I am trying to interpret the Kolmogorov–Smirnov test in the case of predictive analytics to compare three models: a neural network, a decision tree and a logistic regression. The target variable is binary: 0=bads, 1=goods. According to the KS theοry, I compare the cumulative distribution of goods with the cumulative distribution of bads to check whether they come from the same distribution, so I have a null and an alternative hypothesis.
In books about predictive analytics, the comparison among the three predictive models is done according to how large the KS statistic is. So the model with the largest KS statistic is chosen. Though software packages related to predictive analytics and data mining in general do not report the p-value of the KS statistics but only its size. But since the KS is a hypothesis test, the biggest KS statistic might not be significant, although it might be the largest related to the three predictive models.
So the question is: what is the point in checking only the size of the KS statistic, as the predictive analytics books and software do, without checking the p-value.