# Koffka Ring Perception in Digital Environments with Brightness Modulation
## 3 Results
### Analysis of the Effect Behavior in Dark Primary Stimuli  
The following is a presentation of the statistical analysis results of the effect causing the Lab stimuli with L values of 42; a: 0; and b: 0 for different Koffka ring design variants. Test samples 1, 10, and 19 cover Koffka ring design variant a; test samples 2, 11, and 20 cover Koffka ring design variant b; and test samples 3, 12, and 21 cover Koffka ring design variant c (Figure 2) and the different background colors presented in Table 9.  
Variances and standard deviations in the dark stimuli are higher than the values of the same indicators in comparison to the light and medium stimuli (Table 10). The range of the variance values is from \(\sigma^{2}_{21}=16.52\) for test sample 21 to \(\sigma^{2}_{1}=41.35\) for test sample 1. Consequently, the standard deviation achieves the lowest value, \(\sigma_{21}=4.06\), on test sample 21 and the highest, \(\sigma_{1}=6.43\), on test sample 1. The lowest value of the effect caused by the Koffka ring was determined to be on test sample 12, \(Min_{12}=-26.25\). The maximum has lower absolute values than the minimum. The highest maximum was found on test sample 2 and amounted to \(Max_{2}=10.56\). The data clearly indicates a slightly greater data dispersion. This dispersion is expected because the visual effect caused by the Koffka ring on dark stimuli samples is very strong on some test samples. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Samples** & **Sample 4** & **Sample 5** & **Sample 6** & **Sample 13** & **Sample 14** & **Sample 15** & **Sample 22** & **Sample 23** \\ \hline Sample 5 & 0.006 & - & & & & & \\ Sample 6 & 0.014 & 0.000 & - & & & & \\ Sample 13 & 0.879 & 0.018 & 0.008 & - & & & \\ Sample 14 & 0.455 & 0.069 & 0.006 & 0.480 & - & & \\ Sample 15 & 0.129 & 0.000 & 0.546 & 0.106 & 0.001 & - & \\ Sample 22 & 0.014 & 0.000 & 0.569 & 0.028 & 0.009 & 0.289 & - \\ Sample 23 & 0.001 & 0.000 & 0.231 & 0.003 & 0.000 & 0.077 & 0.212 & - \\ Sample 24 & 0.008 & 0.000 & 0.794 & 0.018 & 0.005 & 0.382 & 0.605 & 0.177 \\ \hline \hline \end{tabular} Legend: This table contains the \(p\)-values of the Wilcox tests.  
\end{table} 
Table 8: Results of the Wilcox medium primary stimuli tests. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Sample** & **Variant of Koffka Ring** & **Primary Stimuli** & \multicolumn{2}{c}{**Secondary Stimuli (Background)**} \\ \cline{3-4}  & & **Left Side** & **Right Side** \\ \hline
1 & variant a & L: 42; a: 0; b: 0 & L: 30; a: 69; b: \(-114\) & L: 83; a: \(-128\); b: 87 \\
2 & variant b & L: 42; a: 0; b: 0 & L: 30; a: 69; b: \(-114\) & L: 83; a: \(-128\); b: 87 \\
3 & variant c & L: 42; a: 0; b: 0 & L: 30; a: 69; b: \(-114\) & L: 83; a: \(-128\); b: 87 \\
10 & variant a & L: 42; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-128\); b: 87 \\
11 & variant b & L: 42; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-128\); b: 87 \\
12 & variant c & L: 42; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-128\); b: 87 \\
19 & variant a & L: 42; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-114\) \\
20 & variant b & L: 42; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-114\) \\
21 & variant c & L: 42; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-114\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Overview of test samples, Koffka ring design variants (a, b, c), corresponding dark primary stimuli, and secondary background colors on the left and right sides for each variant. Samples are not normally distributed (Table 10). Therefore, non-parametric Friedman ANOVA was carried out for dependent samples with repeated measurements. This determined the existence of a statistically significant difference in the visual effect manifestation measured by differences in brightness on test samples with dark stimuli on different colored backgrounds and different Koffka ring design variants.