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The marginal statistics for the diffused ultrasound speckle echo has been postulated as exhibiting circularly symmetric Gaussian behavior similar to the laser speckle for monochromatic illumination under the assumption of a large number of unresolvable scatterers per resolution cell. This is known in the literature as the Rayleigh scattering condition. This paper presents a formal statistical test, the Kolmogorov-Smirnov nonparametric goodness of fit statistical test, to test the hypothesis that the unresolvable part (diffuse part) of the backscatter echo follows a Rayleigh scattering condition, and obtain numerical values for the scatterer concentration required for the Rayleigh condition to be valid. In addition, it presents a formal statistical test, the Kolmogorov-Smirnov nonparametric homogeneity statistical test, to compare two regions of interest with different scattering concentrations without prior knowledge of the nature of the scattering conditions (Rayleigh or non-Rayleigh scattering). Unlike all previous parametric testing methods that treat the A-scan or B-scan echo as a random sample, the authors' method presents formal tests based on the colored nature of the diffuse backscattered echo which is a more realistic model of the diffuse scattering component. The tests are demonstrated on simulations of RF scans with different scatterer concentrations per resolution cell as well as on phantom data which mimic tissue.