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MyWikiBiz, Author Your Legacy — Monday November 25, 2024
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In different lights the formula [''m'',''b''] = [''m'',][''b''] presents itself as an "aimed arrow", "fair sample", or "independence" condition.  I had taken the tack of illustrating this polymorphous theme in bas relief, that is, via detour through a universe of discourse where it failsHere's a brief reminder of the Othello example:
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In different lights the formula <math>[\mathrm{m,}\mathrm{b}] = [\mathrm{m,}][\mathrm{b}]</math> presents itself as an ''aimed arrow'', ''fair sample'', or ''statistical independence'' condition.  The concept of independence was illustrated above by means of a contrasting caseFor ease of reference, the details of that counterexample are summarized below.
    
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The condition, "men are just as apt to be black as things in general", is expressible in terms of conditional probabilities as P(''b''|''m'') = P(''b''), written out, the probability of the event Black given the event Male is exactly equal to the unconditional probability of the event Black.
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The condition that "men are just as apt to be black as things in general" can be expressed in terms of conditional probabilities as <math>\operatorname{P}(\mathrm{b}|\mathrm{m}) = \operatorname{P}(\mathrm{b}),</math> which means that the probability of the event <math>\mathrm{b}\!</math> given the event <math>\mathrm{m}\!</math> is equal to the unconditional probability of the event <math>\mathrm{b}.\!</math>
    
Thus, for example, it is sufficient to observe in the Othello setting that P(''b''|''m'') = 1/4 while P(''b'') = 1/7 in order to cognize the dependency, and thereby to tell that the ostensible arrow is anaclinically biased.
 
Thus, for example, it is sufficient to observe in the Othello setting that P(''b''|''m'') = 1/4 while P(''b'') = 1/7 in order to cognize the dependency, and thereby to tell that the ostensible arrow is anaclinically biased.
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