The Simpson's paradox unraveled

Area of Science:

• Statistics
• Causal Inference
• Data Analysis

Background:

• Simpson's paradox presents a well-known statistical conundrum with seemingly contradictory results.
• The paradox arises from a hypothetical data example, challenging conventional statistical interpretation.

Purpose of the Study:

• To clarify the underlying causal structure of Simpson's paradox.
• To demonstrate how subject-matter knowledge resolves the apparent statistical paradox.

Main Methods:

• Explicitly defining the causal structure of Simpson's data example.
• Analyzing the paradox through the lens of causal inference.

Main Results:

• The paradox is resolved when statistical analysis is guided by subject-matter knowledge.
• Previous explanations involving confounding and non-collapsibility are reviewed.
• Causal context is crucial for accurate statistical interpretation.

Conclusions:

• Stripping statistical problems of their causal context can lead to analytical errors.
• Understanding the causal relationships is essential for correct data interpretation.