It happens sometimes in NHST that the theme under investigation is somewhat vague/intuitively in mind in terms of operational conditions that an interpretation is needed in order that a test could be belt: how I want to reach must be translated into the Null Hypothesis H0? Not rarely even the nature of data will change how H0 is expressed. For example the K-W test intends to find out if the sample means are distinguishable, not equal in statistics jargon, then we decide, in order to build H0 to allow all ranks be freely permutable among the samples. In consequence we assume that the only thing that varies is the location under same shape distributions. By other words the Distributions, from where the samples were drawn, are are only shifted and we intend to see though the medians could be equal or alternatively, given data, at least one of them is sufficiently different from the remainders to reject the null hypothesis concerning the k samples: H0: median X1 = median X2 = . . .= median Xk. In what concerns 1-way Anova and Kruskal-Wallis Test both are unable to test Normal/Gaussian data with different variances, Heteroscedasticity. I dare though by a simulative methodology were are able to get a Confidence Interval for K-W test based on the exchangeability/permutability propriety.