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clustering illusion

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    Paradox & Proof Entry #0154

    The reason a fair coin produces unfair-looking runs

    In two hundred fair tosses a run of seven identical results is likely. People asked to fake the sequence almost never allow one, which is how fakes are detected.

    Adept
    The hidden part #0154

    Randomness clusters. The expected longest run in a fair sequence is far longer than intuition permits, so real data looks rigged.

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    Statistical Illusions Entry #0442

    Why a cluster is expected in random data

    Randomness produces clumps. A pattern spread out evenly is the unlikely arrangement, so finding a cluster is not yet finding a cause.

    Adept
    The hidden part #0442

    Independent events arrive in bursts, so a cluster is the expected texture rather than a signal. Evenness is what would need explaining.

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