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TL;DR

A test using the \( \chi^2 \) distribution. The goodness-of-fit test checks if data follows a hypothesized distribution: \( \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \). Also used for independence testing in contingency tables.

By Valenke Exam Prep Team·Last updated 2026-06-03

Chi-Square Test

A test using the \( \chi^2 \) distribution. The goodness-of-fit test checks if data follows a hypothesized distribution: \( \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \). Also used for independence testing in contingency tables.

Why it matters for interviews

Used to test whether return distributions match theoretical models, whether trading signals are independent of market regimes, and in general model validation for quantitative strategies.

Definition and Mathematical Foundation

A test using the \( \chi^2 \) distribution. The goodness-of-fit test checks if data follows a hypothesized distribution: \( \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \). Also used for independence testing in contingency tables.

Application in Quantitative Finance

Used to test whether return distributions match theoretical models, whether trading signals are independent of market regimes, and in general model validation for quantitative strategies.

Related Terms

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Frequently Asked Questions

What are the degrees of freedom?▼
For goodness-of-fit: \( k - 1 - p \) where k is the number of categories and p is the number of estimated parameters. For independence: \( (r-1)(c-1) \) for an r-by-c contingency table.
When should you not use the chi-square test?▼
When expected frequencies are too small (rule of thumb: \( E_i \geq 5 \)). For small samples, use Fisher's exact test for independence or exact binomial tests for proportions.
How is the chi-square distribution related to the normal?▼
If \( Z_1, \ldots, Z_k \) are independent standard normals, then \( \sum Z_i^2 \sim \chi^2(k) \). This is why chi-square tests work: they measure squared deviations from expected values.