# Improving Ship Maneuvering Safety with Augmented Virtuality Navigation Information Displays
## 3 Results
**_The mean distances of the tow train contour from the reference point assumed for the tests using a specific navigator's decision support system and the system in the augmented virtuality method are equal \(m_{b}=m_{AV}\)._  
**Hypothesis 1 (H1). **_The mean distances of the tow train contour points from the reference point assumed for the tests using a specific navigator's decision support system and the system in the augmented virtuality method are different \(m_{b}\
eq m_{AV}\)._  
Depending on the outcome of the test on the homogeneity of the variance of the distribution of the random variable distance of the tow train contour from the assumed reference point in the independent groups of Scenarios 5a,b, two variants of the significance test of the mean differences were used:  
* Student's \(t\)-test in the case where the variances were homogeneous;
* transformation of \(t\)-test--the Cochran-Cox test for heterogeneous variances. For the simulation test Scenarios 1-4, where each statistical analysis was conducted for more than \(k>2\) independent groups (Table 8) of the random variables of the primary criterion \(V_{1}\), \(V_{2}\), \(X_{3}\), \(X_{4}\), the equality of the means in the groups of the given simulation experiment scenario was verified by the parametric test. The specific hypotheses were adopted:  
**Hypothesis 0 (H0). **_The means of random variable distribution in all independent groups for the tests using the decision support systems defined in the assumptions of a given simulation experiment scenario are equal, \(m_{1}=m_{2}=m_{3}=mk\)._  
**Hypothesis 1 (H1). **_At least two means of random variables distributions in independent groups for tests using the decision support systems defined in the assumptions of the given simulation experiment are different._  
Depending on the outcome the homogeneity test of random variables distribution variances \(V_{1}\), \(V_{2}\), \(X_{3}\), \(X_{4}\), in independent groups (Table 8) of Scenarios 1-4, two variants of the significance test of the mean differences were applied:  
* one-factor ANOVA analysis of the variance for independent tests, when the variances were homogeneous;
* Welsh test and Brown-Forsyth test for heterogeneous variances. In the case of heterogeneous variances, the non-parametric Kruskal-Wallis test was excluded as the distributions of the analyzed random variables in independent groups were close to the normal distribution of the same size, their distributions were not similar, and the test is of lower power than parametric tests. For the simulation test Scenarios 1-4, where each statistical analysis was conducted for more than 2 independent groups (\(k>2\)) of the primary criterion \(V_{1}\), \(V_{2}\), \(X_{3}\), \(X_{4}\), and the outcome of the analysis of the mean equality was statistically significant, multiple comparisons between the groups analyzed were conducted using post hoc tests. Depending on the outcome of the test for the homogeneous degree of variance, two variants of the multiple comparisons were applied:  
* Tukey HSD test, where the variances were homogeneous;
* Games-Howell test for heterogeneous variances. The adopted level of significance of the tests was \(\alpha=0.05\).