# Koffka Ring Perception in Digital Environments with Brightness Modulation
## 3 Results
### Analysis of the Effect Behavior in Light Primary Stimuli
The intensity of the visual effect measured by the difference in brightness \(\Delta\)L\({}_{00}\) is small, while the medians for all test samples are equal to zero (Table 4). Therefore, a large number of examinees did not perceive a difference in brightness due to the manifestation of the visual effect in the light stimulus. In test samples 7, 9, 16, and 27, the arithmetic mean of the difference in perceived brightness in relation to the physical value of the brightness is so small that it is not visible (Table 5). This effect is manifested in the opposite direction in test samples 25, 26, and 27. In the group containing test samples 7, 8, 9, 16, 17, and 18, the effect is manifested in the positive brightness scale direction (Table 5). Statistically significant differences in the strength of the effect were found for test sample 8 in relation to test sample 7 (\(p\) = 0.015), test \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Test Sample** & \multicolumn{2}{c}{**Variant of Koffka**} & & & & & & & \\  & **Ring** & **Mean** & **Med.** & **Min.** & **Max.** & **Var.** & **St. Dev.** & **K-S P** \\ \hline
7 & variant a & \(-\)0.179804 & 0.00000 & \(-\)6.5057 & 4.66780 & 2.60748 & 1.614770 & \(p\) \(<\) 0.01 \\
8 & variant b & \(-\)0.845099 & 0.00000 & \(-\)9.5906 & 8.72184 & 6.46539 & 2.542714 & \(p\) \(<\) 0.01 \\
9 & variant c & \(-\)0.136777 & 0.00000 & \(-\)5.8303 & 1.74849 & 0.80772 & 0.898734 & \(p\) \(<\) 0.01 \\
16 & variant a & \(-\)0.140623 & 0.00000 & \(-\)6.2271 & 5.27361 & 2.29454 & 1.514773 & \(p\) \(<\) 0.01 \\
17 & variant b & \(-\)0.655715 & 0.00000 & \(-\)6.1587 & 2.38331 & 3.22580 & 1.796050 & \(p\) \(<\) 0.01 \\
18 & variant c & \(-\)0.728351 & 0.00000 & \(-\)25.1413 & 0.48597 & 11.25118 & 3.354278 & \(p\) \(<\) 0.01 \\
25 & variant a & 0.648876 & 0.00000 & \(-\)5.7770 & 9.22981 & 4.91420 & 2.216800 & \(p\) \(<\) 0.01 \\
26 & variant b & 0.477804 & 0.00000 & \(-\)9.3278 & 16.24118 & 9.42418 & 3.069882 & \(p\) \(<\) 0.01 \\
27 & variant c & 0.159073 & 0.00000 & \(-\)2.8589 & 11.59047 & 2.36234 & 1.536990 & \(p\) \(<\) 0.01 \\ \hline \hline \end{tabular} Legend: This table includes the arithmetic mean, median, minimum, maximum, variance, and standard deviation as well as Kolmogorov–Smirnov \(p\)-values.  
\end{table} 
Table 4: Descriptive statistics of the \(\Delta\)L\({}_{00}\) of light primary stimuli on different background colors. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Samples** & **Sample 7** & **Sample 8** & **Sample 9** & **Sample 16** & **Sample 17** & **Sample 18** & **Sample 25** & **Sample 26** \\ \hline Sample 8 & 0.015 & - & & & & & \\ Sample 9 & 0.958 & 0.026 & - & & & & \\ Sample 16 & 0.570 & 0.001 & 0.789 & - & & & \\ Sample 17 & 0.092 & 0.387 & 0.073 & 0.055 & - & & \\ Sample 18 & 0.492 & 0.136 & 0.177 & 0.332 & 0.306 & - & \\ Sample 25 & 0.011 & 0.000 & 0.014 & 0.040 & 0.001 & 0.002 & - \\ Sample 26 & 0.112 & 0.001 & 0.147 & 0.271 & 0.012 & 0.070 & 0.601 & - \\ Sample 27 & 0.151 & 0.001 & 0.202 & 0.441 & 0.008 & 0.050 & 0.090 & 0.310 \\ \hline \hline \end{tabular} Legend: This table contains the Wilcox tests’ \(p\)-values.  
\end{table} 
Table 5: Wilcox tests’ results for light primary stimuli. sample 9 (\(p\) = 0.026), and test sample 16 (\(p\) = 0.001). No statistically significant differences were found between test samples 8 and test samples 17 and 18 (\(p\) = 0.387, \(p\) = 0.136). On test samples 8, 17, and 18, the difference in brightness was noticeable (Table 5). No difference was observed for test samples 7, 9, and 16. The effect is manifested in the opposite direction for test samples 25, 26, and 27 (Table 5). A difference is observed for test samples 25 and 26. For test sample 25, the arithmetic mean of brightness difference is the largest compared to the others in this group, and it amounts to \(\mu_{25}=0.648\) with a median amount \(Med_{25}=0\) (Table 4).