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Simpson's paradox
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The Simpson's paradox is a paradox in probability and statistics in which a trend appears in several groups of data but disappears or even reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics and is particularly problematic when frequency data is unduly given causal interpretations.
Example: There exist treatment A and treatment B for kidney stones. Treatment A is more effective when used on small stones, and is also more effective when used on large stones, yet treatment B is more effective when considering all stones at the same time.
Different levels of overview:
