Purpose:To provide a method for determining the vector that, when added to the preoperative astigmatism, results in no prediction error (PE) and to specify statistical methods for evaluating astigmatism and determining the 95% confidence convex polygon.Setting:Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California.Design:Retrospective consecutive case series.Methods:An analysis of 3 clinical trials involving toric intraocular lenses was performed. 3 formulas were evaluated (generic vergence formula with zero surgically induced astigmatism, the Barrett toric formula, and the Holladay toric formula). Scalar and vector analyses were performed on each dataset with each formula and the results compared. Since the PE was not a Gaussian distribution, a 95% convex polygon was used to determine the spread of the data.Results:The mean values for the vector absolute astigmatism PEs were not different for the 3 formulas and 3 datasets. The Barrett and Holladay toric calculators were statistically superior to the zero formula for 3 intervals (0.75, 1.0, and 1.25) in the high astigmatism dataset.Conclusions:Residual astigmatism and vector absolute astigmatism PE mean values and SDs are useful but require extremely large datasets to demonstrate a statistical difference, whereas examining percentages in 0.25 diopters (D) steps from 0.25 to 2.0 D reveals differences with far fewer cases using the McNemar test for a P value. Double-angle plots are especially useful to visualize astigmatic vector PEs, and a 95% confidence convex polygon should be used when distributions are not Gaussian.