You failed to talk about the hidden danger of testing multiple hypothesis against a set of data
Any hypothesis based on the data should be assumed as flaky unless tested by independent data. Lets go through an example:
You throw your perfect coin 10 times and have a 100 people (subjects) trying to control the result by mind power. There are 2**10 = 1024 possible outcomes. The result will probably be disappointing, even with very hard concentration your subjects should not be able to control the coin more than 50% of the time. But once you got that result, you might break down the group of subjects into subgroups -- wouldn't it make sense that the power is stronger in some than in others? Lets split the group in male and female, large and small, sort them by skin color and eye color, age and place of birth. Suddenly you have 1000 possible sub-groups and you will forcibly find a statistically significant control over the coin toss in some sub-group. But every extra hypothesis actually reduces the significance of your result -- so the correlation is worthless. The correlation must be tested against new data to be significant.
This problem does occur in serious academic research and a quite senior professor recently reported that some humans have a statistically undisputable ability of foresight (but only the males , only involving sexual pictures, ... and whatever else was required to make his data talk).