This article is concerned with estimating percentage points for the RST (R-statistic) many outlier procedure. This procedure has been introduced in [5] and a brief discussion is given in Section 1. The algorithm used to estimate the percentage points is given in Section 2. Percentage points are given for α = .10, .05, .01,N= 10(5) 20(10) 50(25) 100,k= 2:N= 20(10) 50(25) 100,k= 3;N= 20(10) 50(25) 100,k= 4. Two examples illustrating the use of the procedure are given in Section 3. Finally some potential weaknesses of the method are discussed in Section 4: namely, when the actual number of outliers in a sample is larger than the maximum number of outliers assumed by the procedure. Alternatives are proposed for possibly modifying the procedure to allow for this contingency.