4.2. 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. 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.
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.
(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.
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.
(D) Female subjects:
Figure 16 shows the histogram of the difference of the different measurements for the female subjects. In this figure it is difficult to observe if any of this has a normal distribution.
Figure 17 shows the Q–Q plot for all measurements of the female subjects, and we observe that for all the variables, there appears to be divergences from normality in all data. However, this is not conclusive.
Table 13 shows the table with the results of the
p-value for each type of measurement for male subjects. From this table, we observe that three of the measurements can use a paired
t-test, and one requires the use of a Wilcoxon
t-test. We observe that null hypothesis for “breathing frequency” is in the border to be rejected.
The ratio of the larger to the smaller sample variance for breathing frequency, heart rate, sleep rhythm, and body temperature sensors for males are 1.53213, 0.25152, 0.66405, and 1.15626 respectively; therefore, we consider all measurements to have equal variance.
Table 14 shows the results of the paired
t-test for all measurements. We observe that, statistically, the means of the conditions in both scenarios, no-sensors and sensors, are different for “Breathing frequency”, “Heart rate”, “Sleep rhythm”, but not for “Body temperature”.
From the above analysis, we conclude that in general “Breathing frequency”, “Heart rate” and “Sleep rhythm” measures for female subjects are affected when they know they are under the system.
4.4. Perceptions of Men and Women
In order to corroborate the perceptions of men and women, we conducted a survey based on a Likert scale with the following values: 0 = very bad, 1 = bad, 2 = OK, 3 = Good, 4 = Great. This survey was conducted every day of the week, and a general average was obtained.
Figure 19 and
Figure 20 show a radial map of perception, with concentric radii from 0 to 4, which are the previously mentioned sensation values of the scale. We observe that the days when people feel better with the presence of the network is from Monday to Friday and, specifically, on Monday, Tuesday, and Wednesday. In this aspect, both sexes coincide. Subsequently, women have a 10% greater sense of well-being than men. On weekends (Saturdays and Sundays), people feel good (or OK) with the care they could receive from the network. This may be because these are days when people receive more visits from family or friends, so people feel safer because they are not alone.
After a detailed analysis based on women and men separately to understand their degree of unconscious affectation, we will study the usefulness of the sensor network.
Figure 17 describes the number of alerts by each sensor, due to an abnormality, per day of the week. The days of the week correspond to the colored boxes that each sensor has. The “x” axis has the labels of the types of sensors that make up the network. The “y” axis presents the number of alerts sent by each sensor on each day of the week. For example, on Sunday, the level sensor had 1 alert, the PTH sensor had 3 alerts, the motion sensor had 2 alerts, the noise sensor had 2 alerts, the gyroscope had 1 alert, the light and the air sensors did not present alerts. This graph gives an idea of the usefulness of the network for people. However, it is important to consider the false positives of the sensor alerts. In reality, an alert could have been the alarm of a possible accident or a cause that threatened the person’s health. With this figure, we observe the use of sensors by day of the week and its impact on sending alerts. We observe that the PTH sensor has the most significant impact due to the characteristics it measures. However, it only gives an idea of the general parameters of the home and that they could not necessarily put the person’s health at risk. The level sensor is the second sensor with the most significant impact on the network. It gives an idea of the person’s anomalous positions, which can indicate a fall. Light and air sensors contribute little to health care, but they improve people’s quality of life and comfort.
Although
Figure 21 helps to know the impact of each sensor on the person’s health care, it is vitally important to know the true usefulness and degree of reliability of each sensor. The sensors can send alerts of possible attention situations, but these can be false positives, and the person is not necessarily in danger.
Table 15 shows each sensor’s degree of confidence regarding the relationship between true alerts and alerts that were not at risk. It is essential to remember that not all sensors have the same degree of importance when detecting a possible danger. For example, the level sensor can be more accurate in detecting a possible fall of the person, and the motion sensor detects the presence of people in strange places at times that do not coincide with the person’s routine. This table only indicates the individual work of each sensor, but when we take the complete sensor network, this can be more useful for daily life. The light sensor does not apply to this degree of confidence because the luminaries are not directly related to the person’s health care. Therefore, this sensor only contributes to comfort and convenience. It is pertinent to consider that the network of this work is studied for the comfort, comfort, and health care of the older adult, without losing their independence. For this reason, all network sensors are essential to the extent that they contribute to people’s well-being.