## 4 Results
### Results of the Sensor Network over the Sleep Metrics
#### 4.2.2 Correlational Analysis  
We then performed a correlation analysis between the metrics for both scenarios, with and without the use of the sensor network. At this point, to perform the appropriate correlation coefficient we examined whether each separate metric follows a normal distribution or not. If a couple of metrics from the same scenario (with the sensor network or without the sensor network) follow a normal distribution we can use a parametric correlation coefficient. Otherwise, we have to use a non-parametric correlation coefficient. As in the paired hypothesis, test analysis with the graphical methods was difficult to determine if the metrics are normally distributed, and we used a statistical normality test. Tables 11 and 12 show the results of the Kolmogorov-Smirnov test for the nine metrics for each scenario.  
As the nine metrics with and without the use of the sensor network do not follow the normal distribution, we used the Spearman correlational coefficient to examine the correlations between each pair of metrics in both scenarios (with and without the sensor  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & \(p\)**-Value** & **Test** & **Statistically** & **Difference** \\  & & & **Different** & **Direction** \\ \hline DS & 0.000 & [PERSON] & Yes & \(SN>NSN\) \\ HR & 0.006 & \(t\)-test & Yes & \(SN<NSN\) \\ BF & 0.000 & \(t\)-test & Yes & \(SN<NSN\) \\ T & 0.000 & [PERSON] & Yes & \(SN<NSN\) \\ REMS & 0.000 & [PERSON] & Yes & \(SN>NSN\) \\ OS & 0.004 & [PERSON] & Yes & \(SN>NSN\) \\ HRV & 0.000 & \(t\)-test & Yes & \(SN>NSN\) \\ S & 0.000 & [PERSON] & Yes & \(SN<NSN\) \\ TST & 0.000 & [PERSON] & Yes & \(SN>NSN\) \\ \hline \hline \end{tabular}
\end{table}
Table 10: Results of paired tests between metrics with and without the use of the sensor network.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & \(p\)**-Value** & **Normal Distribution** \\ \hline DS & 0.000 & No \\ HR & 0.021 & No \\ BF & 0.037 & No \\ T & 0.000 & No \\ REMS & 0.010 & No \\ OS & 0.000 & No \\ HRV & 0.008 & No \\ S & 0.003 & No \\ TST & 0.000 & No \\ \hline \hline \end{tabular}
\end{table}
Table 11: Results of Kolmogorov–Smirnov test for metrics without the sensor network.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & \(p\)**-Value** & **Normal Distribution** \\ \hline DS & 0.014 & No \\ HR & 0.002 & No \\ BF & 0.000 & No \\ T & 0.000 & No \\ REMS & 0.010 & No \\ OS & 0.000 & No \\ HRV & 0.000 & No \\ S & 0.004 & No \\ TST & 0.000 & No \\ \hline \hline \end{tabular}
\end{table}
Table 12: Results of Kolmogorov–Smirnov test for metrics with the sensor network.  
network). The following statistically significant correlations in the metrics without the use of the sensor network scenario were found:  
1. Temperature and heart rate present negative correlations of \(-0.331\) with a \(p\)-value of \(0.001\).
2. Temperature and REM sleep present a positive correlation of \(0.221\) with a \(p\)-value of \(0.027\).
3. Breathing frequency and heart rate variability present a positive correlation of \(0.211\) with a \(p\)-value of \(0.035\). On the other hand, with the use of the sensor network the following statistically significant correlations were found:  
1. Temperature and REM sleep present a negative correlation of \(-0.314\) with a \(p\)-value of \(0.001\).
2. Total sleep time and snoring present a negative correlation of \(-0.282\) y with a \(p\)-valor of \(0.004\).