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But the stats really need to be that high.

So itís OK for a scout to avoid certain ethnic neighborhoods when the odds are over 1000:1, but not when itís just 2:1? What is the threshold below which it is no longer OK?

When other unanalysed effects would dominate. It works fine if everything else can be assumed equal. However usually everything else is not equal, that is there tends to be other meaningful properties other than that one that is apparent or understood.

If one could arrive at a proof that the population is really homogenous in respect to unanalysed properties then slighter effects could be focused on. But there is a big difference between the population appearing homogenous because you can't analyse it sufficently and it actually being homogenous.
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