### Procedure 1: Color Scheme Group, Number of Colors
#### 4.1.3 Interaction of Color Scheme Group and the Number of Colors  
In two previous post hoc tests, the data were analyzed individually with respect to the color scheme group and the number of colors. Since each map belongs to a specific color scheme group and is created with a specific number of colors, the interaction of these variables must be considered as a factor that can be associated with the accuracy of the user readings.  
Figure 11 shows interaction plots for the two-way interaction between color scheme group and number of colors. The mean error in user readings is calculated with respect to this interaction and the results of the Kruskal-Wallis rank sum test are shown.  
As shown in Figure 11, sequential color schemes achieve almost the same results regardless of the number of colors (low error: \(-0.360\) for three colors, \(-0.427\) for six colors, and \(-0.357\) for nine colors). For qualitative color schemes, on the other hand, the results  
Figure 11: Interaction plot of the error means for different color scheme groups and numbers of colors.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Comparison** & **Z** & **_p_** & **Cohen’s d** \\ \hline
3–6 & 0.214 & 0.831 & 0.064 \\
3–9 & 2.951 * & 0.009 & 0.328 \\
6–9 & 2.712 * & 0.013 & 0.274 \\ \hline \hline \end{tabular}  
* Statistically significant values with \(p<0.05\).  
\end{table}
Table 8: The results of the post hoc test and effect size (Cohen’s d) for number of colors.  
vary depending on the number of colors (from a mean of \(-0.176\) for six colors to a mean of \(-5.92\) for nine colors).  
Table 9 shows the results of the post hoc test for interaction. Looking for a combination that is significantly different from all others, we can find only one combination, namely a qualitative color scheme with nine colors. According to the interaction plot (Figure 11), this is the combination with the highest error, i.e., the lowest accuracy.  
Considering each color scheme group individually, the interaction results (Figure 11 along with Table 9) can be interpreted as follows:  
* For maps using qualitative color schemes, the reading accuracy is significantly better for six colors than for any other number of colors.
* For maps using sequential color schemes, the reading accuracy is not significantly different for a different number of colors.
* For maps using diverging color schemes, the reading accuracy of the values for three colors is significantly better than for the other colors.  
However, compared to all combinations of color scheme groups and number of colors, neither of these two significant combinations is better than all other combinations. Therefore, we can conclude that the interaction analysis does not give the best combination of color scheme group and number of colors, while the worst combination is the qualitative scheme with nine colors.  
In summary, Procedure 1 has shown that sequential color schemes achieve the lowest error, i.e., the highest accuracy in user reading, and that this result is invariant to the number of colors used in particular maps. Thus, we can conclude that the sequential color scheme group is the dominant group, and that further analysis can be performed to find out whether the accuracy of user readings is related to a particular sequential color scheme (Procedure 2) and to the order of colors in sequential maps (Procedure 3).