# Breast Geometry Characterization of Young American Females Using 3D Image Analysis
## 3 Result and Discussion
### Shape and Placement Relationship  
The chi-square test was followed to see whether there is any significant relationship between four shape clusters and three placement clusters. The outcomes are summarized in Table 9, indicating that breast shapes and placements were strongly associated (\(p=0.000\)). Post-hoc analysis indicated which shape and placement group was associated with each other, and the resulting contingency table analysis is shown in Table 10. The significance was determined based on the \(p\)-value corrected by the Bonferroni method, which was 0.0042. According to the post-hoc analysis, large breasts were located significantly lower than other breast types (\(p=0.0000\)), and small breasts were located higher than others (\(p=0.0000\)). The droopy breasts were found not to take low placement (\(p=0.0000\)). The shape cluster 3 did not show any significance in terms of their placement. Considering each cluster's breast dimensions (Table 6), it could be concluded that longitudinal breast placement is highly correlated with breast size. One of the notable observations was that drooped breast shapes were clearly distinguishable from low breast placement. It was evidenced by the fact that there was no drooped breast located significantly low. In addition, the upward breasts were not always located high as well (Table 10). The breast placement clusters had a strong correlation with dimensional characteristics of breasts but were irrelevant to the vertical skewedness of the breast shapes. This indicates that drooping may need to be understood differently from being inferiorly located. This finding strongly supports the necessity to investigate the breast placement separated from its shapes. The proportion of the population belonging to each shape and placement cluster is also shown in Table 10. Breast shape analysis concluded that there are 31% of droopy breasts, 19% of small/flat breasts, 24% of upward breasts, and 26% of large/inward breasts in young American females aged 26 to 35. The proportion of small and large breasts was lower than 26% (small) and 40% (large and extra-large) reported in Australian st \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Placement Clusters**} \\ \cline{3-6}  & & \multicolumn{2}{c}{**3**} & **1** & **2** & **Total** \\ \cline{3-6}  & & \multicolumn{2}{c}{**(High)**} & **(Medium)** & **(Low/Open)** & \\ \hline \multirow{5}{*}{Shape clusters} & **1** & **count** & 21 (43.8\%) & 27 (56.3\%) & 0 (0.0\%) & 48 (30.8\%) \\  & **(drooped)** & \(\chi^{2}\) & 1.9 (\(p=0.1615\)) & 4.5 (\(p=0.0357\)) & 17.9 (\(p=0.0000\)) & \\ \cline{2-6}  & **2** & **count** & 27 (90.0\%) & 3 (10.0\%) & 0 (0.0\%) & 30 (19.2\%) \\  & **(small/flat)** & \(\chi^{2}\) & 6.9 (\(p=0.0000\)) & 17.0 (\(p=0.0000\)) & 0.49 (\(p=0.0000\)) & \\ \cline{2-6}  & **3** & **count** & 8 (21.6\%) & 22 (59.5\%) & 7 (18.9\%) & 37 (23.7\%) \\  & **(upward)** & \(\chi^{2}\) & 4.3 (\(p=0.0357\)) & 5.0 (\(p=0.0278\)) & 0.1 (\(p=0.7642\)) & \\ \cline{2-6}  & **4** & **count** & 0 (0.0\%) & 16 (39.0\%) & 25 (61.0\%) & 41 (26.3\%) \\  & **(large)** & \(\chi^{2}\) & 31.1 (\(p=0.0000\)) & 0.5 (\(p=0.4839\)) & 55.8 (\(p=0.0000\)) & \\ \hline \multicolumn{6}{c}{**Total**} & 56 (35.9\%) & 68 (43.6\%) & 32 (20.5\%) & 156 (100\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Contingency table analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Value** & **df** & **Asymptotic Significance (2-Sided)** \\ \hline Pearson Chi-square & 102.739 & 6 & 0.000 \\ Likelihood ratio & 118.226 & 6 & 0.000 \\ Linear-by-linear association & 6.933 & 1 & 0.008 \\ N of valid cases & 156 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Chi-square tests. generation (18-84) was involved (Table 1). Detailed direct comparisons were not possible since the current research included other shape factors beyond the breast size. The breast shape was clustered differently compared to Korean studies (Table 1).