302 JOURNAL OF COSMETIC SCIENCE RESULTS AND DISCUSSION DISTRIBUTIONS OF SKIN TRANSLUCENCY SCORES Clinically graded skin translucency scores of the 36 subjects were in a range of 1 to 7 on a 10-point scale. Its distribution is shown in Figure 3A, which appeared to cover most of the scale and was considered acceptable for multiple regression analysis. The high–low pairs formed from the translucency scores showed a wide distribution of the differences between translucency scores in 54 paired images (Figure 3B), which provided various levels of difference in skin conditions for panelists to evaluate. DISTRIBUTIONS OF OBJECTIVELY MEASURED SKIN VISUAL ATTRIBUTES Image analysis on the facial ROIs of 36 study subjects resulted in raw datasets of various skin parameters. Shapiro–Wilk tests were performed as the first step of data analysis to check the normality of such datasets, and the key properties of their distributions are shown in Table III where values of the mean, standard deviation, W-value (a statistical parameter for normality test), and p value (probability) are listed. Since Shapiro–Wilk normality test assumed that a dataset was from a normal distribution (null hypothesis), a p value greater than 0.05 would not reject the null hypothesis. Therefore, the results in Table III indicate that all datasets were normally distributed, which was essential for numerical modeling. In addition, of the 11 attributes listed in Table I, three variables (L*, a*, and b*) were excluded from the modeling process due to their direct correlations with other variables such as ITA° and HUE. The remaining eight variables Figure 2. Flow chart of Ideal Complexion Score modeling process.

303 Characterizing and Modeling Complexion were independent and represented skin properties of color, hue, and evenness (ITA°, HUE, CUE) subsurface light reflection (DRR) surface texture smoothness (SVS) and skin shine (dINT), as well as the contrast between red or dark spots and the normal skin (daStar and dbStar, respectively). Values of ΔPs of the above parameters for the 54 unique pairs of images, necessary for constructing a Logit(A) model, were obtained using Equation 1. PANEL RESPONSES AND MODELING The responses of 77 panelists to the 54 pairs of images were first quantified by the results of Logit(A). Image pairs with larger differences of perceived ideal complexion resulted Figure 3. Range and distribution of the clinically graded skin translucency scores of the 36 study subjects (A) and the difference between high and low scores in 54 unique pairs of skin images (B). Table III Properties of Data Distributions of Objectively Measured Skin Parameters Parameters Mean SD W value p value DRR 23.4371 2.3488 0.9497 0.1020 SVS 5.6430 0.7577 0.9802 0.8114 L* 54.8954 2.2996 0.9865 0.9376 a* 12.2484 1.1128 0.9761 0.6137 b* 19.9842 1.3718 0.9553 0.1532 ITA° 13.6615 6.2456 0.9828 0.8368 CUE 0.0641 0.0102 0.9669 0.3465 dINT 27.6884 2.4299 0.9683 0.3811 HUE 1.0203 0.0534 0.9776 0.6646 daStar 5.2635 0.6537 0.9807 0.7678 dbStar 3.4000 0.4341 0.9746 0.5628