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Ball covariance is a statistical measure that can be used to test the independence of two random variables defined on metric spaces.[1] The ball covariance is zero if and only if two random variables are independent, making it a good measure of correlation. Its significant contribution lies in proposing an alternative measure of independence in metric spaces. Prior to this, distance covariance in metric spaces[2] could only detect independence for distance types with strong negative type. However, ball covariance can determine independence for any distance measure.
Ball covariance uses permutation tests to calculate the p-value. This involves first computing the ball covariance for two sets of samples, then comparing this value with many permutation values.