## 3 Results  
All scales attained acceptable levels [25], as shown in Table 4. To evaluate the instrument's reliability, we performed a Cronbach's alpha reliability analysis: values of Cronbach's alpha coefficients: \(\alpha>0.9\) is excellent, \(\alpha>0.8\) is good, \(\alpha>0.7\) is acceptable, \(\alpha>0.6\) is acceptable for scales with less than 10 items, and \(\alpha>0.5\) is poor [25]. [PERSON]'s sphericity test was applied to ensure that each competency's correlation matrix was meaningful (\(p<0.05\)) and to be able to reject the hypothesis of independence of variables [26]. Kaiser-Meyer-Olin (KMO) sample adequacy measures were also obtained for each competency. To be acceptable, the KMO index must be greater than 0.5 [27], as shown in Table 5.  
For the six competencies' KMO sample adequacy measures, feasibility of factor analysis was observed. For each competency, [PERSON]'s sphericity test was statistically significant (\(p<0.05\)), resulting in rejection of the hypothesis of variables' independence. In each competency's unifactorial structure, as observed in sedimentation graphs, the number of factors suggested by a self-value criterion greater than one (K1 rule) is one, and clearly, after the first factor, the slope stabilized. For each competency we obtained these criteria; in Figure 2, Transformations of Society; in Figure 3, Researcher Training; in Figure 4, Originality and Innovation; in Figure 5, Teaching; Figure 6, Ethics and Citizenship; and in Figure 7, Teachers' Digital Competence. \begin{table}
\begin{tabular}{c c} \hline \hline
**Competence** & **Cronbach’s Alpha** \\ \hline Transformation of society (14 items) & 0.911 \\ Researcher training (6 items) & 0.871 \\ Originality and innovation (3 items) & 0.718 \\ Teaching (4 items) & 0.678 \\ Ethics and citizenship (3 items) & 0.523 \\ Teachers’ digital competence (3 items) & 0.658 \\ \hline \hline \end{tabular} Source: Authors.  
\end{table} 
Table 4: Cronbach’s Alpha of Scale for Each Research-professor Competency. \begin{table}
\begin{tabular}{c c c} \hline \hline
**School** & **Frequency** & **Percent** \\ \hline ECSG & 18 & 5.6 \\ EHE & 50 & 15.6 \\ EIC & 120 & 37.5 \\ EM & 18 & 5.6 \\ EN & 35 & 10.9 \\ EAAD & 9 & 2.8 \\ \hline \hline \end{tabular} Source: Authors. Note: ECSG: School of Government; EHE: School of Humanities and Education; EIC: School of Engineering and Science; EM: School of Medicine and Health Sciences; EN: Business School; EAAD; School of Architecture, Art, and Design.  
\end{table} 
Table 2: Frequency and Percentage of Professors by School (N = 250). \begin{table}
\begin{tabular}{c c} \hline \hline
**Competence Level** & **Performance Level** \\ \hline X \(<\) 1 & Initial \\
1 \(<\) X \(<\) 2 & Basic \\
2 \(<\) X \(<\) 3 & Autonomous \\ X \(>\) 3 & Consolidated \\ \hline \hline \end{tabular} Source: Authors.  
\end{table} 
Table 3: Competence and Performance Levels of Research Professors. Figure 3: Sedimentation graph of the competence of Researcher Training. Source: Authors. Figure 2: Sedimentation graph of the competence of Transformation of Society. Source: Authors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Barletlet’s Sphericity Test**} \\ \hline
**Competence** & **KMO** & \(\mathbf{X^{2}}\) & **gl** & \(\boldsymbol{p}\)**-Value** \\ \hline Transformation of society & 0.924 & 1473.422 & 91 & 0.001 \\ Researcher training & 0.869 & 572.419 & 15 & 0.001 \\ Originality and innovation & 0.659 & 150.023 & 3 & 0.001 \\ Teaching & 0.539 & 505.375 & 6 & 0.001 \\ Ethics and citizenship & 0.581 & 45.045 & 3 & 0.001 \\ Teachers’ digital competence & 0.609 & 110.219 & 3 & 0.001 \\ \hline Source: Authors. & & & & \\ \end{tabular}
\end{table} 
Table 5: KMO Sample Adequacy Measures and Bartlett’s Sphericity Tests. Figure 4: Sedimentation graph of the competence of Originality and Innovation. Source: Authors. Figure 5: Sedimentation graph of the competence of Teaching. Source: Authors. Figure 6: Sedimentation graph of the competence of Ethics and Citizenship. Source: Authors.