Estimating precipitation frequency is important in engineering, agriculture, land use planning, and many other disciplines. The index flood method alleviates small sample size issues due to short record length by calculating normalized quantile estimates for averaged data from a "region" of gauges. For a perfectly homogeneous region this adds no error; heterogeneity statistics seek to quantify a real-world region's deviation from this assumption. Hosking and Wallis (1997) introduced a Monte Carlo heterogeneity statistic called here H-1 and used a simulation study to assess its utility while rejecting two similar statistics called here H-2 and H-3. A nearly linear relationship was found between Ill and the percentage root mean square error (RMSE) increase due to heterogeneity, establishing H-1 as a "reasonable proxy" of quantile error. The H-1-percent RMSE added relationship found in the simulation experiment was used to find equivalent RMSEs for heterogeneity thresholds against which all three H statistics were tested. In this study the "reasonable proxy" relationship is evaluated across a highly skewed daily precipitation dataset in Minnesota for H-1, H-2 and H-3. Simulated regions used in quantile error estimation are generated using at-site L-moment ratios scaled toward the regional mean with a shrinkage multiplier. A linear relationship is found between Monte Carlo estimates of quantile RMSE and both Ill and Hy across all possible regionalizations of twelve gauges. H-2's relationship is less linear than H-1's as quantified by Pearson's r. A synthetic study is also undertaken using the same sample sizes, regional L-moment averages, and between-site variations as the Hosking and Wallis (1997) simulation. The H-2-percent RMSE added relationship is found to be nearly as linear as for H-1, complementing the enumeration study's findings. Because H-2's linear relationship with percent RMSE added has approximately one-fourth the slope of theH(1) -RMSE relationship, heterogeneity thresholds calculated with reference to H3 should not be applied to H-2. Hy thresholds can be derived from the H2-percent RMSE added relationship in analogous fashion to the method used in Hosking and Wallis (1997) for H-1. The resulting thresholds are one-fourth the magnitude of the H-1 thresholds. Published by Elsevier B.V.