Chi-Square Test: Detecting Default Rate Differences Across Loan Types

The Scenario

Meridian Bank is a mid-sized regional bank with a portfolio of 800 recently closed loans spread across four product categories: Personal, Auto, Home, and Business loans. In its latest quarterly risk review, the CFO flagged a rising volume of charge-offs and asked a pointed question: are all loan types equally likely to default, or are some categories significantly riskier than others? Before the bank restructures interest rates, tightens underwriting criteria, or exits any lending segment, the leadership team wants statistical evidence — not just gut feeling — that default rates genuinely differ across loan types.

The Statistical Challenge

The risk analytics team has pulled records for all 800 loans, noting the loan type and whether each loan ended in default (1) or was repaid in full (0). While a quick look at the raw percentages suggests that Personal loans default more often than Home loans, the question is whether this difference is real or simply a product of random sampling variation. You have been brought in as the data analyst to apply a Chi-Square Test of Independence — a method that tests whether two categorical variables (loan type and default status) are statistically associated. The test will tell you whether the pattern you see in the data is strong enough to be trusted, or whether it could plausibly have arisen by chance.

What's at Stake

The outcome of this analysis will directly shape Meridian Bank's lending strategy. If default rates are statistically different across loan types, the risk committee will move immediately to reprice high-default categories, tighten credit score requirements, and potentially reduce exposure to the riskiest segments — decisions with multi-million dollar implications. If the analysis shows no statistically significant difference, the bank will refocus its risk management efforts elsewhere. Your statistical conclusion is the decision trigger.