Five thousand randomized ellipsoids for each of 19 color centers comprising the RIT-DuPont dataset were generated based on both the tolerance median (T50) and visual uncertainty (fiducial limits). When plotted as two-space projections, they provided a qualitative description of the ellipsoid reliability, this reliability was dependent on. visual uncertainty. The ellipsoids were considered as local color-difference equations. STRESS was calculated for each ellipsoid, quantifying the deviation between visual color differences and numerical color differences calculated by the T50-based ellipsoids, the randomized ellipsoids and three color-difference equations: CIELAB, CIE94, and CIEDE2000. F-tests comparing STRESS determined statistical significance between calculated and visual color differences. The percentage of randomized ellipsoids that were beyond the critical F values was used as a metric for determining whether a color difference equation was under- or over fitting the visual data. A nonellipsoid method and an average standard error method were developed and tested for cases when the dataset may not enable ellipsoid fitting and where uncertainty has been reported only as an average standard error. In the latter case, only equation under-fitting could be determined. Thus visual uncertainty can be used as a criterion in both equation development and evaluation. (C) 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 375-390, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20521