# Viability of ABO Blood Typing with ATR-FTIR Spectroscopy
## 3 Results and Discussion
### Single-Antigen Identification  
Based on the results presented earlier, it becomes apparent that the algorithms exhibit a superior ability to differentiate samples containing the B antigen from the rest. Consequently, we proceeded to employ the aforementioned algorithms to ascertain whether they yield improved outcomes in identifying each antigen individually. Conversely, it was crucial to assess the feasibility of employing a distinct chemometric approach for the identification of each antigen. Hence, we conducted tests utilizing LDA and NBC to discern between samples classified as A and Non-A, as well as B and non-B, the results of which are recorded in Table 7.  
All the results presented in Table 7 exhibit statistically significant differences compared to the outcomes derived from random classification, with a _p_-value of less than 0.01. However, it is crucial to note that the classification of A demonstrates less desirable scenarios; the ratios of true positive (T+) and true negative (T-) using LDA, as well as T- using NBC, indicate lower success rates than those achieved randomly. Similarly, the false positive ratio (F+) using NBC surpasses the random counterpart. This further substantiates our previous thesis that the B antigen is more effectively detected by FTIR than its A counterpart. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**NBC Classification**} & \multicolumn{4}{c}{**Random Classification**} \\ \hline  & \multicolumn{4}{c}{**Assigned Class**} & \multicolumn{4}{c}{**Assigned Class**} \\ \hline  & & A & B & AB & 0 & & & A & B & AB & 0 \\ \cline{2-10}  & \multirow{2}{*}{A} & A & 4\% & 7\% & 1\% & 9\% & & & A & 5\% & 8\% & 3\% & 6\% \\ \cline{2-10}  & \multirow{2}{*}{B} & B & 5\% & 32\% & 4\% & 5\% & & & B & 8\% & 15\% & 5\% & 10\% \\ \cline{2-10}  & \multirow{2}{*}{AB} & AB & 0\% & 7\% & 6\% & 0\% & & & AB & 3\% & 5\% & 2\% & 3\% \\ \cline{2-10}  & \multirow{2}{*}{0} & 0 & 11\% & 8\% & 0\% & 5\% & & & 0 & 6\% & 10\% & 3\% & 7\% \\ \hline  & \multicolumn{4}{c}{T+} & T- & F+ & F- \\ \hline \multicolumn{4}{c}{A-type success rate} & \multicolumn{2}{c}{\(\downarrow\) 3.5\%} & \multicolumn{2}{c}{\(\uparrow\) 67.7\%} & \multicolumn{2}{c}{\(\
earrow\) 13.1\%} & \multicolumn{2}{c}{\(\searrow\) 15.7\%} \\ \hline \multicolumn{4}{c}{B-type success rate} & \multicolumn{2}{c}{\(\searrow\) 31.8\%} & \multicolumn{2}{c}{\(\searrow\) 31.3\%} & \multicolumn{2}{c}{\(\downarrow\) 23.7\%} & \multicolumn{2}{c}{\(\
earrow\) 13.1\%} \\ \hline \multicolumn{4}{c}{AB-type success rate} & \multicolumn{2}{c}{\(\downarrow\) 5.6\%} & \multicolumn{2}{c}{\(\uparrow\) 83.8\%} & \multicolumn{2}{c}{\(\uparrow\) 4.0\%} & \multicolumn{2}{c}{\(\uparrow\) 6.6\%} \\ \hline \multicolumn{4}{c}{0-type success rate} & \multicolumn{2}{c}{\(\downarrow\) 5.1\%} & \multicolumn{2}{c}{\(\
earrow\) 63.1\%} & \multicolumn{2}{c}{\(\
earrow\) 13.1\%} & \multicolumn{2}{c}{\(\searrow\) 18.7\%} \\ \hline \multicolumn{4}{c}{NBC Success rate} & \multicolumn{2}{c}{\(\downarrow\) 11.5\%} & \multicolumn{2}{c}{\(\
earrow\) 61.5\%} & \multicolumn{2}{c}{\(\
earrow\) 13.5\%} & \multicolumn{2}{c}{\(\
earrow\) 13.5\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: PC-NBC results for A, B, AB, and 0. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **T+** & **T-** & **F+** & **F-** \\ \hline Identifying A with LDA & \(\downarrow\) 9.6\% * & \(\uparrow\) 50.0\% * & \(\
earrow\) 19.2\% & \(\
earrow\) 21.2\% \\ \hline Identifying B with LDA & \(\uparrow\) 46.5\% & \(\uparrow\) 42.4\% & \(\downarrow\) 35.4\% & \(\uparrow\) 7.6\% \\ \hline Identifying A with NBC & \(\searrow\) 21.2\% & \(\
earrow\) 35.3\% * & \(\downarrow\) 31.3\% * & \(\uparrow\) 12.1\% \\ \hline Identifying B with NBC & \(\uparrow\) 44.4\% & \(\searrow\) 26.8\% & \(\
earrow\) 16.2\% & \(\uparrow\) 12.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Classification as A and B independently with LDA or NBC. * marks worse results than the random classification.