Why in the heck does a demonstration of telekinesis need a statistical analysis?
Because telekinesis (really psychokinesis) is more broadly defined. It is defined as the ability of someone to influence a remote physical system using only thought. ("Remote" meaning, of course, not connected to the brain. Obviously thoughts control the physical system of the organism the thoughts arise in.)
Commonly we define psychokinesis as the ability to
move things with the mind, but remote locomotion is not the only purported effect. Adding heat, for example. The PEAR experiments centered around a random number generator. That is, a random bit generator. This is a problem computer scientists should be familiar with, as a bottomless source of true entropy is an attractive goal for many applications. For purposes of understanding the experiment, just imagine it as a machine where you push a button and one of two lights comes on -- one for a 1-bit and the other for a 0-bit. Which light comes on for each trial is, it is alleged. completely random. It is said to be theoretically impossible to predict from any sequence of prior of outcomes, however long, what the next outcome will be.
Over time, the law of large numbers says you should accumulate an equal number of ones and zeros. More precisely, this translates into an ability of a human predictor to predict the next outcome of the machine with an accuracy that, over a large number of trials, approaches 50 percent. But the law of pretty-large (as opposed to truly large) numbers says that there will be a statistical variance in the actual demonstrated ability. That is, if you do 10 trials at predicting a truly random binary event, you will most probably succeed five times, plus-or-minus some variance attributable to sampling granularity. And that granularity is most likely to give you four or six correct guesses if not five. You can't reckon fractions of guesses. The more trials you do, the more you can expect your performance to approach the true center of the distribution, with decreasing variance because the granularity increases.
So the null hypothesis here looks like a random variable that is the likelihood function of conflating the actual probability of the machine to exhibit a truly random bit with the statistical parameters of the sampling factors.
The psychokinesis variable comes from the subject being able to actually influence the machine to produce an outcome that she has predetermined regardless of what its mechanism or algorithm would otherwise have produced. That is, the pyschokinetic effect is assumed to arise when the subject can psychically compel the machine to produce a string of outcomes that are, naturally enough, predicted at a higher rate because the person predicting is the person psychokinetically influencing. One parameter of the model is the baseline performance of the machine. Another is the baseline performance of a non-psychokinetic subject. Also you have the suspected performance of the machine in a run of
N trials, absent any external effect. And at the end you have the discrete set out outcomes, both from the machine and from the human subject.
The statistical methodology centers on properly computing likelihoods, properly accounting for these parameters for that trial. The result is a likelihood function that represents the null hypothesis quantitatively. The goal then, most simply put, is to determine whether the properly parameterized null hypothesis has a probability
p < 0.05 of explaining the outcomes. Or more accurately stated, whether the subject truly has predicted more outcomes than chance would allow -- presumably because she affected the machine to do so. But because we have a finite number of trials, the question of whether the outcomes were anomalous is always that statistical question that includes a margin of error. Thus one way to fudge your numbers is to complicate the reckoning of the null hypothesis and thereby get a better P-value that you would have otherwise seen. It effectively narrows the expected outcomes such that small changes within the margin of error can be improperly attributed to changes in the variable.
Another way to fudge your numbers is simply to relax the empiricism so that other variables creep in, such as experimenter bias. We find that PEAR did all of that, but Buddha seems to want to talk about only the few straw men he's trotted out.