I ran an experiment that illustrates the problem Sheldrake points out. I wrote a computer program to simulate the output of a biased binary random number generator. I collected the statistics and presented my data to two sets of mathematicians and statisticians.

To the first group I said that the data represented a hardware random number generator I was building and I wanted to know if the behavior of the device was truly random or if it showed a significant bias. The unanimous conclusion was that the deviation from expected outcomes was unquestionably statistically significant.

To the second group I said that the data represented the outcome of a series of ESP tests and I wanted to know if the results were truly random or if there was evidence of some ESP effect. The unanimous conclusion was that the results were unquestionably purely random and showed no significant deviation.

The same data was seen as evidence of an effect, or as evidence of no effect depending of what the "objective" mathematicians were told was the cause of the effect.

The data itself was generated by computer to have a significant deviation from random, but that deviation became invisible to those who wished not to see it.

I'm reminded of another statistical paper I read wherein it was pointed out that everybody seems to put a lot of faith in the beneficial effect of an aspirin regimen for heart patients, and no faith at all in experiments for ESP. But the fact is that the evidence for ESP is over 100 times more significant than the evidence for the aspirin regimen. (Specifically, the p of the aspirin effect being chance was about 100X the p of the ESP results being due to chance.) So objectivity goes out the window when a scientist is confronted with data that goes counter to his preconceptions.