# Koffka Ring Perception in Digital Environments with Brightness Modulation
## 3 Results
### Analysis of the Effect Behavior in Dark Primary Stimuli
Friedman ANOVA Chi-square has 8 degrees of freedom \(df=8\) and amounts to \(\mathrm{x^{2}=37.569}\), with the corresponding \(p\)-value amounting to \(p=0.000<0.05\). There are statistically significant differences between the visual effect strengths on test samples with a dark stimulus on different colored backgrounds and in different Koffka ring design variants. Therefore, post hoc Wilcox tests of equivalent pairs were carried out to identify statistically significantly different pairs. A level of significance of \(\hat{\alpha}=0.05\) was chosen, which is standard in this type of research. Results of descriptive statistics (Table 10) show that the effect measured by the difference in brightness \(\Delta\)L\({}_{00}\) is most pronounced in test samples 1, 2, 10, and 11, among which statistically significant differences in the strength of the effect were not found. The visual effect that occurs on the Koffka ring is adequately visible in test samples 1, 2, 10, and 11. The effect is manifested most strongly in test sample 2 with the b variant design of the Koffka ring on a blue/green background, with the arithmetic mean amounting to \(\mu_{2}=-4.58\) and a median of \(Med_{2}=-3.90\). Test sample 10 has almost the same arithmetic mean value, which is variant b on a red/green background. On test sample 10, the arithmetic mean amounts to \(\mu_{10}=-4.55\) with a median of \(Med_{10}=-1.88\). The arithmetic mean of the Koffka ring effect strength of test sample 1 is \(\mu_{1}=-4.44\), which is variant a on blue/green background, with a median of \(Med_{1}=-2.14\). A somewhat weaker effect was observed on test sample 11, which is variant b on a red/green background. The arithmetic mean of test sample 11 is \(\mu_{11}=-4.13\) while the median value is \(Med_{11}=0\). According to the Wilcox tests' results, there are no statistically significant differences in the manifestation of the effect in this group (Table 11). The empirical \(p\)-value between test samples 1 and 2 is \(p=0.807\), between test samples 1 and 10 it is \(p=0.947\), between test samples 1 and 11 it is \(p=0.693\), between test samples 2 and 10 it is \(p=0.798\), between test samples 2 and 11 it is \(p=0.639\), and between test samples 10 and 11 it is \(p=0.806\). The visual effect manifested in this group of test samples differed statistically significantly in relation to the visual effects of other test samples (Table 8). A pair of test samples 10 and 12 make an exception, and no statistically significant difference in effect strength was found (\(p=0.055\)). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Test Sample**} & \multicolumn{2}{c}{**Variant of Koffka**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**Med.**} & \multirow{2}{*}{**Min.**} & \multirow{2}{*}{**Max.**} & \multirow{2}{*}{**Var.**} & \multirow{2}{*}{**St. Dev.**} & \multirow{2}{*}{**K-S P**} \\  & & & & & & & & \\ \hline
1 & variant a & \(-4.43659\) & \(-2.13522\) & \(-20.6536\) & 7.13976 & 41.35189 & 6.430543 & \(p<0.05\) \\
2 & variant b & \(-4.58269\) & \(-3.89754\) & \(-18.3156\) & 10.56289 & 33.08924 & 5.752324 & \(p<0.05\) \\
3 & variant c & \(-1.71339\) & \(0.00000\) & \(-18.1381\) & 9.88852 & 35.27470 & 5.939251 & \(p<0.01\) \\
10 & variant a & \(-4.55246\) & \(-1.87748\) & \(-22.6144\) & 8.22937 & 40.76960 & 6.385108 & \(p<0.01\) \\
11 & variant b & \(-4.13296\) & \(0.00000\) & \(-18.4316\) & 5.28696 & 33.63150 & 5.799267 & \(p<0.01\) \\
12 & variant c & \(-2.62506\) & \(0.00000\) & \(-26.7668\) & 2.47656 & 32.19058 & 5.673674 & \(p<0.01\) \\
19 & variant a & \(-1.80000\) & \(0.00000\) & \(-14.4400\) & 6.54448 & 17.92289 & 4.233544 & \(p<0.01\) \\
20 & variant b & \(-1.69553\) & \(0.00000\) & \(-14.0321\) & 8.64973 & 20.17079 & 4.491190 & \(p<0.01\) \\
21 & variant c & \(-1.41859\) & \(0.00000\) & \(-16.9244\) & 3.43761 & 16.52070 & 4.064566 & \(p<0.01\) \\ \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}