## 3 Study Evaluation
### Descriptive Statistics  
Descriptive statistics are represented by descriptive coefficients, which aim to summarize a set of numerical data. The idea is to graphically show whether the considered features assume different values, respectively, for the _healthy_ and _disease_ population and for the lung disease distributions (i.e., _asthma_, _bronchietasis_, _bronchiitis_, _COPD_, _LRTI_, _pneumonia_, and _URTI_). For feature representation, a scatterplot is considered, i.e., a type of visual representation exploiting Cartesian coordinates to show values for two features. Additionally, we considered a scatterplot as other studies have exploited it for graphical and immediate impact regarding the potential effectiveness of the proposed feature set for lung disease characterisation. We present four different scatterplots, but closer explanation can be made also for the other plots. The rationale behind the adoption of scatterplots is to empirically demonstrate that the distribution of features is different for healthy and lung disease-affected patients: as a matter of fact, the more the numerical value assumed by the features is similar for a class to be identified, but at the same time it is different from the value assumed by the features for another class, the more the machine learning algorithms will be able to create models with good discriminatory ability. Figures 2 and 3 show the scatterplots related to the _lung disease detection_ (i.e., with \(l_{detection}\in\{health\_{t}\_{t}\_{t}\_{t}\_{t}\_{t}\_{t}\_{t}\_{t}\_{t}\_{t}\_{t}\_ {t}\_{t}\_{t}\_{t}\)). In detail, Figure 2 shows the scatterplot for the \(F3\) (i.e., Spectral Centroid) and \(F2\) (i.e., Root Mean Square) features. As emerges from the scatterplot in Figure 2, the healthy distributions (i.e., the red points) are highly concentrated in the lower left corner if compared to the blue ones (i.e., the values obtained for the disease instances), occupying a much larger space in the scatterplot. In Figure 3 is depicted the scatterplot related to the feature \(F4\) (i.e., Bandwidth) and the feature \(F5\) (i.e., Spectral Roll-Off). Figure 3: Scatterplot for the \(F4\) (i.e., Bandwidth) and \(F5\) (i.e., Spectral Roll-Off) features. Figure 2: Scatterplot for the \(F3\) (i.e., Spectral Centroid) and \(F2\) (i.e., Root Mean Square) features. Similar considerations can be made; in fact, the distribution of the healthy points is more localised in comparison with the disease ones. From this observation, it emerges that the disease instances with respect to the \(F4\) and \(F5\) features are ranging in an interval that is wider than the healthy instances. Clearly, the more that the points of the healthy and disease cases are distant (i.e., the two distributions do not overlap), the more the classification algorithms will be able to generate effective models. Figures 4 and 5 are related to the scatterplots of the _lung disease detection_ (i.e., with \(I_{characterisation}\in\{\)_asthma_, _bronchiectasis_, _bronchiolitis_, _COPD_, _LRTI_, _pneumonia_, and _URTI_)). In particular, Figure 4 shows the scatterplot for the \(F8\) (i.e., Zero Crossing Rate) and \(F4\) features (i.e., Bandwidth). We note that the widest area is covered by the _COPD_ instances, symptomatic of the fact that the \(F8\) and \(F4\) features range in a wider interval if compared to the remaining features. For the instances of the remaining lung diseases, particularly _pneumonia_ and _asthma_, the range is in a similar interval, as confirmed by the instances overlapping. Figure 5 shows the scatterplot for the \(F9\) (i.e., Poly) and \(F3\) features (i.e., Spectral Centroid). Figure 4: Scatterplot for the \(F8\) (i.e., Zero Crossing Rate) and \(F4\) (i.e., Bandwidth) features. Figure 5: Scatterplot for the \(F9\) (i.e., Poly) and \(F3\) features (i.e., Spectral Centroid). Similarly to the considerations made for the scatterplots in Figure 4, the _COPD_ instances cover a more extended area in the scatterplot, confirming that the values of these instances are ranging in a wide interval.