average of averages paradox


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  • What is Simpson's paradox example?

    One of the most famous examples of Simpson's paradox is UC Berkley's suspected gender-bias.
    At the beginning of the academic year in 1973, UC Berkeley's graduate school had admitted roughly 44% of their male applicants and 35% of their female applicants.

  • What is the Simpson effect in psychology?

    Simpson's paradox—also called the reversal paradox and amalgamation paradox—is a statistical phenomenon in which an apparent paradox arises because aggregate data at the group level (or at the level of a set of groups) can support a conclusion that is either not observed or is opposite from that suggested by the same

  • What is a paradox in statistics?

    Simpson's paradox, in statistics, an effect that occurs when the marginal association between two categorical variables is qualitatively different from the partial association between the same two variables after controlling for one or more other variables.

  • Simpson's paradox, or the Yule–Simpson effect, is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.
    It is sometimes given the descriptive title reversal paradox or amalgamation paradox.

It is only true if all of the averages are computed over sets having the same cardinality, otherwise it is false. In fancy terms, the average is not distributive though it is algebraic. This phenomenon has a name: the fact that the average of averages is not the average is an instance of Simpson's Paradox.
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