### Procedure 1: Color Scheme Group, Number of Colors  
In the first procedure, we analyze the difference between the color scheme groups as well as between the number of colors in the color schemes. Table 3 shows the header of the first procedure, which brings the details about the questions used and the values of all variables in the analysis. The first analysis considers two independent categorical variables, the color scheme group, and the number of colors in the color scheme, so the factorial two-way ANOVA is applied. First, we examine the assumptions for ANOVA, i.e., normality of the data and homogeneity of variance. The Shapiro-Wilk test shows that the data are not normally distributed for each color scheme group (W = 0.8999, \(p\) = 2.2 \(\times\)\(10^{-16}\) for the sequential; W = 0.87775, \(p\) = 1.06 \(\times\)\(10^{-13}\) for the diverging; and W = 0.90789, \(p\) = 1.189 \(\times\)\(10^{-11}\) for the qualitative group). Normality is also not confirmed for the number of colors (W = 0.89177, \(p\) = 8.514 \(\times\)\(10^{-13}\) for three colors; W = 0.85452, \(p\) = 4.714 \(\times\)\(10^{-15}\) for six colors; and W = 0.86512, \(p\) = 2.2 \(\times\)\(10^{-16}\) for nine colors). [PERSON]'s test shows that the variances of the data are not equal (F = 68.964, \(p\) = 2.2 \(\times\)\(10^{-16}\) for color scheme groups and F = 8.0426, \(p\) = 0.0003435 for number of colors). In an additional analysis, the Shapiro-Wilk test and [PERSON]'s test show quite similar results for both log-transformed data and root-transformed data. Log-transformation of data is the transformation of initial data (in this case: color schemes and number of colors variables) by replacing x variable with log(x). The same applies for root-transformation of the data: the variable x is replaced by sqrt(x). Since normality and homogeneity of variance are not satisfied for either the original or transformed data, the rank-based ANOVA type statistic is applied as an appropriate non-parametric method [50; 51]. The ANOVA-type statistic is the modern and robust alternative to rank transformation in factorial ANOVA design [50; 52]. The ANOVA-type statistic can be used in data analytic situations in which ANOVA is traditionally used. Data analysis is performed using the R package GFD for nonparametric factorial tests [51]. The method is robust and resistant to unbalanced data [51]. The descriptive statistics of this analysis can be found in Tables 4 and 5. A more detailed look at the distribution of the results is provided by the spread of error in Figures 9 and 10. \begin{table}
\begin{tabular}{c c c} \hline
**Color Scheme Group** & **Nr of Samples** & **Mean** & **Standard Deviation** \\ \hline Sequential & 440 & \(-\)0.37 & 2.04 \\ Diverging & 264 & \(-\)0.82 & 2.48 \\ Qualitative & 264 & \(-\)2.60 & 4.02 \\ \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistics of the error for the color scheme group. \begin{table}
\begin{tabular}{l c} \hline
**Procedure 1** & **Color Scheme Group, Number of Colors** \\ \hline Questions: & all \\ Color scheme groups: & sequential, qualitative, diverging \\ Number of colors: & 3, 6, 9 \\ Order: & ascending, descending, none \\ Color schemes: & YLOrRd, Reds, Spectral, Set1 \\ \hline \end{tabular}
\end{table} 
Table 3: Header of the first procedure. The results of the rank-based ANOVA-type statistics [53] are shown in Table 6. There are statistically significant differences in the means of the errors by each factor, color scheme group, and number of colors, but also by the interaction of these factors, with extremely low \(p\)-values in all tests (\(p<<0.001\)). The \(p\)-values are rounded to three decimal places in the table, as will be the case in the other tables of results later in the paper. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Colors** & **Nr of Samples** & **Mean** & **Standard Deviation** \\ \hline
3 & 264 & \(-0.60\) & 2.46 \\
6 & 264 & \(-0.76\) & 2.53 \\
9 & 440 & \(-1.61\) & 3.40 \\ \hline \hline \end{tabular}
\end{table}