What characteristic of the Kolmogorov-Smirnov test is most valued in its results?

The Kolmogorov-Smirnov test is a non-parametric test used to determine if a given sample comes from a specified probability distribution. One of the primary characteristics that is most valued in the results of this test is the maximum vertical distance between the empirical distribution function (EDF) of the sample and the cumulative distribution function (CDF) of the theoretical distribution. This distance is referred to as the D statistic.

In this context, a lower maximum vertical distance between the theoretical and actual distributions indicates a closer fit between the empirical data and the theoretical model being tested. A small D statistic suggests that the empirical distribution closely follows the theoretical distribution, providing stronger evidence that the assumption of the specified distribution is valid for the given data.

Options that involve higher ratios or deviations are not as relevant in the context of how the Kolmogorov-Smirnov test is measured. Specifically, the likelihood ratio is more related to maximum likelihood estimation and not directly applicable to the K-S test. Mean squared deviation relates more to comparing variances or using different testing approaches rather than the primary characteristic being scrutinized with K-S. Sample size, while important in statistical testing in general (since larger samples can provide more reliable results), does not represent a characteristic being evaluated directly by