## 4 The Results
Figure 10: Simulated distributions of the angle \(\eta\) for group 53. Figure 9: Simulated distributions of the angle \(\delta_{D}\) for group 53.  
values (for 10,000 simulations) of the statistical tests of the \(\delta_{D}\) and \(\eta\) angles, as well as the standard deviations of these values. They present the results of statistical tests for isotropic distributions of \(\delta_{D}\) and \(\eta\) angles simulated using our method (assuming that the distribution of galaxy orientations in space is isotropic). The end result of the simulation was obtaining new \"theoretical isotropic distributions\". Verification of the effectiveness of the proposed new research method is possible by calculating new statistical tests using \"theoretical isotropic distributions\" obtained from numerical simulations. Tables 11 and 12 present the results of the analysis for the real distributions of \(\delta_{D}\) and \(\eta\) angles, taking into account their morphological types. The same experimental data were used in the calculation of the statistical tests presented in Tables 3, 4, 11 and 12. The difference was that, in the case of Tables 3 and 4, information on the morphological type of each galaxy was used separately, and in Tables 11 and 12, a simulated \"theoretical isotropic distribution\" was used, which already took into account the information on morphological types. This means that, in the second case, simulated distributions was used instead of ideal theoretical isotropic distributions (i.e., cosine distribution in the case of \(\delta_{D}\) angle, and uniform distribution in the case of \(\eta\) angle) Comparison of the results obtained in both cases shows that the alignment was obtained for the same groups. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Group** & \(N\) & \(\chi^{2}\) & \(\sigma(\chi^{2})\) & \(C\) & \(\sigma(C)\) & \(\lambda\) & \(\sigma(\lambda)\) & \(W^{2}\) & \(\sigma(W^{2})\) & \(U^{2}\) & \(\sigma(U^{2})\) \\ \hline  
\hline \end{tabular}
\end{table} 
Table 7: Result of the numerical simulations—mean values of \(\delta_{D}\) angle statistical tests with standard deviations—part 1. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Group** & \(N\) & \(P(\Delta_{1})\) & \(\sigma(P(\Delta_{1}))\) & \(P(\Delta)\) & \(\sigma(P(\Delta))\) & \(\Delta_{11}\) & \(\sigma(\Delta_{11})\) & \(\frac{\Delta_{11}}{\sigma(\Delta_{11})}\) & \(\sigma(\frac{\Delta_{11}}{\sigma(\Delta_{11})})\) \\ \hline
11 & 626 & 0.5730 & 0.2938 & 0.5587 & 0.3181 & 0.0068 & 0.0717 & 0.1156 & 1.2271 \\
12 & 332 & 0.5877 & 0.2976 & 0.5748 & 0.3117 & 0.0049 & 0.0981 & 0.0605 & 1.2217 \\
13 & 128 & 0.5716 & 0.2900 & 0.5597 & 0.3086 & 0.0082 & 0.1533 & 0.0636 & 1.1860 \\
14 & 426 & 0.5612 & 0.2868 & 0.5538 & 0.2953 & 0.0064 & 0.0807 & 0.0905 & 1.1389 \\
15 & 130 & 0.5205 & 0.2952 & 0.5104 & 0.2987 & 0.0072 & 0.1239 & 0.0560 & 0.9657 \\
17 & 80 & 0.5787 & 0.2937 & 0.5678 & 0.3035 & 0.0057 & 0.1910 & 0.0347 & 1.1681 \\ \hline \end{tabular}
\end{table} 
Table 8: Result of the numerical simulations—mean values of \(\delta_{D}\) angle statistical tests with standard deviations—part 2. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Group** & \(N\) & \(\chi^{2}\) & \(C\) & \(P(\Delta_{1})\) & \(P(\Delta)\) & \(\Delta_{11}\) & \(\sigma(\Delta_{11})\) & \(\frac{\Delta_{11}}{\sigma(\Delta_{11})}\) & \(\lambda\) & \(W^{2}\) & \(U^{2}\) \\ \hline \(11\) & 626 & **51.09** & **34.516** & **0.0000** & **0.0000** & 0.3  
The next step is to take into account not only the effect of different \(q_{0}\) values depending on the morphological type, but also to convert \(q\) to the standard photometrical axial ratios according to Fouque and Paturel formulae ([PERSON] and [PERSON], 1992). Our results are presented in Tables 13 and 14. It is easy to see that the strong anisotropy effect in the alignment of galaxies, observed when the values of the inclination angles were taken as the original values from the NBG catalog, now disappears.