## 4 Discussion
### Statistic Analysis
Therefore, we must use \(t\)-test to obtain the mean difference between the two conditions and determine if the means of the monitored variables are different or not. Figure 11: Histogram of difference between two conditions, without and with sensors. Red line is estimated mean. A paired \(t\)-test is used to test whether the means of the samples of both conditions are equal or not. Since a \(t\)-test requires us to know if the compared signals have the same variance, as a rule of thumb, we can assume that the populations have equal variances if the ratio of the larger sample variance to the smaller is less than 4:1. Since the variances for breathing frequency, heart rate, sleep rhythm, and body temperature sensors are 1.24269, 0.58489, 1.31356, and 1.30130, respectively, we consider that all measurements have equal variance. Table 10 shows the results of the paired \(t\)-test for all measurements. We observe that the means of the conditions on both scenarios, with and without sensors, are statistically different. From the above analysis, we conclude that, in general, the subjects' measurements are affected when subjects are aware of the presence of the system. (B) Analysis by gender:  
By plotting the box plot for the categories, we visualize associations between these two scenarios. Figure 13 shows box plots that allow us to visualize the type of association between \"sensor\" and \"no-sensor\" categories for men and women. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Variables** & \(p\)**-Value for “Paired \(t\)-Test”** &
\begin{tabular}{l} **H0 = Samples Means Are the Same** \\ **(with 95\% Confidence)** \\ \end{tabular} \\ \hline Breathing frequency & 0.000322 & H0 rejected \\ Heart rate & \(1.43\times 10^{-5}\) & H0 non-rejected \\ Sleep rhythm & \(1.91\times 10^{-36}\) & H0 non-rejected \\ Body temperature & 0.027598 & H0 non-rejected \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Result of difference of means test. Figure 12: Q–Q plot of measurements captured for two conditions: without and with sensors. (C) Male subjects:  
Figure 14 shows the histogram of the different measurements for male subjects. As shown, it is difficult to observe if any of this has a normal distribution. In the visual inspection it looks moderately normal and it is not conclusive. That is why it is to be complemented with a statistical test. Figure 15 shows the Q-Q plot for all measurements of the male subjects. Note that for all the variables, there appears to be normality violations across the data. Nevertheless, this is still not conclusive. Figure 14: Histogram of difference between two conditions, without and with sensors, for male subjects. Red line is estimated mean. Figure 13: Box plots for sensor and no-sensor categories for men and women. Table 11 shows the results of the \(p\)-values for each type of measurement for the male subjects. From this table, we observe that three of the measurements can use the paired \(t\)-test and one requires the use of the Wilcoxon \(t\)-test. The ratios of the larger to the smaller sample variance for breathing frequency, heart rate, sleep rhythm, and body temperature sensors for the male subjects are 1.11312, 0.34287, 2.32417, and 1.42631, respectively; therefore, we consider that all measurements have equal variance. Table 12 shows the results of the paired \(t\)-test for all the measurements. Note that the means of the conditions on both scenarios, with and without sensors, are statistically different. From the above analysis, we conclude that, in general, the \"breathing frequency\" and the \"sleep rhythm\" measurements for male subjects are affected when subjects are aware of the presence of the system.