# Pitfalls in the Detection of Hearing Loss via Otoacoustic Emissions
## 3 Results
### Discriminant Analysis  
The aim of the discriminant analysis was to determine which variables among the hearing thresholds and SNR data best distinguished the three classification groups (i.e., refer-refer, pass-pass, pass-refer). Based on assessed hearing thresholds, a discriminant analysis revealed two discriminant functions. The first one explained 95.2% of the variance (canonical \(R^{2}\) = 0.60), whereas the second explained 4.8% of the variance (canonical \(R^{2}\) = 0.07). In combination, both discriminant functions significantly differentiated the three groups (for the first function, \(\Lambda\) = 0.37; \(\chi^{2}\) = 176.87; \(p\) < 0.001; for the second: \(\Lambda\) = 0.93; \(\chi^{2}\) = 13.04; \(p\) = 0.042). Standardized discriminant function coefficients for the two functions are given in Table 4. The largest contribution to the first variate was made by thresholds at 1 and 2 kHz, while the 4 kHz threshold made the largest contribution to the second variable. The first function discriminates the refer-refer group from the pass-pass group (i.e., the distance between centroids is large). The second function discriminates the pass-refer group from the other two groups but is less powerful in differentiating them (Figure 2A). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hearing Threshold Elevated at** & **Refer-Refer** & **Pass-Pass** & **Pass-Refer** \\
**Frequencies:** & & & \\ \hline Only mid & 2 (20.0) & 6 (60.0) & 2 (20.0) \\ Only high & 1 (8.3) & 9 (75.0) & 2 (16.7) \\ Low+high & 0 & 1 (100) & 0 \\ Mid+high & 16 (26.2) & 24 (39.3) & 21 (34.4) \\ Low+mid+high & 26 (65.0) & 7 (17.5) & 7 (17.5) \\ All frequencies below 25 dB & 1 (1.6) & 50 (82.0) & 10 (12.4) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Agreement between both Accuscreen devices in ears with hearing thresholds above 25 dB in low and/or mid and/or high frequencies. Number of ears (and percent values) are given. Based on SNR results, the discriminant analysis revealed two discriminant functions. The first one explained 97.4% of the variance (canonical \(R^{2}=0.64\)), whereas the second explained only 2.6% of the variance (canonical \(R^{2}=0.04\)). The contribution of the first function was statistically significant (\(\Lambda=0.35\); \(\chi^{2}=189.80\); \(p<0.001\)), whereas the contribution of the second function was not statistically significant (\(\Lambda=0.96\); \(\chi^{2}=8.21\); \(p=0.084\)). Standardized discriminant function coefficients for the two functions are given in Table 4. The SNR at 2 kHz was the most important for the first function, while SNR at 1.4 kHz was the most important for the second. The first function discriminates the refer-refer \begin{table}
\begin{tabular}{c c c} \hline \hline
**A** & **Function 1** & **Function 2** \\ \hline \multicolumn{3}{c}{Coefficients} \\ \hline
125 Hz & \(-0.197\) & \(0.591\) \\
250 Hz & \(-0.543\) & \(-0.273\) \\
500 Hz & \(0.039\) & \(0.314\) \\
1000 Hz & \(0.753\) & \(0.384\) \\
2000 Hz & \(0.894\) & \(0.022\) \\
4000 Hz & \(-0.064\) & \(-1.421\) \\
8000 Hz & \(-0.123\) & \(0.463\) \\ \hline \multicolumn{3}{c}{Group centroids} \\ \hline Refer-refer group & \(1.988\) & \(0.159\) \\ Pass-pass group & \(-0.967\) & \(0.142\) \\ Pass-refer group & \(0.055\) & \(-0.503\) \\ \hline
**B** & **Function 1** & **Function 2** \\ \hline \multicolumn{3}{c}{Coefficients} \\ \hline SNR 1000 & \(-0.007\) & \(0.169\) \\ SNR 1414 & \(0.254\) & \(-1.285\) \\ SNR 2000 & \(0.786\) & \(0.450\) \\ SNR 2828 & \(0.052\) & \(0.613\) \\ SNR 4000 & \(0.007\) & \(0.140\) \\ \hline \multicolumn{3}{c}{Group centroids} \\ \hline Refer-refer group & \(-1.837\) & \(0.220\) \\ Pass-pass group & \(1.195\) & \(0.059\) \\ Pass-refer group & \(-0.747\) & \(-0.376\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of discrimination analysis based on PTA thresholds (**A**) and on SNR results (**B**). Figure 2: Discriminant function plots in which discrimination is based on hearing thresholds (**A**) and on SNR (**B**).