Due to technological influence on the production process there are variations of the chromaticity coordinates that may cause visible differences of the perceived color of LEDs of the same production batch. To minimize the negative impact of such variations for the user the manufacturers carry out colorimetric measurements of LEDs and sort them into tolerance groups of similar chromaticity coordinates. The corresponding groups are defined by their respective center point surrounded by a quadrangular tolerance limit whereas the tolerance limits are based on tolerance ellipses gained in the 1940s by MacAdam. However, due to another scientific target of MacAdam's experiments, applying his ellipses as a base for grouping the chromaticity coordinates has to be questioned. With a view toward a method for grouping according to chromaticity coordinates for white LEDs with phosphor conversion, the results of research with test subjects regarding their discrimination and magnitude perception of chromatic differences are presented. In this research three chromaticities with the correlated color temperatures of 2700, 4000, and 6500 K and variations of color transitions are investigated, which match realistic luminaire designs for practical applications. The empirically determined thresholds are expanded according to the transformation to different chromatic adaptation conditions as per von Kries that are then compared to the results by MacAdam and the influence on adaptation is being discussed. A new concept for the calculation of tolerance limits for LED binning is presented. (C) 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 457- 467, 2016; Published Online 26 August 2015 in Wiley Online Library (wileyonlinelibrary.com).