# Koffka Ring Perception in Digital Environments with Brightness Modulation
## 3 Results
### Analysis of the Effect Behavior in Light Primary Stimuli  
The results of the statistical effect analysis caused by the stimuli's Lab values are shown as follows: L: 85; a: 0; and b: 0. These occur in different variants of the Koffka ring design, where test samples 7, 16, and 25 cover variant a of the Koffka ring design; test samples 8, 17, and 26 cover variant b of the Koffka ring design; and test samples 9, 18, and 27 cover variant c of the Koffka ring design (Figure 2). The different background colors are as follows: left side Lab values: L: 30; a: 69; b: \(-\)114 and right side: L: 83; a: \(-\)128; b: 87 (test samples 7, 8, 9); left side Lab values: L: 63; a: 90; b: 78 and right side: L: 83; a: \(-\)128; b: 87 (test samples 16, 17, 18); and left side Lab values: L: 63; a: 90; b: 78 and right side: L: 30; a: 69; b: \(-\)114 (test samples 25, 26, 27) (Table 3). The results of descriptive statistics show that the variances and standard deviations are within the limits that are common in the study of visual effects in graphic media, which means that the scattering of data was not significant (Table 4). Standard deviations and variances range from the lowest \(\sigma_{9}=0.90,\ \sigma_{9}^{2}=0.81\), which is obtained for test sample 9, to the highest \(\sigma_{18}=3.35,\ \sigma_{18}^{2}=3.35\), on test sample 18. Additionally, the ranges between the minimum and maximum are not big. \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{3-4}  & & & **Left Side** & **Right Side** \\ \hline
7 & variant a & L: 85; a: 0; b: 0 & L: 30; a: 69; b: \(-\)114 & L: 83; a: \(-\)128; b: 87 \\
8 & variant b & L: 85; a: 0; b: 0 & L: 30; a: 69; b: \(-\)114 & L: 83; a: \(-\)128; b: 87 \\
9 & variant c & L: 85; a: 0; b: 0 & L: 30; a: 69; b: \(-\)114 & L: 83; a: \(-\)128; b: 87 \\
16 & variant a & L: 85; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-\)128; b: 87 \\
17 & variant b & L: 85; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-\)128; b: 87 \\
18 & variant c & L: 85; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 83; a: \(-\)128; b: 87 \\
25 & variant a & L: 85; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-\)114 \\
26 & variant b & L: 85; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-\)114 \\
27 & variant c & L: 85; a: 0; b: 0 & L: 63; a: 90; b: 78 & L: 30; a: 69; b: \(-\)114 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of test samples, Koffka ring design variants (a, b, c), corresponding light primary stimuli, and secondary background colors on the left and right sides for each variant. The Kolmogorov-Smirnov test showed that no sample was aligned with the normal distribution (Table 4). As samples were not normally distributed, the non-parametric Friedman ANOVA was selected for dependent samples with repeated measurements to examine the existence of statistically significant differences in the strength of the visual effect caused by the Koffka ring measured by the differences in the test samples with a bright stimulus on different colored backgrounds and different variants of the Koffka ring design. The following results are obtained: The Friedman ANOVA Chi-square has 8 degrees of freedom \(df=8\), its value is x\({}^{2}\) = 64.551, and its the corresponding \(p\)-value is \(p\) = 0.000 \(<\) 0.05. This establishes the existence of statistically significant differences between the strengths of the visual effects on the Koffka rings in test samples with a light stimulus on different colored backgrounds and in different Koffka ring design variants. Wilcox tests of equivalent pairs were carried out to identify pairs in which the visual effects differed significantly from a statistical point of view. A significance level of \(\delta\) = 0.05 was chosen.