Distribution of discrepancy degree in 500 simulated isotropic datasets. The upper two panels show the results of statistical isotropic analyses (isotropy). The lower two panels show the results of statistical isotropic analyses that preserve the spatial inhomogeneity of real data (isotropy RP). The purple and blue represent the statistical results of Ω_m and H₀. The black curve is the best fit to the Gaussian function. The solid black and vertical dashed lines are commensurate with the mean and the standard deviation, respectively. The red lines represent the discrepancy degree from the real data. For the isotropy analyses, the statistical significance of the real data are 3.68σ for Ω_m anisotropy and 3.01σ for H₀ anisotropy. For the isotropy RP analyses, the statistical significance of the real data are 2.09σ and 1.35σ for Ω_m and H₀ anisotropy, respectively.