## 3 The Results of the Statistical Analysis of the Work of the Optical and Electrochemical Methods
### Analysis of an Electrochemical Method for Measuring the Concentration of Exhaust Gas  
In the case of the electrochemical method, the measurements are strongly influenced by the humidity of the exhaust gas. In order to confirm this assumption, a laboratory installation was built with the supply of a drained sample and then with the supply of  
Figure 11: Errors in concentration. humidity by a humidifier with a potentiometer regulator that works on the ultrasound principle. The water particles were introduced by tubes, which imitated the installation, and a reference gas was used for the measurement. The electrochemical device was recommended by the Promanalyt LLP for the content determination. The results of the test are shown in figures that are supplied in the Supplementary Materials. In this case, the measurements of the drained sample had stable readings of 537 ppm, then the humidity was increased by the addition of water particles into the installation. When humidity was added to the sample, the readings decreased to a value of 393 ppm. In this case, the POLAR ultrasonic gas analyzer was used. Data collection was also carried out in the operating conditions of a coal-fired power plant. In this case, the readings had a different pattern. The values obtained during the data collection are shown in Table 5. Moreover, the measurements transformation was conducted considering a reference oxygen content equal to 6% [49]. Due to the small number of measurements, the application of the proposed technique in [55] to analyze the obtained values is difficult, but, according to the Breusch-Pagan test, it can be concluded that the remaining squares in this sample are independent of the measurement of the test sample. By analyzing these values in a similar way, statistical parameters can be presented as in Table 3 (Table 6). However, in this case, index 1 indicates POLAR measurements. The comparison of measurements is presented via mean values in the bar graph (Figure 12). For a more accurate analysis, graphs were plotted (Figure 13). The analysis of statistical significance was carried out by the _t_-test and the ANOVA test, and the data were written in Table 7. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Component** & \(\overline{y}_{1}\) & \(\overline{y}_{2}\) & **RMD1** & **RMD2** & **S1** & **S2** & **f** \\ \hline SO\({}_{2}\) & 1595.4 & 938.6 & 30.69 & 75.57 & 1177.3 & 7139.3 & 6.06 \\ NO\({}_{x}\) & 336 & 613 & 17.1 & 80.1 & 365.5 & 6416.5 & 17.56 \\ O\({}_{2}\) & 7.15 & 7.98 & 0.15 & 0.147 & 0.03 & 0.0027 & 11.11 \\ CO & 187.2 & 184.4 & 207.32 & 181.32 & 53,727.7 & 41,094.8 & 1.31 \\ \hline \end{tabular}
\end{table} 
Table 6: Results of statistical analysis of measurements of the traditional system in comparison with the standard. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Component** & **f (Fisher’s Test)** & **t-Value (t-Test)** & **F-Value (ANOVA)** & **_p-Value (t-Test)_ & **_p-Value (ANOVA)_** \\ \hline SO\({}_{2}\) & 6.06 & 16.1044 & 259.3525 & 0 & 0 \\ NO\({}_{x}\) & 17.56 & 7.5212 & 56.5681 & 0.0011 & 0.0001 \\ O\({}_{2}\) & 11.11 & 6.5320 & 42.6667 & 0.0006 & 0.0006 \\ CO & 1.31 & 0.0203 & 0.0004 & 0.9843 & 0.9843 \\ \hline \end{tabular}
\end{table} 
Table 7: The results of statistical analysis in comparison with three methods: Fisher’s test, _t_-test, ANOVA test.