Understanding the Chi-Square Test Beyond the Formula | Towards Data Science

Towards Data Science

by Nikhil Dasari

February 19, 2026

AI-Generated Deep Dive Summary

The Chi-Square test is a statistical method used to determine if there's a significant association between two categorical variables. In the example provided, an author tests whether his book cover designs (high-cost or low-cost) influence sales outcomes (sold or not sold). By analyzing the observed data, he aims to understand if the cover type impacts sales beyond random chance. The test involves comparing observed counts (actual sales numbers) with expected counts (predicted sales under the assumption of independence). If the null hypothesis holds—meaning cover type and sales are independent—the expected counts would align closely with the observed ones. However, any significant deviation suggests a relationship between the variables. The Chi-Square statistic measures this discrepancy, and a low p-value (like 0.043 in the example) indicates that the observed difference is unlikely due to chance alone. Calculating the Chi-Square statistic involves summing the squared differences between observed and expected counts, divided by expected counts. This value helps determine whether the variables are independent or associated. The test also considers degrees of freedom, which depends on the dataset's dimensions. In the example, the low p-value (below 0.05) suggests that cover design does influence sales. Understanding the Chi-Square test is crucial for data scientists and AI practitioners as it allows them to make informed decisions based on categorical data. By testing hypotheses and identifying relationships between variables, this method enhances predictive models and supports evidence-based conclusions in fields like marketing, healthcare, and social sciences. It underscores the importance of statistical rigor in deriving meaningful insights from data.

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Originally published on Towards Data Science on 2/19/2026