katlaughing writes:

Bagpuss, do you have any references? Do you know how much statistics can be manipulated, including those in "famous experiments?"

kat,
which point do you want to make with the second sentence of that statement? Sure, it's true (and no sane person would ever believe anything else), that there have been errors in the statistical analysis of experiments (more so in pro-paranormal experiments from my reading experience, but that's a different story). In addition, there has been fakery of data (less so in pro-paranormal experiments, but that again is another story), outright fraud, 'improving' of data, wrong interpretations of rock solid data and all that. So what? In science, there is never reliance on single unrepeated (or worse: unrepeatable) experiments. Only after loads of experiments giving a kind of consistent pattern (you'll hardly ever find any area of science in which all articles find identical results), scientists think they start to know something about their subject.
So it is trivially true that there are individual articles not to be trusted. But to ask someone (Bagpuss) whether (s)he knows this simple fact is about the same as asking someone who tells you about something (s)he has read in a newspaper whether (s)he knows that there have been lies in newspapers.
As I read your sentence you mean nothing else than 'I don't believe you, I don't want to believe you and I won't believe you'. Since each single experiment can be brushed away with your type of argumentation, you are in the comfortable position that you can choose whatever you want to believe. This type of argumentation is below your usually high standard of arguing.

Now for the first sentence: One reading is that you want to say 'back up or shut up' with a bit nicer words, but another reading is that you are genuinely interested. Assuming that this is true, here's my knowledge of the state of the art:

There are several hundred articles about individual differences in propensity to cognitive illusions, to suboptimal statistical reasoning, to illusions of memory,.... Some dozen of them use amount of belief in paranormal phenomena as a variable to study, usually but not necessarily in two groups, believers (sheep) and disbelievers (goats). What are the findings? Quite typical for the study of human behaviour, it is not easy to get a clear picture after so few articles (yes, some dozens is still 'few'). As for the first part of Bagpuss' statement ('less understanding of statistics' in sheep), there is mixed evidence (e.g., Blackmore, British J. of Psychology, 1997, 88, 683-689). It seems to be that general knowledge of statistics may be (there are several dissenting articles you can find referenced in Blackmore's) not worse in sheep (no article claims it is worse in goats). As for the second part of Bagpuss' statement (sheep 'underestimate the frequency of chance occurrences'), there is considerable and largely consistent evidence that this is true. They (sheep) seem to have a biased memory in counting their successes and failures (tend to remember their successes and to forget their failures; tend to underestimate how many successes are to be expected by chance alone; tend to see skill at work where there was nothing but chance; Blackmore and Troscianko, Brit. J. Psychology, 1985, 81, 455-468). This is consistent with other research on their memory. They forget disconfirming (for their paranormal belief system) evidence much more often than goats forget disconfirming evidence for their preconceptions. The memory is equally good for facts confirming the respective conviction (Wiseman and Morris, Brit. J. Psychology, 1995, 86, 113-125; Jones and Russel, European J. Social Psychology 1980, 10, 309-312). In short, their memory is good in general, but highly selective when it comes to things they do not (want to) believe. Paranormal belief correlates positively with general gullibility (Psychological Reports 1987, 61, 435-438). You want to hear something good for sheep, for a change? No problems, they are less likely to get a depression (sorry, no reference at hand, but I could find it easily).
Mind you other readers that the results are not in general true for all persons believing in something supernatural as, e.g. the Christian god. There are large differences between believers in traditional religions of many kinds and, e.g., believers in New Age thinking.

So, that should be enough for a start if you really want to know, kat. I'm happy to oblige in future, if you are interested in scientific research and in most cases I will be able to provide you references. If you only want to make a point in an argument, be careful. I'm here and watch even if I don't post.

Wolfgang