# Improving Ship Maneuvering Safety with Augmented Virtuality Navigation Information Displays
## 3 Results
### Analysis of Multiple Comparisons of the Means Using the Post Hoc Test
#### 3.8.3 Analysis of Multiple Comparisons of the Parameters in Scenario 4. Cruise Ship  
Similar values of the significance level of test statistics were observed for the cruise ship variant in passages using the decision support system with AV-based navigational information display.  
For the distributions of the random variable of the primary criterion, i.e., the distances X4 of the sea ferry from the eastern berth of Gryfia Island in the independent group X4_AV, the differences of the means turned out to be significant for the level assuming values \(p\)\(<\) 0.0001, compared with independent groups X4_Visual, X4_ECDIS, X4_Pmax and X4_Pprecise, obtained for variants 4_Visual, 4_ECDIS, 4_Pmax and 4_Pprecise, of Scenario 4 (Table 17). Thus, there was a basis for rejecting hypothesis H0 stating the equality of the means in the examined independent groups.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{Multiple Comparison for Variants of Scenario 3 (Sea Ferry)} \\ \hline \multicolumn{6}{c}{Dependent Variable:} & \multicolumn{6}{c}{Distance (m)} \\ \hline \multicolumn{6}{c}{Games–Howell Test} \\ \hline \hline \multirow{4}{*}{(I) Variant} & Difference & \multirow{2}{*}{Standard Error} & \multirow{2}{*}{Significance} & \multicolumn{2}{c}{95\% Confidence Level} \\ \cline{3-6}  & Between the Means (I–J) & & & & Lower & Upper \\ \cline{3-6}  & & & & & Limit & Limit \\ \hline \multirow{4}{*}{3\_AV} & 3\_Visual & \(-1.80917\) * & 0.33613 & 0.002 & \(-2.8956\) & \(-0.7227\) \\  & 3\_ECDIS & \(-1.90417\) * & 0.22309 & 0.000 & \(-2.6247\) & \(-1.1836\) \\ \cline{1-1}  & 3\_Pmax & \(-1.08333\) * & 0.14672 & 0.000 & \(-1.5564\) & \(-0.6102\) \\ \cline{1-1}  & 3\_Pprecise & \(-0.67667\) * & 0.07903 & 0.000 & \(-0.9297\) & \(-0.4236\) \\ \hline \hline \end{tabular}  
* green color—the difference between the means is significant at the level 0.05.  
\end{table}
Table 16: The falsification of the hypotheses on the equality of mean distributions of the random variable of the ferry distance from the assumed reference point.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{Multiple comparison for variants of scenario 4 (cruise ship)} \\ \hline \multicolumn{6}{c}{Games–Howell test} \\ \hline \hline \multirow{4}{*}{(I) Variant} & Difference & \multirow{2}{*}{Standard Error} & \multirow{2}{*}{Significance} & \multicolumn{2}{c}{95\% Confidence Level} \\ \cline{3-6}  & Between the Means (I–J) & & & Lower & Upper \\ \cline{3-6}  & 4\_Visual & \(-2.34650\) * & 0.09033 & 0.000 & \(-2.6164\) & \(-2.0766\) \\ \cline{1-1}  & 4\_ECDIS & \(-2.51700\) * & 0.23620 & 0.000 & \(-3.2266\) & \(-1.8074\) \\ \cline{1-1}  & 4\_Pmax & \(-1.44650\) * & 0.04953 & 0.000 & \(-1.5926\) & \(-1.3004\) \\ \cline{1-1}  & 4\_Pprecise & \(-0.14150\) * & 0.02657 & 0.000 & \(-0.2178\) & \(-0.0652\) \\ \hline \hline \end{tabular}  
* green color—the difference between the means is significant at the level 0.05.  
\end{table}
Table 17: The falsification of the hypotheses on the equality of means of the random variable: distance of the cruise ship from the east berth of Gryfia Island.