality of ESP. It shows instead that there is only one way forward: for both sides of the debate to agree on their models for the results that emerge from ESP experiments. That, in turn, means working together in good faith to devise tests whose outcome can be agreed by all. For the key lesson of the mathematics of scientific inference is ultimately very simple: the credibility of all evidence is a matter of trust.

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η σχέση μεταξύ Δασκάλων και μαθητών περνάει από τέτοιες εμπειρίες, και οι ίδιοι οι Δάσκαλοι θεωρούνται πιό σημαντικοί αν έχουν τέτοιου είδους
"ικανότητες"

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