Simpson's paradox is an interesting example of what can happen when an unrecognized confounding factor is present in a skewed distribution.
Conditions for Simpson's paradox:
(1) Data from several observational studies for a treatment or intervention are pooled.
(2) The effectiveness of the treatment or intervention based on analysis of the pooled data is the exact opposite of the conclusions reached in the original observational studies (either something that appeared to be effective is not, or something that appeared to be ineffective is).
where:
• The problem may not be realized until the pooled analysis is performed. It can often be detected if it is specifically looked for.
Cause: Unequal group assignment for a significant confounding factor, resulting in an unbalanced distribution in the original studies
The paradox can be avoided:
(1) in the experimental design with randomized group assignments
(2) by making an appropriate adjustment to the data
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