## 4 Survey Exploratory Analysis
### Exploratory Factor Analysis  
To assess the suitability of using EFA, we used the Kaiser-Meyer-Olkin (KMO) measure and the Bartlett test of sphericity (see Table 6). The KMO value of 0.877 (i.e., greater than 0.8) suggested that the sample size was adequate [57; 58]. The \(p\)-value for the Bartlett test of less than 0.001 indicated that the variables were not orthogonal and therefore correlated. We note that this test uses a chi-square distribution that assumes normality; nevertheless, many authors have shown, using theoretical distributions, that the Pearson correlation is robust to skewness and non-normality [56; 59; 60; 61; 62].  
To explore the latent factors, EFA was applied using the Principal Axis Factoring (PAF) method and the varimax rotation technique. To establish a cutoff for the eigenvalue, the Kaiser criterion was employed. In FA, the eigenvalues represent the variance explained by each factor, and when this criterion is used, factors with eigenvalues greater than one are retained.  
Four factors were extracted that explained 61.96% of the total variance (see Table 7). The first factor explained 37.384% of the total variance, the second factor 12.01%, the third 6.548% and the fourth 6.018%, with eigenvalues of 6.729, 2.162, 1.179 and 1.083, respectively. The extraction and rotation sums of the squared loadings displayed in Table 7 provide similar information but are based only on the shared variance among variables. The four extracted factors explained 51.54% of this common variance. Table 8 displays the obtained rotated factor matrix. After examining the absolute loadings that exceeded 0.45, it was  
\begin{table}
\begin{tabular}{c c} \hline \hline
**KMO Measure of Sampling Adequacy** & 0.877 \\ \hline
**Bartlett test of sphericity (chi-square approximation)** & 903.893 \\
**Degrees of freedom** & 153 \\
**Significance** & \(8.43\times 10^{-107}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Results of Kaiser-Meyer-Olkin (KMO) and Bartlett tests.  
found that variables D2, D3, D4 and D6 were strongly loaded onto factor 1, while variables E1, E2, G2 and G3 had high loadings for factor 2, variables C2, C3, D5, G1 and G2 for factor 3, and variables E3, E4, E5 and C3 for factor 4. Factor 1 could be interpreted as the educational usefulness and academic benefits of MaGraDa, whereas factor 2 refers to the users' perceptions of its usability. Factor 3 mainly represents the perceptions of the quality of its content as a tool for graph learning, while factor 4 seems to represent the perceptions of its user-friendliness.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & \multicolumn{2}{c}{**Initial**} & \multicolumn{2}{c}{**Extraction Sums**} & \multicolumn{2}{c}{**Rotation Sums**} \\  & & \multicolumn{2}{c}{**Eigenvalues**} & \multicolumn{2}{c}{**of Squared Loadings**} & \multicolumn{2}{c}{**of Squared Loadings**} \\ \cline{2-10}
**Factor** & **Total** & **\begin{tabular}{c} **\% of** \\ **Variance** \\ \end{tabular} & **\begin{tabular}{c} **Cumulative** \\ **\%** \\ **\%** \\ \end{tabular} & **Total** & **\begin{tabular}{c} **\% of** \\ **Variance** \\ \end{tabular} & **\begin{tabular}{c} **Cumulative** \\ **\%** \\ **\%** \\ \end{tabular} & **Total** & **\begin{tabular}{c} **\% of** \\ **Variance** \\ \end{tabular} & **Total** & **\
\begin{tabular}{c} **\% of** \\ **Variance** \\ \end{tabular} & **
\begin{tabular}{c} **Cumulative** \\ **\%** \\ **\%** \\ \end{tabular} \\ \hline  
\hline \end{tabular}
\end{table}
Table 7: Total variance explained by factor analysis (FA) with the principal axis factoring (PAF) extraction method.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Item** & **Factor 1** & **Factor 2** & **Factor 3** & **Factor 4** \\ \hline  
\hline \end{tabular}
\end{table}
Table 8: Rotated factor matrix from FA with PAF extraction method, varimax rotation (see Table 3 for a description of each variable).