Chi-Squared Distance Chi-squared distance is a measure of dissimilarity between two distributions, often used in categorical variables. It measures the “distance” between two distributions based on how similar or different their probability mass functions are.

### How to Calculate?

The chi-squared distance is calculated by subtracting the probability of each category from the conditional probability. The result is then squared and summed for all categories. This gives an indication of how closely related or distinct two distributions are.

### Applications of Chi-squared Distance

Generally speaking, the larger the difference between two distributions, the greater the Chi-squared distance. This metric is useful for comparing nominal data such as gender, race, religion and age group as it takes into consideration differences in proportions rather than absolute values. In this way, it can be applied to data where observations with similar proportions may have significantly different population’s sizes; for example, comparing a small population of young adults to a large population of seniors could yield very different results when measuring absolute numbers but yield much closer results when using relative proportions.

The Chi-squared distance can also be used to compare two populations and determine whether they share any common attributes (e.g., do they have more females than males). Further, it has application in classification problems such as clustering and anomaly detection because it can help identify which combinations of features are most likely to belong to one set versus another. Finally, it is also useful for feature selection tasks since it can detect which features best differentiate between classes; for example, if you wanted to determine which combination of features best distinguish people who purchase luxury cars from those who purchase economy cars, you would calculate the Chi-squared distance between these groups across all variables and use this to select those that most effectively separated them out from one another.