A p-value is a statistical measure that represents the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. In the context of a KS test, it is used to determine whether there is a significant difference between two data sets.
The p-value from a KS test can be calculated by first calculating the test statistic, which is the maximum absolute difference between the cumulative distribution functions of the two data sets. This test statistic is then compared to a critical value from a table or using a statistical software. The p-value is then determined based on the test statistic and the chosen significance level.
A high p-value from a KS test indicates that there is no significant difference between the two data sets being compared. This means that the null hypothesis cannot be rejected, and the data sets are considered to be from the same underlying distribution.
A low p-value from a KS test indicates that there is a significant difference between the two data sets being compared. This means that the null hypothesis can be rejected, and the data sets are considered to be from different distributions.
The p-value from a KS test can be interpreted as the probability of obtaining the observed test statistic or a more extreme one, assuming that the null hypothesis is true. Typically, a p-value less than 0.05 is considered statistically significant, indicating a rejection of the null hypothesis and a significant difference between the data sets being compared.
