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Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, [ 1 ] [ 2 ] [ 3 ] and is particularly problematic when frequency data are unduly given ...
When [=, =] [=, =] does not depend on , the Simpson's paradox is exactly the omitted variable bias for the regression of Y on X where the regressor is a dummy variable and the omitted variable is a categorical variable defining groups for each value it takes. The application is striking because the bias is high enough that parameters have ...
This is a special case of Simpson's paradox. Simpson's paradox, or the Yule–Simpson effect: A trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data.
Simpson's paradox, a term introduced by Colin R. Blyth in 1972; but Edward Simpson did not actually discover this statistical paradox. The Simson line in geometry is named for Robert Simson, but cannot be found in Simson's works. Instead, it was first discovered by William Wallace in 1797.
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Simpson published an article on the measurement of diversity in Nature in 1949. [11] Subsequently, "The Interpretation of Interaction in Contingency Tables" was published in 1951 in the Journal of the Royal Statistical Society. [6] This is the paper that gave rise to the phrase Simpson's paradox twenty years later.
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