# Facial Soft Tissue Thickness Values for Romanian Adult Population
## 3 Results  
Figure 2 presents the overall distribution (as density curves) of all numerical variables in the 100-case dataset. Some variables, such as _glabella_ and _l_mid_supraorbital_ are more concentrated around their central values, whereas others, such as _nasion_ and _supraglabella_, are more scattered. The Shapiro-Wilk test of normality (not shown) reveals that _age_years_ is the only numeric variable with a normal distribution. This determines the types of tests to be chosen when assessing the statistical significance of the differences among groups or the correlation among variables. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & & \\ \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Statistic**} & \multirow{2}{*}{**Overall,**} & **a.Underweight,** & **b.Normal weight,** & **c.Overweight,** & \\  & & **N = 100** & **N = 50** & **N = 42** & **N = 8** & **_p-Value 1_ \\ \hline
**age\_years** & Median (IQR) & 52 (42, 65) & 52 (42, 65) & 52 (45, 58) & 67 (22, 67) & 0.8 \\
**sex** & & & & & 0.4 \\
**Female** & n (\%) & 42 (42\%) & 21 (42\%) & 16 (38\%) & 5 (62\%) & \\
**Male** & n (\%) & 58 (58\%) & 29 (58\%) & 26 (62\%) & 3 (38\%) & \\
**height\_mm** & Median (IQR) & 168 (165, 176) & 168 (165, 176) & 168 (166, 176) & 162 (159, 185) & 0.7 \\
**supraglabella** & Median (IQR) & 2.80 (2.00, 3.00) & 2.45 (2.00, 2.98) & 2.80 (2.30, 3.10) & 3.60 (2.80, 4.30) & 0.002 \\
**glabella** & Median (IQR) & 3.10 (2.80, 3.30) & 3.10 (2.60, 3.45) & 3.00 (3.00, 3.18) & 3.70 (310, 4.20) & 0.038 \\
**nasion** & Median (IQR) & 3.15 (2.77, 3.92) & 3.50 (2.94, 4.38) & 3.00 (2.70, 3.20) & 4.10 (3.20, 5.00) & -0.001 \\
**thinion** & Median (IQR) & 2.00 (1.88, 2.50) & 1.90 (1.80, 2.22) & 2.25 (2.00, 2.60) & 2.20 (1.90, 2.40  
Tables 2 and 3 provide descriptive statistics by grouping the results by sex (Table 2) and weight category (Table 3). The last column in both tables refers to the \(p\)-value of the statistical tests concerning group differences (Wilcoxon rank sum test and Kruskal-Wallis test). Table 2 provides the descriptive statistics when grouping the results by sex. Last column in the table contains the \(p\)-value of the statistical tests concerning group differences (the Wilcoxon rank sum test). Of the 100 (deceased) people in the dataset, 48 were females and 52 males. Overall median age was 52 years (54 for females and 52 for males). The difference on age distribution between females and males was not statistically significant (\(p\)-value = 0.4). By contrast, Table 2 suggests that the differences on height between females and males are statistically significant (\(p\)-value \(<\) 0.001). According to Table 2, only one landmark appeared to manifest statistically significant differences between sexes, i.e., _nasion_. For _l_mid_zygomatic_, at 0.05 significance level (alpha), the difference is not significant. Because the Shapiro-Wilk normality test reports W = 0.896, \(p\)-value \(<\) 0.001 for _nasion_, and W = 0.755, \(p\)-value \(<\) 0.001 for _zygomatic_, the statistical differences between sexes on both variables were assessed with the non-parametric Mann-Whitney test--see Figure 3.  
For variable _nasion_ (Figure 3 (left)), the Mann-Whitney test assesses the null hypothesis that, for randomly selected values of _nasion_ for females (X) and values of _nasion_ for males (Y), the probability of X being greater than Y is equal to the probability of Y being greater than X. The \(p\)-value (0.03) is smaller than the 0.05, and the effect size is medium (\(-\)0.25 CI95% [\(-\)0.45, \(-\)0.03]); thus, there is sufficient evidence to reject H0. _Nasion_ median is larger for males than females (3.49 vs. 3.00) and the differences between the two distributions are statistically significant. As for variable _l_mid_zygomatic_ (Figure 3 (right)), not only the \(p\)-value exceeds 0.05, but also the 95% confidence interval of the effect size covers the value of zero; therefore, the differences between sexes for _l_mid_zygomatic_ are not significant.