## 2 Materials and Methods
### Method
#### 2.1.2 Descriptive Statistics  
For each sequence based on speech, the measures of \(ET_{d}\) and their correspondent descriptive statistics measures (i.e., mean value [41], variance [42], skewness, and kurtosis [43]) were extracted, obtaining, specifically, the average ET (\(\overline{et_{s}}\)), variance of the ET \(\left(\overline{e_{t_{s}}}\right)\), skewness of the ET \(\left(\overline{\mu}_{et_{s_{3}}}\right)\), and kurtosis of the ET \(\left(Kurt_{et_{s}}\right)\).  
* \(ET_{d}\): the discrete emotional temperature of the recording (see Section 2.1.1);
* Average of the continuous emotional temperature \(\overline{(et_{s}})\): refers to the continuous emotional temperature vector values and describes the mean value of the different ET values of the sound fragments in a recording. It is estimated using the following estimator of the arithmetic mean [42]: \[\overline{(et_{s})}=\frac{\sum_{i=1}^{N}et_{c_{i}}}{N}\] (3)where \(et_{c_{i}}\) is the value of \(et_{c}\) for each fragment \((S_{1},S_{2},\ldots,S_{N})\) into which each voice recording \(\{S_{i}\}\) is divided;
* Variance in the continuous emotional temperature \(\big{(}\sigma_{et_{c}}^{2}\big{)}\): refers to the continuous emotional temperature vector values and describes the variation in the different fragments in a recording. It is estimated using the following estimator of the variance [42]: \[\sigma_{et_{c}}^{2}=\frac{\sum_{i=1}^{N}\big{(}et_{c_{i}}-\overline{et_{c}} \big{)}^{2}}{N-1}\] (4)
* Skewness of the continuous emotional temperature \(\bigg{(}\widetilde{\mu}_{et_{S_{n}}}\bigg{)}\): refers to the continuous emotional temperature vector values. This measure allows for characterising the behaviour of the probability distribution function of the ET values of the different fragments. This measure quantifies [43] the lack of symmetry of the average ET values of the voice fragments. Positive or negative values of \(\widetilde{\mu}_{et_{c}}\) indicate data skewed to the right of their distribution curve or to the left, respectively. The skewness of ET of speech is calculated using the following estimator: \[\widetilde{\mu}_{et_{S_{3}}}=\frac{\sum_{i=1}^{N}\big{(}et_{c_{i}}-\overline{et _{c}}\big{)}^{3}}{N\cdot\left(\sqrt{\sigma_{et_{c}}^{2}}\right)^{3}}\] (5) where \(et_{c_{i}}\) is the ET value of each sound fragment, \(\overline{et_{c}}\) is the average of the ET values, \(\sigma_{et_{c}}^{2}\) is the variance in the ET values, and \(N\) is the number of sound fragments in the sample of speech;
* Kurtosis of the continuous emotional temperature (\(Kurt_{et_{c}}\)): refers to the continuous emotional temperature vector values. This is a measure that allows for characterising another aspect of the behaviour of the probability distribution function of the ET values of the different fragments. This measure states the quantity of sound fragments in a recording with an ET value that is close to the average ET (\(\overline{et_{c}}\)). The larger the value of \(Kurt_{et_{c}}\), the steeper its distribution curve. \(Kurt_{et_{c}}\) is calculated using the following estimator [43]: \[Kurt_{et_{c}}=\frac{\sum_{i=1}^{N}\big{(}et_{c_{S_{i}}}-\overline{et_{c}} \big{)}^{4}}{N\cdot\left(\sqrt{\sigma_{et_{c}}^{2}}\right)^{4}}\] (6)  
Once the results of the emotion study were obtained for each sample, the five variables were stored in a single text document. From these measures, univariate and multivariate analyses were performed using Stata(r) software, version 13.0 [44].