We used the inferred matches to compute a color constancy index (CCI) for each target and test illuminant:
In the formula,
b denotes the Euclidian distance between the subjects' inferred match in the illuminant-changed condition and the reflectance match for the target (competitor R), computed in CIELAB space;
a denotes the Euclidean distance between the inferred match in the illuminant-constant condition and the reflectance match for the target (Arend, Reeves, Schirillo, & Goldstein,
1991). In other words, the closer the subject's inferred match is to the reflectance match, the closer the CCI is to 1 (see
Figure 4A and
B). In computing the value of
a for our main analyses, we chose to use the subjects' inferred match in the illuminant-constant condition rather than the values of the physical tristimulus match (T). We made this choice because using the subject's inferred matches in the illuminant-constant condition accounts for any bias observed in this condition (Burnham, Evans, & Newhall,
1957; Brainard, Brunt, & Speigle,
1997; Ling & Hurlbert,
2008). Indeed, across our experiments, the inferred matches for the illuminant-constant condition revealed small but consistent shifts away from the physical tristimulus match (T) toward the blue competitors. In secondary analyses, we also computed constancy indices with
a computed with respect to the physical tristimulus match. In the results below, we note cases in which features of the data depend on which version of the constancy index is used.