## 3 The Results of the Statistical Analysis of the Work of the Optical and Electrochemical Methods
### Analysis of the Optical Method for Measuring the Concentration of Exhaust Gas  
According to the existing knowledge of optical methods, different spectra of several wavelengths are used to measure gas components. In [53], it is indicated in which frequency ranges absorption and luminescence are carried out (Figure 6). Therefore, from the known data, it can be noted that the main part of the absorbed energy of SO2 is superimposed with the absorption spectrum of NO in the ultraviolet range. Moreover, it is also superimposed on the absorption spectrum of water particles in the entire range. On the other hand, in the inter-infrared and far-infrared ranges, the change is influenced by the measurement of NO and NO2. On the other hand, during luminescence, the spectra of SO2 and NO2 do not overlap. However, if there is a high concentration of nitric oxide in the gas, the measurement may also have a large error. Figure 6: Absorption spectrum of components [53] (* is used for the components that emit light). In turn, to determine the influence exerted on the measurement, it is worth noting that an analysis of the spectral pattern of absorption frequencies by light radiation elements is necessary. The measured values from two different measurement systems were presented in Table 1 for SO\({}_{2}\), NO, and NO\({}_{2}\), and in Table 2 for NOx, O\({}_{2}\), and CO. Moreover, the measurements transformation was conducted by considering the reference O\({}_{2}\) content equal to 6% [49]. In order to verify the accuracy of the SOLER-500 system, the method specified in the ISO-13752 standard was used [56]. According to the requirements, using the Breusch-Pagan test, it was determined that the values of the residues are independent of the measurements in this sample [57]. Consequently, the Fisher method was used for the evaluation. The obtained values have high similarity, and the f-values took values in most cases from 1 to 1.05, except for measurements of CO for which the f-value was 1.52 (Figure 7). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Time**} & \multirow{2}{*}{**SO\({}_{2}\) (mg/m\({}^{3}\))**} & **SO\({}_{2}\)** & **NO** & **NO** & **NO\({}_{2}\)** & **NO\({}_{2}\)** \\  & & **(1500)** & **(mg/m\({}^{3}\))** & **(mg/  
Therefore, in order to determine the possibility of using tuning coefficients, as well as to evaluate the operation of the device, the Fisher coefficient was used for a complete sample of measurements. Therefore, parameters such as the expectation values for the \(\overline{y}_{1}\) and \(\overline{y}_{2}\) for the Inspector 500 are used for the calculation. The values of the standard deviation RMD1 and RMD2, the unbiased variance S1 and S2, and the Fisher criterion f are also used. All the values obtained were entered in Table 3.  
Firstly, according to Table 3, the distribution of the mean values can be presented as a bar graph (Figure 8). With the aim of statistical significance and zero-hypothesis testing, the additional mathematical operations Student's test and ANOVA test (dispersion test) needed to be carried out (Table 4) for statistical significance that does not exceed 0.01. The results are presented in the bar graph. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Component** & \(\overline{y}_{1}\) & \(\overline{y}_{2}\) & **RMD1** & **RMD2** & **S1** & **S2** & **f** \\ \hline SO\({}_{2}\) & 343.27 & 320.24 & 88.05 & 109.41 & 8458.08 & 13,058.62 & 1.54 \\ NO & 61.49 & 110 & 20.9 & 36.75 & 476.72 & 1472.95 & 3.09 \\ NO\({}_{2}\) & 378.44 & 5.09 & 128.59 & 1.96 & 4.18 & 18,038.19 & 3958.2 \\ NO\({}_{x}\) & 165.49 & 154.1 & 19.06 & 48.46 & 396.33 & 2561.76 & 6.46 \\ O\({}_{2}\) & 16.18 & 15.75 & 0.51 & 1.2738 & 0.2852 & 1.77 & 6.21 \\ CO & 13.97 & 35.64 & 1.98 & 4.29 & 4.28 & 2.01 & 4.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of statistical analysis of measurements of the traditional system in comparison with the standard. Figure 8: Comparison of mean values for concentration: (**a**)—for SO\({}_{2}\), NO.