## 4 Discussion
### Statistic Analysis  
We are particularly interested in determining whether the subjects' data suffer significant changes when subjects are aware that they are being observed by cameras. To validate this hypothesis, for each subject, we also captured data prior to installing the cameras. Since the observed measurements were captured under two different conditions (with and without cameras), we obtained a pair of observations for each subject. We want to verify if the observations collected under these two different conditions have an effect on the subjects. This is achieved using the \"paired sample test\", also called the \"dependent sample test\". If the observations are normally distributed or if the number of samples is \"large enough\", we can use the \(t\)-test, otherwise, we have to use a non-parametric approach. In statistics, non-parametric tests are statistical analysis methods that do not require a distribution that meets the required assumptions to be analyzed (especially if the data are not normally distributed). Due to this reason, they are sometimes referred to as distribution-free tests. Non-parametric tests serve as an alternative to parametric tests, such as \(t\)-test or ANOVA, which can be employed only if the underlying data satisfy certain criteria and assumptions--the Kruskal-Wallis test. (A) Testing Normality:  
By plotting the box plot for categories, we visualize associations between these two categories. Figure 10 shows these box plots that allow us to visualize the type of association between \"sensor\" and \"no-sensor\" categories. Visually, the statistic association between the monitored values for \"Breathing frequency\", \"Heart rate\" and \"Body temperature\" for all subjects before and after installing sensors are positive. Not one of them shows a much higher association than the others. On the other hand, visually, the statistic association between the monitored values for \"Sleep rhythm\" for all subjects before and after installing sensors are strongly negative. The first step in this analysis is to test if data are normally distributed. We use a histogram to see if the sampled data follow a normal distribution; we also draw a box plot to see how well balanced are each of the quartiles. Figure 11 shows the histogram of the difference of the different measurements taken; in red we also draw a red line with the sample mean. From this figure, it is difficult to observe if any of these signals have a normal distribution. A Q-Q plot, short for \"quantile-quantile\", is typically used to assess whether a set of data potentially comes from a normal distribution. If the data are normally distributed, the points in the Q-Q plot will lie on a straight diagonal line. Conversely, the more the points in the plot deviate significantly from the straight diagonal line, the less likely the set of data follows a normal distribution. Figure 12 shows the Q-Q plot. Note that for all the variables, it appears there are normality violations across the data. Nevertheless, this is still not conclusive. Therefore, we need to test this statistically to verify if the data are normally distributed. To this end, we used the Shapiro-Wilk test for normality. The null hypothesis for this test is that the data are normally distributed. The Prob < W value listed in the output is the \(p\)-value. If the chosen level is 0.05 and the \(p\)-value is less than 0.05, then the null hypothesis (i.e., the data are normally distributed) is rejected. If the \(p\)-value is greater than 0.05 the null hypothesis is not rejected. Table 9 shows the table with the results of the \(p\)-value for each type of observed measurement; it shows if the null hypothesis H0 is rejected or not. Finally, it shows the paired test to use. We observe that, for all measurements' differences with and without sensors, if the \(p\)-value is larger than 0.05 (95% confidence), the normality is not rejected.