A billion bits in the bitstream at under each condition you want to study; a billion bits for the control stream, a billion under the "think 'one' thoughts," and a billion under "think 'zero'" if you want to test that as well.
...snip...
If, as you suggested, you can generate random numbers at 1000/second, it will take about a million seconds, or approximately thirty years, to run the experiment.
Hmmm. So suppose you generated random bits at 1 million/second. Would that allow you to run the experiment in practical time?
And even if you could run the experiment, it would still probably not be accepted by either side. Limbo's already explained about the "known parapsychological effects" like "the sheep-goat effect and the parapsychological experimenter effect." These effects basically "mean" that any time an incompetent researcher produces a finding that evaporates in the lab of a competent one, that means the competent researcher is doing something wrong; in other words, the PEAR hypothesis is unfalsifiable, because anyone who can't duplicate it must be subconsciously suppressing it.
I understand and accept that; trying to convince everybody is obviously futile. What one could show however is that "under the described conditions, at confidence p=.95, the effect if any would have to have been less than 1 in X bits". That doesn't logically "disprove" the effect under different conditions even to some rational observers (we'll leave the wildly irrational out), but as a thought experiment it would nevertheless have some meaning. The conditions could potentially be made rigorous while still more or less supporting asserted prerequisites. For example, as many meditators as desired could hang out in the next room (smile).
Beyond this, there's the simple fact that such an ability, even if confirmed, would be of no practical significance whatsoever; even if the statistical significance were tremendous, the "clinical" significance, or usefulness in explaining real-world phenomena, would be negligible.
I agree that Home Depot is unlikely to begin selling mind control light switches any time soon, even if such a slight effect were confirmed.
I believe however that confirming such a phenomenon would have major impact, in the same way that some high energy physics experiments which imply a new force or particle may require tweaking or discarding theories - tho often with no practical utility. Sometimes the investigated effect in those cases is one in 10^8 or less. What practical utility is there to much of the more abstruse neutrino research, other than to give experimental feedback to our models and theories?
(Do remember that my personal guess is that an unbiased test would more likely be disconfirming. But most folks expected the speed of light to vary depending on the Earth's motion through the ether - it's the exceptions that cause breakthroughs.)
Zeph