# An Analysis of Visibility Requirements and Reaction Times of Near-Field Projections
## 3 Results
Table 2 checks the detection grey scale levels for their significant dependency concerning the parameter content (text, symbol) and distance (1 and 5 m) looking at the \(p\)-value  
Figure 6: Logistic regression curves of detection probability (blue curves) and corresponding mean data points (blue crosses, black circles) and mean reaction time (orange curves) versus Weber contrast for the content symbol at distances 1 m (dashed) and 5 m (solid) averaged over all subjects. Figure 7: Logistic regression curves of detection probability (blue curves) and corresponding mean data points (blue crosses, black circles) as well as mean reaction time (orange curves) over Weber contrast for the content text at distances 1 m (dashed) and 5 m (solid) averaged over all subjects. using the chi-square test. Additionally, the Cramer's V as effect size V is calculated. Since eight different stimuli have been presented in one scenario, the degrees of freedom are m = \(8-1\) = 7. There is a considerable influence of the distances 1 and 5 m for the content text (\(p\) = 1.46 \(\times\) 10\({}^{-9}\), V = 0.203 (moderate)) and the content symbol (\(p\) = 1.079 \(\times\) 10\({}^{-6}\), V = 0.184 (weak)). Therefore, the illuminance required for detection is significantly higher at 5 m than at 1 m for both text and symbol. When looking at the different contents, there is a significant difference at a viewing distance of 5 m. The content text requires significantly higher illuminance levels for detection (\(p\) = 0.352 \(\times\) 10\({}^{-3}\), V = 0.139 (weak)) than the content symbol at 5 m. On the other hand, at a viewing distance of 1 m, the resulting illuminance levels of the content text are higher than those of the symbol, but this difference is not significant according to the chi-square test (\(p\) = 0.138, V = 0.0866). Figures 8 and 9 show the logistic regression curves of the detection probability for different age groups of the subjects for the presented text and symbol at distances of 1 and 5 m. The subjects were divided into the age groups 20-29, 30-39, 40-49, and older than 50 years to investigate possible influences of age on the detection contrast. Due to the lower number of participants in each age group (approx. 10), the logistic regression cannot saturate at a detection probability level 1, specifically for age groups older than 40. On examining the curves, there are no significant differences concerning the age groups in the detection contrasts (\(\alpha\) = 0.05, \(p\) = 0.138). Thus, the age groups shown in Figures 8 and 9 could summarized and analyzed. The visibility level related to the threshold luminance difference was considered to generalize the results. The results shown in Figure 10 indicate that a visibility level of approximately 5 for a distance of 1 m and a visibility level of approximately 7.5 for a distance of 5 m is required to detect the symbol with a probability of 90% (see Figure 10 left). Again, the text (Figure 10 right) also requires a higher visibility level of approximately 12 for both distances. Thus, the results of the contrast analysis are confirmed by the visibility level analysis. \begin{table}
\begin{tabular}{l l l} \hline
**Investigated Independent Parameters** & **Other Independent Parameter** & **Significance** \\ \hline Distance: 1 and 5 m & Content: Text & \begin{tabular}{l} \(X^{2}(7)\) = 49.879 \\ \(p\) \(<\) 0.05 \\ V = 0.203 \\ \end{tabular} \\ \hline Distance: 1 and 5 m & Content: Symbol & \begin{tabular}{l} \(X^{2}(7)\) = 35.721 \\ \(p\) \(<\) 0.05 \\ V = 0.184 \\ \end{tabular} \\ \hline Content: Text and Symbol & Distance: 1 m & \
\begin{tabular}{l} \(X^{2}(7)\) = 8.351 \\ \(p\) = 0.138 \\ V = 0.0866 \\ \end{tabular} \\ \hline Content: Text and Symbol & Distance: 5 m &
\begin{tabular}{l} \(X^{2}(7)\) = 22.891 \\ \(p\) \(<\) 0.05 \\ V = 0.139 \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 2: Statistical values of the detection illuminance using the chi-square test (\(X^{2}\)(m), \(p\)) and Cramer’s V for the effect size (V).