# Improving Ship Maneuvering Safety with Augmented Virtuality Navigation Information Displays
## 3 Results
### The Comparison of the Random Variables of Scenarios 5a and 5b. The Two Train
To determine the significance of the mean differences for all variants of the simulation experiment scenarios, parametric tests were conducted. For Scenarios 1-4, in which each time a statistical analysis was conducted for more than two independent groups (\(k>2\)) of the primary criterion, i.e. :  
1. the resultant speed of the container ship determined at the moment of contact with the render obtained for four variants of Scenario 1: V1_Visual, V1_ECDIS, V1_Pprecise, V1_AV;  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{5a\_Pprecise} & \multicolumn{2}{c}{5a\_AV} & \multicolumn{2}{c}{5b\_Pprecise} & \multicolumn{2}{c}{5b\_AV} \\ \cline{2-10}  & \multicolumn{4}{c}{Distance of the Tow Train Contour Points} & \multicolumn{4}{c}{Distance of the Tow Train Contour Points} \\  & \multicolumn{4}{c}{from the Assumed Reference Point of the} & \multicolumn{4}{c}{} & \multicolumn{4}{c}{from the Assumed Reference Point of the} \\  & \multicolumn{4}{c}{Maneuvering Area (m)} & \multicolumn{4}{c}{Maneuvering Area (m)} \\ \hline Sector & Mean & Maximum & Mean & Maximum & Sector & Mean & Maximum & Mean & Maximum \\ \hline
1 & 125.68 & 125.88 & 98.00 & 109.84 & 1 & 106.32 & 119.45 & 85.29 & 95.33 \\ \hline
4 & 125.0  
2. the resultant speed of the general cargo ship determined at the moment of contact with the fender obtained for five variants of Scenario 2: V2_Visual, V2_ECDIS, V2_Pmax, V2_PPrecise, V2_AV;
3. distances of the sea ferry from the assumed reference point obtained for five variants of Scenario 3: X3_Visual, X3_ECDIS, X3_Pmax, X3_PPrecise, X3_AV;
4. distances of the cruise ship from the east quay of Gryfia Island obtained for five variants of Scenario 4: X4_Visual, X4_ECDIS, X4_Pmax, X4_Pprecise, X4_AV; and the random variables of the secondary criterion:  
1. time of maneuvering obtained for four variants of Scenario 1: T1_Visual, T1_ECDIS, T1_Pprecise, T1_AV,
2. time of maneuvering obtained for five variants of Scenario 2: T2_Visual, T2_ECDIS, T2_Pmax, T2_Pprecise, T2_AV, and at the same time, the variances were found to be heterogeneous in the above groups, and the equality of the mean distributions of the above random variables in the independent groups was verified by the Welsh test and the Brown and Forsyth test. The results of Welsh tests and Brown and Forsyth tests showed no statistically significant differences between the mean distributions of the random variables of the container ship's speed \(V_{1}\) determined at the moment of contact with the fender and the time of maneuvering \(T_{1}\) in the independent groups obtained for all four simulation variants of Scenario 1. The significance level of the test statistic for Scenario 1 assumed the value of \(p>0.05\), which was the basis for accepting H\({}_{0}\) at the set level of significance \(\alpha=0.05\). There were no statistically significant differences between the mean distributions of the random variable \(V_{1}\) in the independent groups V1_Visual, V1_ECDIS, V1_Pprecise, V1_AV and the random variable \(T_{1}\) in the independent groups T1_Visual, T1_ECDIS, T1_Pprecise, T1_AV, which gave no basis for further thorough analysis--multiple comparisons--of the means using post hoc tests. The results of the Welsh tests and Brown and Forsyth tests showed significant differences between the mean distributions of the random variables \(V_{2}\), \(T_{2}\), \(X_{3}\), \(X_{4}\) in \(k>2\) independent groups obtained for all the simulation variants of Scenarios 2-4. The significance level of the test statistic for the given Scenario 2-4 had a value \(p<0.05\), which was the basis for rejecting H\({}_{0}\) at the set level of significance \(\alpha=0.05\). The statistically significant differences between the mean distributions of the random variables were found:  
1. V2 in the independent groups V2_Visual, V2_ECDIS, V2_Pmax, V2_Pprecise, V2_AV and T2 in the independent groups T1_Visual, T1_ECDIS, T2_Pmax, T1_Pprecise, T1_AV in Scenario 2 for the general cargo ship,
2.