# Effect of Exposure Time on Thermal Behaviour: A Psychophysiological Approach
## 4 Data Analysis and Findings
### Temporal Change  
Another visible observation was the change of physiological reaction to similar conditions over time within the same day. As speculated beforehand, this study is not only interested in how different spaces with different thermal setups affect the human body, but also when and for how long. In that regard, the same SCL data was plotted against time. A k-means clustering (elbow joint at k = 2) revealed a change in regression around lunchtime in most of the cases (see Figure 10). It must be noted that in all of the following analyses,  
Figure 8: Boxplots of tonic EDA over temperatures, *: \(p\) < 0.05 **: \(p\) < 0.01 (Kruskal-Wallis H test with Bonferroni correction on multiple comparisons). Figure 7: Boxplots showing daily EDA tonic ranges. the dataset is only for when the participants were inside the Sense Lab. Therefore, the gaps in the timelines show the breaks. Scatter plots with temperature and SCL values illustrate the overall effect (Figure 11). The differences in morning and afternoon clusters are clearly visible in some participants (Participants 1 and 5), more moderate in some others (Participants 3 and 4), and an insignificant difference can be seen in one (Participant 2). The correlation of the tonic EDA values with temperature of all participants was checked for morning and afternoon cluster. The correlation of the EDA and temperature was greater for the afternoon cluster (\(r\) = 0.449, \(p\) < 0.001) in relation to the morning cluster (\(r\) = 0.332, \(p\) < 0.001). The statistical significance of the morning and afternoon correlation was checked using the Williams's Test [52]. The data were transformed according to the Fischer transformation  
\[{r^{\prime}}_{1}=\frac{1}{2}\ln(\frac{1+r_{1}}{1-r_{1}}){r^{\prime}}_{2}=\frac{ 1}{2}\ln(\frac{1+r_{2}}{1-r_{2}}) \tag{1}\]  
in order to be normally distributed. The statistic \(z\) of the test is given by the formula  
\[z=\frac{{r^{\prime}}_{1}-{r^{\prime}}_{2}}{\sqrt{S_{1}^{2}+S_{2}^{2}}}=\frac{ 1}{\sqrt{\frac{1}{n_{1}-3}\,+\,\frac{1}{n_{2}-3}}}{r^{\prime}}_{1}-{r^{\prime }}_{2} \tag{2}\]  
where \(r_{1}\), \(r_{2}\) are the correlation coefficients between EDA and temperature of the morning and evening cluster, respectively, and \(n_{1}\), \(n_{2}\) are the samples of the morning and evening cluster, respectively. The William's Test resulted in statistically significant higher correlation between tonic EDA and temperature in the afternoon cluster (\(z\) = 6.534, \(p\) < 0.001) in relation to the morning cluster. At first glance, there were several possible explanations for the differences in \"morning\" and \"afternoon\" clusters:  
1. The participants left the climate chamber for lunch, walked to a nearby restaurant (less than 10 min) and walked back. This rise in activity level, especially after having the entire morning spent sitting in front of a desk, might have resulted in higher EDA overall. Figure 9: Examples showing different relationships with EDA activity and temperature. (**A**): An expected drop in tonic levels after a short break in the cold room; (**B**): An immediate rise in the EDA tonic level after coming back to the climate chamber, after a large thermal change; (**C**): A rise in tonic levels with no changes in temperature, potentially unobserved clothing change; (**D**): Many breaks but no observable impact on EDA, however EDA activity is not particularly high either; (**E**): Similarly no correlation between breaks and EDA, however EDA has an upwards consistent trend. Figure 10: The morning and afternoon clusters of SCL of each participant, 25 \({}^{\circ}\)C, 27 \({}^{\circ}\)C, 28 \({}^{\circ}\)C, 29 \({}^{\circ}\)C, and 30 \({}^{\circ}\)C test days and overall trends shown in the final images. A contradiction to the hypothesis, Participant 2, is both a smoker who takes several smoking breaks outside and is the person with the latest starting schedule (11.00–19.00). Whether either or both of these resulted in levelled morning and afternoon clusters is not known at the moment.