## 4 Results
### System Impact on the Person
We find that the metric that varies the most is the Respiratory Rate at 13%. Subsequently, we have the Heart Rate at 5% and Temperature at 2%. This may lead us to think that the most conclusive metric of relationship with and without the sensor system is RR, with more strength in its variation for the majority of the sample. After, we perform 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 examine if 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 it was difficult to determine if the metrics are normally distributed and we used a statistical normality test. Tables 5 and 6 show the results of the Kolmogorov-Smirnov test for the nine metrics for each scenario. The Spearman correlation coefficient is a non-parametric method that measures the strength and direction of the association between two variables. It is advantageous because it can be used with ordinal, interval or ratio data and does not require the variables to be normally distributed, making it robust to outliers and suitable for data with non-normal distributions. Additionally, the calculation of the Spearman coefficient can detect monotonic relationships, which are relationships that increase or decrease consistently but may not necessarily be linear. Therefore, the Spearman coefficient is a useful tool for examining correlations between pairs of metrics, particularly when the data are not normally distributed or when outliers are present. These metrics do not follow the normal distribution with and without the system. We use the Spearman correlational coefficient to examine the correlations between each pair of metrics in both scenarios (with and without the sensor network). The following statistically significant correlations in the metrics without the use of the sensor network scenario were found: \begin{table}
\begin{tabular}{l l l} \hline \hline
**Metric** & \(\mathbf{p}\)**-Value** & **Normal Distribution** \\ \hline HR & 0.002 & No \\ RR & 0.000 & No \\ T & 0.000 & No \\ REMS & 0.010 & No \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of Kolmogorov–Smirnov test for metrics with the system. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Metric** & **Metric Average without System** & **Metric Average with System** \\ \hline HR & 73.51 & 69.88 \\ \hline RR & 16.90 & 14.59 \\ \hline T & 37.33 & 36.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Relationship of metrics with and without the sensor system. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Metric** & \(\mathbf{p}\)**-Value** & **Normal Distribution** \\ \hline HR & 0.021 & No \\ RR & 0.037 & No \\ T & 0.000 & No \\ REMS & 0.010 & No \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of Kolmogorov–Smirnov test for metrics without the system. Temperature and heart rate present negative correlations of \(-0.331\) with a \(p\)-value of \(0.001\). Temperature and REM sleep preset a positive correlation of \(0.221\) with a \(p\)-value of \(0.027\). Respiratory Rate and heart rate variability present a positive correlation of \(0.211\) with a \(p\)-value of \(0.035\). With the sensor network the following statistically significant correlations were found: Temperature and REM sleep present a negative correlation of \(-0.314\) with a \(p\)-value of \(0.001\). The results of the correlation analysis revealed some trends, although the correlations are not strong. The negative correlation between total sleep time and snoring with the use of the sensor network suggests that elderly people slept more and with fewer interruptions.