The trouble with psychic powers, runs the conventional argument, is that if they really existed they would be easily demonstrable.  So how come the psychic crackpots in their laboratories are obsessed with experiments that measure trivially small variations from chance expectation?

Statistically speaking, the ease with which you can measure such effects in the laboratory depends on two factors: the size of the experimental effect, and the size of the sample, or number of trials used.

When an effect is very strong, you need only a few trials to expose it, just as you need only a second or two at the dial of your radio to know that you are tuned in to your local rock-music station. When signals are weak, however, the amount of data collected becomes critical: you may need to spend quite a time at your radio dial just to identify the language of a foreign station.

The problem in the past has been that Psychokinesis and ESP have rarely been exposed repeatably because they are very weak effects ranging from less than 1 per cent to only 2 or 3 per cent above what one would expect due to chance. Note that the important point here is not the strength of the effect, it is the number of trials compared with that strength. And what has happened on many occasions over the past fifty years or so is that parapsychology researchers have carried out experiments with a number of trials that is either inadequate or marginal in exposing such weak effects.

Once you get a number of trials that will show up even a very weak effect, then you can get very clear-cut experimental results -- in any field, not just in parapsychology. For example, in 1986 a large scale trial was begun in the United States to see if aspirin can help combat heart disease. What statisticians call the 'effect size' of aspirin is small (only 0.03). If the researchers had studied only 3,000 subjects they would have found that aspirin is no better than a placebo. But because they had a huge number -- 22,000 subjects -- the effect became very obvious immediately: the experimenters found that there were 45 per cent fewer heart attacks in the experimental group and they felt the effect so pronounced they could morally no longer withhold aspirin from the control group, and so discontinued the study.

What has happened in parapsychology in recent years is a new approach called meta-analysis -- a new way of combining the results of many different parapsychology studies to make the aggregate results statistically significant.

Researchers have taken hundreds of small-scale experiments that, on their own, are incapable of exposing weak paranormal abilities, and assembled them into a super-experiment that gives the sort of numbers of test subjects available with the aspirin trials. And when this aggregation of results in done systematically it shows that -- amazingly -- the 'effect size' of some paranormal abilities is very substantially bigger than that of the effect size for aspirin and heart disease -- as much as 0.55 (against 0.03).

Some of the most outstanding results so far have come from meta-analysis of experiments like those carried out by Robert Jahn and Roger Nelson of the Princeton Engineering Anomalies Research (PEAR) programme at Princeton University, where researchers have accumulated years of statistical trials on microscopically small psychokinetic effects -- known in the jargon of the paranormal business as Micro-PK.

Test subjects are asked to try to consciously influence electronic devices whose output should be random, rather like an electronic version of coin tossing.

in December 1989 Dean Radin of Princeton's Psychology Department and Roger Nelson of the PEAR lab published a paper on the meta-analysis of micro-PK experiments not, as might be expected, in a parapsychology journal but in the respected physics journal Foundations of Physics. Their paper was entitled, 'Evidence for consciousness-related anomalies in random physical systems.' In their analysis, Radin and Nelson tracked down 152 reports describing 597 experimental studies and 235 control studies by 68 different investigators involving the influence of consciousness on microelectronic systems.

Radin and Nelson's article showed that the aggregate of all these trials dramatically provided powerful evidence for micro-PK. For they found that the odds against the overall result being the result of chance was 1 in 10³⁵. 

To understand how unlikely it is that this result was obtained by chance, it is like finding a lottery ticket in the street, finding that it is the winning ticket and you have won first prize of millions -- and then continuing to find the winning lottery in the street every week for a thousand years.