How does higher variance affect the overlap between control and treatment groups in a distribution?

How does higher variance affect the overlap between control and treatment groups in a distribution?

• A. Increases overlap
• B. Decreases overlap
• C. No effect
• D. Increases separation

Answer: (A)

When comparing two distributions, how spread each group is relative to how far apart their centers are determines how much their probability ranges intersect. Higher variance broadens each distribution, so more of the value range falls into the region where both groups have probability mass. In other words, with the same difference between the group means, wider distributions have more shared area where outcomes from either group could occur, increasing overlap. This is why higher variance tends to make control and treatment distributions overlap more.

When comparing two distributions, how spread each group is relative to how far apart their centers are determines how much their probability ranges intersect. Higher variance broadens each distribution, so more of the value range falls into the region where both groups have probability mass. In other words, with the same difference between the group means, wider distributions have more shared area where outcomes from either group could occur, increasing overlap. This is why higher variance tends to make control and treatment distributions overlap more.