Kolmogorov-Smirnov (K-S) Test: Understanding the p-value

The p-value in a K-S test represents the probability of observing the current sample data, or data even more extreme, assuming the null hypothesis is true. The null hypothesis states that there is no significant difference between the sample data and the theoretical distribution function.

Therefore, a smaller p-value indicates a larger discrepancy between the sample data and the theoretical distribution function. Conversely, a larger p-value suggests a smaller discrepancy.

Generally, if the p-value is less than the significance level (commonly set at 0.05), the null hypothesis is rejected, implying a significant difference between the sample data and the theoretical distribution function. If the p-value is greater than the significance level, the null hypothesis cannot be rejected, meaning there is no significant difference between the sample data and the theoretical distribution function.