# Koffka Ring Perception in Digital Environments with Brightness Modulation
## 3 Results
### Analysis of the Effect Behavior in the Medium Primary Stimuli
According to the descriptive statistics results (Table 7), the strength of the visual effect is measured with \(\Delta\)L\({}_{00}\); it is strongest in test sample 5, where the difference in the measured \(\Delta\)L\({}_{00}\) of the amount \(\mu_{5}=-4.54\) is clearly visible, with median value \(Med_{5}=-0.78\). The strength of the Koffka ring effect is somewhat weaker on test sample 14, where it amounts to \(\mu_{14}=-2.82\) with a median value \(Med_{14}=0\), in which the difference in \(\Delta\)L\({}_{00}\) borders between the values when the effect is visible and adequately visible. The Wilcox test did not find statistically significant differences between the strength of the effect on test samples 5 and 14 (Table 8., \(p=0.069\)). Therefore, in the group where the effect is strongly manifested, or in test samples 5 and 14 where it is adequately visible, that would be variant b of the Koffka ring on a red/green, i.e., blue/green background. There are statistically significant differences between test sample 5 and all other samples except for test sample 14 (Table 8). In test samples 4 and 13, the visual effect is less manifested than in test samples from the first group. On these test samples, \(\Delta\)L\({}_{00}\) is such that the effect is visible. According to the results of the Wilcox equivalent pairs test, there are no statistically significant differences in the manifestation of this effect on test samples 4 and 13 (Table 8, \(p=0.879\)). Based on the presented results, it can be concluded that test samples 4 and 13 are in the second group, which is a variant of the Koffka ring on a red/green, i.e., blue/green back \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Test Sample**} & **Variant of Koffka** & \multirow{2}{*}{**Mean**} & **Med.** & **Min.** & **Max.** & **Var.** & **St. Dev.** & **K-S p** \\  & **Ring** & & & & & & & \\ \hline
4 & variant a & \(-2.17050\) & \(0.000000\) & \(-15.7583\) & \(8.83015\) & \(21.78931\) & \(4.667902\) & \(p<0.01\) \\
5 & variant b & \(-4.53790\) & \(-0.781969\) & \(-19.2605\) & \(10.36977\) & \(38.58277\) & \(6.211503\) & \(p<0.01\) \\
6 & variant c & \(-0.49132\) & \(0.000000\) & \(-15.9106\) & \(11.35623\) & \(12.57916\) & \(3.546711\) & \(p<0.01\) \\
13 & variant a & \(-2.21468\) & \(0.000000\) & \(-17.3418\) & \(15.00615\) & \(28.92547\) & \(5.378241\) & \(p<0.01\) \\
14 & variant b & \(-2.82521\) & \(0.000000\) & \(-21.1476\) & \(13.65467\) & \(33.22954\) & \(5.764507\) & \(p<0.01\) \\
15 & variant c & \(-0.85072\) & \(0.000000\) & \(-15.1765\) & \(19.55850\) & \(19.18819\) & \(4.380433\) & \(p<0.01\) \\
22 & variant a & \(-0.32957\) & \(0.000000\) & \(-28.1734\) & \(24.19551\) & \(35.69081\) & \(5.974179\) & \(p<0.01\) \\
23 & variant b & \(0.48307\) & \(0.000000\) & \(-17.0061\) & \(26.26080\) & \(23.82916\) & \(4.881512\) & \(p<0.01\) \\
24 & variant c & \(-0.44207\) & \(0.000000\) & \(-20.7100\) & \(4.20868\) & \(8.26660\) & \(2.875170\) & \(p<0.01\) \\ \hline \hline \end{tabular} Legend: This table includes the arithmetic mean, median, minimum, maximum, variance, and standard deviation and Kolmogorov-Smirnov \(p\)-values.  
\end{table} 
Table 7: Descriptive statistics of \(\Delta\)L\({}_{00}\) of medium primary stimuli on different backgrounds. ground. The effect strengths on these samples are \(\mu_{4}=-2.17\), \(Med_{4}=0\) (Table 7) and \(\mu_{13}=-2.21,\ Med_{13}=0\). Test samples 6, 15, 22, 23, and 24, on which the effect is observed, are in the third group; the Wilcoxon tests of equivalent pairs did not find statistically significant differences in the strength of the effect on any pair of test samples from this group (Table 8).