"T-Testing" Group Differences at Various Percentiles

While the standard t-test compares means, somewhat less clear is what to do if one wants to test, e.g., whether group differences at various percentiles achieve statistical significance. In a recent Statalist discussion (click here), the specific question posed involves an effort to determine whether “Black-White wealth differences at p10 (10^th percentile) and p90 (90^th percentile)” systematically vary.

Possible options, described in the responses, range from using the qreg and ttest commands.