## 3 Data Management Maturity Model
### Phase 4--Test
#### 3.3.2 Evaluation of Process Dimensions and Maturity Levels  
Since the different process dimensions have different influences on each other, and not all dimensions can be tackled at the same time after determining an overall maturity level, it is advantageous to understand if correlations exist and to capture these relationships when weighting the maturity level calculation. For this purpose, the expert knowledge from six data management consultants was used. The following weightings and their feasibility are illustrated using two process dimensions as examples. An initial validation of the correlations and the feasibility of the questionnaire structure was performed in the form of a short assessment in the deploy phase. The six process dimensions are included in the overall maturity level with equal proportions. To calculate the correlations within a process dimension, the AHP method was used. First, an evaluation matrix was set up for each process dimension. The calculation of the weighting of capabilities within the process dimension strategy is used as an example. The capabilities are compared in rows and columns, which allows for a pairwise evaluation. This evaluates whether the row is more important than the column. The rating scale (1 to 9) used was [PERSON]'s scale, which measures the importance or difference of one element from another. The diagonal contains a \"1\" in each case, as these are only the criteria against themselves. This applies to the elements of the matrix:  
\[a_{j,i}=\frac{1}{a_{i,j}} \tag{1}\]  
After a complete, independent evaluation by six experts in the field of data management, the weighting of each criterion was calculated. First, the average of all opinions was considered to continue the further calculation with this result. An example of a pairwise comparison matrix is shown in Table 11.  
Eigenvalues (EVs) were required for the evaluation. This means that the criteria could be evaluated as independently of each other as possible. Because six experts filled in the pairwise comparison matrix, the geometric mean of all ratings was used for further analysis. Table 12 in the annex contains the matrix with geometric mean values as an example of the process dimension of strategy. The equation of weighting is given by the weight of each criterion and is the sum of the normalized criteria. For this purpose, the matrix is successively squared, and the eigenvector is determined. The calculation stops when the difference between two consecutive computational steps is negligible. For the calculation of the eigenvector EV, the series sum is formed and normalized. Table 13 in the annex shows the normalized matrix. From this, the EV was derived. If we look at the eigenvector as a percentage, the criteria weights are represented in a Pareto representation (Figure 6). For the assessment of inconsistencies, a consistency ratio CR is introduced, whereby CR \(<0.1\) is considered harmless. For this purpose, the \(\lambda_{max}\) and the consistency ratio CR must first be determined. The consistency ratio (CR) is calculated using the formula CR = \(CI\)/RI. RI is related to the dimension of the matrix and has a random consistency index from [PERSON] and Wang [28]. The formula for calculating the consistency index \(CI\) is as follows:  
\[CI=\frac{\lambda_{max}-n}{n-1} \tag{2}\]  
This calculation was performed for all process dimensions with their capabilities. The results are shown in the following Table 7.  
The CI values are all above and, in some cases, significantly above the permissible limit of \(0.1\). This indicates an inconsistency in the pair comparison judgments in the initial evaluation \begin{table}
\begin{tabular}{c c c} \hline \hline
**\#** & **Process Dimension** & **CI** \\ \hline D1 & Strategy & \(1.07\) \\ D2 & Processes & \(0.75\) \\ D3 & Organization & \(0.48\) \\ D4 & Data & \(0.62\) \\ D5 & IT Architecture & \(0.27\) \\ D6 & Operations, Support, and Innovation & \(0.23\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Calculated consistency index CI.