Interactive statistics model

Simpson’s Paradox Model

Applicants arrive continuously at two banks. Bank A has the higher approval probability in both risk groups, but different applicant composition can make Bank B look more generous overall.

Overall rate = low-risk share × low-risk rate + high-risk share × high-risk rate

Question: Can B lead overall while A leads inside every group?

Applicants per bank

Applicants per second

Low-risk share at Bank A

Low-risk share at Bank B

Approval	Low risk	High risk
Bank A	90%	40%
Bank B	80%	30%

Each model step sends one new applicant to each bank and draws approval using the fixed group-specific probabilities above.

Applicants processed

0 / 1,000

Bank A overall

—

Bank B overall

—

Aggregate B − A

—

Within-group A advantage

+10 pp

Observed within-group rates

Sampling noise fades as more applicants arrive.

Aggregate rates through time

Blue: Bank A. Orange: Bank B.

Ready: Press Start to watch the aggregate ranking emerge.