# Koffka Ring Perception in Digital Environments with Brightness Modulation
## 3 Results
### Analysis of the Effect Behavior in the Medium Primary Stimuli  
The effect which occurs on the Koffka ring causes the stimuli Lab values L: 66; a: 0; and b: 0 for different Koffka ring design variants, where test samples 4, 13, and 22 cover Koffka ring design variant a; test samples 5, 14, and 23 Koffka ring design variant b; and test samples 6, 15, and 24 Koffka ring design variant c (Figure 2), and the different background colors are divided as follows: left side Lab values: L: 30; a: 69; b: \(-\)114 and right side: L: 83; a: \(-\)128; b: 87 (test samples 4, 5, 6); left side Lab values: L: 63; a: 90; b: 78 and right side: L: 83; a: \(-\)128; b: 87 (test samples 13, 14, 15); and left side Lab values: L: 63; a: 90; b: 78 and right side: L: 30; a: 69; b: \(-\)114 (test samples 22, 23, 24) (Table 6). The results of the descriptive statistics for the medium-brightness stimuli show that the variances and standard deviations are not high (Table 7). The variance is in the range of \(\sigma^{2}{}_{24}=0.83\) for test sample 24 to \(\sigma^{2}{}_{5}=3.86\) for test sample 5. The same applies to standard deviations, with the lowest value \(\sigma_{24}=2.86\) on test sample 24 and the highest \(\sigma_{5}=3.86\) \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test Sample**} & \multirow{2}{*}{**Variant of Koffka Ring**} & \multirow{2}{*}{**Primary Stimuli**} & \multicolumn{2}{c}{**Secondary Stimuli (Background)**} \\ \cline{3-5}  & & & **Left Side** & **Right Side** \\ \hline
4 & variant a & L: 66; a: 0; b: 0 & L: 30; a: 69; b: \(-\)114 & L: 83; a: \(-\)128; b: 87 \\
5 & variant b & L: 66; a: 0; b: 0 & L: 30; a: 69; b: \(-\)114 & L: 83; a: \(-\)128; b: 87 \\
6 & variant c & L: 66; a: 0; b: 0 & L: 30; a: 69; b: \(-\)114 & L: 83; a: \(-\)128; b: 87 \\
13 & variant a & L: 66; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-\)128; b: 87 \\
14 & variant b & L: 66; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-\)128; b: 87 \\
15 & variant c & L: 66; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-\)128; b: 87 \\
22 & variant a & L: 66; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-\)114 \\
23 & variant b & L: 66; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-\)114 \\
24 & variant c & L: 66; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-\)114 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Overview of test samples, Koffka ring design variants (a, b, c), corresponding medium primary stimuli, and secondary background colors on the left and right sides for each variant. on test sample 5. Also, the ranges between minimum and maximum are not big (Table 7), which means there are no deviations in the perception of the visual effect that will have been bigger than expected for the planned experiment. The Kolmogorov-Smirnov test proved that all samples deviate from normal distribution laws (Table 7). Therefore, the non-parametric Friedman ANOVA was chosen for dependent samples with repeated measurements. The occurrence of statistically significant differences in visual effect strength measured by differences in the brightness of medium-level stimuli on test samples on different colored backgrounds and different variants of the Koffka ring designs was studied. It was found that [PERSON]'s ANOVA Chi-square had 8 degrees of freedom \(df=8\) and its value was \(x^{2}=64.551\), with a corresponding \(p\)-value of the amount \(p=0.000<0.05\). This result points to the existence of statistically significant differences between the strengths of the visual effects on test samples with medium stimuli on different colored backgrounds and in different variants of the Koffka ring design. Wilcox tests of equivalent pairs were chosen as post hoc tests to identify pairs in which the visual effects were statistically significantly different. \(\dot{\alpha}=0.05\) was chosen as the level of significance, which is standard in this type of research.