# Increasing Photovoltaic Systems Efficiency Through the Implementation of Statistical Methods
## 4 Results
### Analysis of the ANOVA Method Results
The value thus obtained is compared with \(\chi^{2}\) obtained from the _Chi-Square Distribution Table_ for 2 degrees of freedom (df = 2) and alpha = 0.05 (statistical confidence interval of 95%), and the value obtained is  
\[\chi^{2}=5.991 \tag{7}\]  
According to the theory, hypothesis \(H_{0}\), for which the three distribution probabilities are equivalent, is denoted by \(H_{STAT}>\chi^{2}\), meaning that hypothesis \(H_{0}\) is rejected due to a significant difference between the groups. As a conclusion, for case A, the \(H_{0}\) hypothesis is rejected because the value of \(H_{STAT}\) is greater than the \(\chi^{2}\). There is a significant difference between the analysed groups. Next, the same algorithm was applied for case B, as presented in Table 8.  
Table 8 is similar to the above-presented Table 5, with the May, July, and September triad replaced by June, July, and August. Table 9 presents the table of values for Case B, similar to Table 6. Table 10 presents the table of ranks for Case B, which is identical to Table 7.  
Tables 9 and 10 resemble Tables 6 and 7 above, built for June, July, and August. \[H_{STAT}=-7.3 \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c} \hline
**Orientation** & **May** & & **July** & **September** \\ \hline
10\({}^{\circ}\) & 150 & 18 & 166 & 23.5 & 119 & 3 \\
20\({}^{\circ}\) & 151 & 19 & 166 & 23.5 & 127 & 6 \\
30\({}^{\circ}\) & 149 & 17 & 163 & 22 & 132 & 8 \\
37\({}^{\circ}\) & 146 & 15 & 159 & 21 & 134 & 10 \\
40\({}^{\circ}\) & 144 & 14 & 157 & 29 & 135 & 12 \\
50\({}^{\circ}\) & 137 & 13 & 147 & 16 & 134 & 10 \\
60\({}^{\circ}\) & 126 & 5 & 134 & 10 & 130 & 7 \\
70\({}^{\circ}\) & 112 & 1 & 118 & 2 & 122 & 4 \\ Rang sum & & 102 & & 147 & 60 \\ \hline
**(Rang sum)2** & & **10,404** & & **21,609** & & **3600** \\ \hline \end{tabular}
\end{table} 
Table 7: Case A: The analysis (table of ranks) for May, July, and September. \begin{table}
\begin{tabular}{c c c c} \hline
**Orientation** & **June 2024** & **July 2024** & **August 2024** \\ \hline
10\({}^{\circ}\) & 157 & 166 & 155 \\
20\({}^{\circ}\) & 156 & 166 & 159 \\
30\({}^{\circ}\) & 152 & 163 & 160 \\
37\({}^{\circ}\) & 148 & 159 & 159 \\
40\({}^{\circ}\) & 146 & 157 & 158 \\
50\({}^{\circ}\) & 136 & 147 & 152 \\
60\({}^{\circ}\) & 123 & 134 & 142 \\
70\({}^{\circ}\) & 107 & 118 & 129 \\ \hline \end{tabular}
\end{table} 
Table 8: Case B: Monthly energy production (in MWh) and ranks related to the panel’s angle for June, July, and August. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Rank** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** \\ \hline Value & 107 & 118 & 123 & 129 & 134 & 136 & 142 & 146 & 147 & 148 & 152 & 152 \\
**Avg rank** & & & & & & & & & & **11.5** \\ \hline
**Rank** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** & **21** & **22** & **23** & **24** \\ Value & 155 & 156 & 157 & 157 & 158 & 159 & 159 & 160 & 163 & 166 & 166 \\
**Avg rank** & & & **157** & & & **159** & & & & **23.5** \\ \hline \end{tabular}
\end{table} 
Table 9: Case B: A table of values with explanation of ranks. For case B, the \(H_{0}\) hypothesis cannot be rejected because the value of \(H_{STAT}\) is smaller than the \(\chi^{2}\), as presented in Equation (8). In this case, with the analysed months having similar energy production values, there is no significant difference between the analysed groups, as indicated by the Kruskal-Wallis \(H\) test.