**4. Results**

The results are divided into three sub-sections: factor analysis, index of Industry 4.0, and verification and evaluation of Industry 4.0 index.

#### *4.1. Results of Factor Analysis*

Factor analysis was based on the variables the enterprises were asked about in relation to their implementation of Industry 4.0. Several variants of factor analysis were performed with various parameters with di fferent items of the questionnaire.

Firstly, all 17 monitored items from the questionnaire were included in the exploratory factor analysis. The results of the principal component analysis method showed that four factors explained a total of 51% variance. However, the fourth factor contained only two items, of which drones had a negative factor loading of *f4* = −0.45 and autonomous vehicles reported a factor loading of *f4* = +0.78. Further rotation and testing did not improve the situation, and these items were, therefore, excluded from the analysis. The highest factor loadings for additive manufacturing *f2* = +0.37 and nanotechnology *f2* = +0.32 were very low (<0.4). Items which have a load less than 0.4 on any factor should be removed and the analysis should be re-run [114]. This means that these items did not saturate the factors su fficiently. In addition, they were not used to a grea<sup>t</sup> extent in the enterprises surveyed (usage of these variables in our results: nanotechnology 4.0%, drones 0.7%, additive manufacturing only 9.1%, and autonomous vehicles 2.9%). These items were, therefore, also eliminated from the factor analysis.

Finally, 13 variables were selected for the final design. As mentioned in the methodology, the suitability of the factor analysis was verified using the KMO index and the Bartlett test.

#### 4.1.1. Factors Extraction

Factor extraction was performed using the principal component analysis method. This method is based on a large number of variables to find a smaller set of new variables (Table 2 with less redundancy to provide the best possible data representation [115]. The three factors found accounted for a total of 52.8% variance. The first factor explained 34.6% variance. The Eigen value of the second factor was 1.2, and the variance explained by this factor was 9.3%. The third factor then explained 8.9% of the variance (see Table 2). The remaining factors were always less than 5% of the total variance and their Eigen values were less than one. Based on the Kaiser–Guttman criterion, it was, therefore, appropriate to interpret only the first three factors, as they explained more variance than the original variables.


**Table 2.** Factor extraction using principal component analysis.

#### 4.1.2. Factor Loadings and Rotation

In factor extraction, factor loads were calculated for each item, representing the correlations between the factors and the variables. They could be used to interpret the factors. Thus, by processing the data, three rather consistent factors were extracted (without rotation). Since initial factor extraction usually does not provide interpretable results, it was done using the Varimax method. The primary factor load aggregate variables are marked in bold in Table 3. The values in Table 3 represent the factor loads of the rotating factors. The sign of factor load expresses the opposite relation to the given factor. In addition to the Varimax method, other methods were used, but it was shown that these results are best interpretable.

**Table 3.** Factor loadings. Primary factor load aggregate variables are marked in bold. IT—information technology; MES—manufacturing execution system; ERP—enterprise resource planning; M2M—machine-to-machine communication; 3D—three-dimensional.


In terms of interpretation and for model purposes, the factors were identified as levels 1–3 of Industry 4.0 in the enterprises. It is clear from Table 3 that level 1 was primarily saturated with the human capital variable, collecting data, storing data in the cloud, and analyzing data. These variables have in common that they focus on working with data and the availability of human capital, i.e., the need to operate equipment and technology. Level 2, on the other hand, included all the variables related to the core infrastructure of industry 4.0. This means IT infrastructure, the presence of MES and ERP information systems, M2M-based data interconnection, the use of robots and their arms in production, mobile devices, and sensors. Level 3 included a higher level of Industry 4.0 that can be expressed through the use of learning software, data sharing with suppliers, and virtual reality. The items autonomous vehicles, additive manufacturing, nanotechnology, and drones were eliminated in the preliminary factor analysis (see Section 4.1) and not used for this run of factor analysis.

#### *4.2. Index of Industry 4.0*

The results of the factor analysis were further used to create an index for the implementation level of Industry 4.0 (VPi4) in the enterprise. Based on these data, it was possible to divide 13 areas into three levels of Industry 4.0 implementation into the enterprise, using factor analysis, where the numbers after each area represent their factor load.

The first level of introducing Industry 4.0 into an enterprise consists of the following areas:


The second level of introducing Industry 4.0 into an enterprise consists of the following areas:


The third level of introducing Industry 4.0 into an enterprise consists of the following areas:


Figure 1a below shows the data distribution in terms of VPi4 percentage; the intervals were created automatically for legibility. The most frequent interval was 39%–52% with a frequency of 37 enterprises, followed by an interval of 26%–39% with a frequency of 36 enterprises. The least represented interval was 78%–91%, where there were seven enterprises.

**Figure 1.** The enterprises by the index of Industry 4.0 (VPi4) percentage: (**a**) distribution of the enterprises by intervals; (**b**) total distribution.

Figure 1b shows the 164 enterprises evaluated under the first wave of the research (*x*-axis) with their percentage of Vpi4 (*y*-axis). As seen from the chart, most of the enterprises were between 29% and 60%. Conversely, in the lower quartile, there were 29% of enterprises, while there were 60% of enterprises in the upper quartile.

#### *4.3. Verification and Evaluation of Industry 4.0 Index*

The results of the second wave of the research and supplementary questions identifying the subjective perception of the enterprises and the impact of the technological intensity of the industry were also used to assess the results of the Vpi4 index.

On the basis of the results, a scorecard was designed, such that an enterprise is able to determine the level of implementation of Industry 4.0 inside the enterprise based on the answers to the questions. The enterprise finds out the overall score and the fulfilment of different levels of Industry 4.0. At the

same time, it can also compare the result with other enterprises in the industry where a set of five icons shows the position compared to other enterprises. Each icon shows a 20% sample distribution (see Figure 2).


**Figure 2.** Vpi4 index.

#### 4.3.1. Industry 4.0 Index Distribution

The data of the first and second wave of the research were used to evaluate the data distribution. Figure 3 below shows the enterprises at levels 1–3, which are color-coded (each enterprise is shown three times on the graph), with the *y*-axis showing the values of each level and the *x*-axis showing the total Vpi4 as a percentage.

**Figure 3.** Evaluation of enterprises by VPi4: (**a**) distribution of the enterprises in the first wave of the research; (**b**) distribution of enterprises in the second wave of the research.

Figure 3a shows how the levels overlap; however, most of the enterprises reached the higher level 1, while the second and third levels featured a score pf zero. The distribution of the enterprises in the second wave of Figure 3b was similar. It is interesting to note, for example, that one enterprise achieved a very high overall Vpi4 at 88%, while, at the same time, it had a level 1 score of 93%, level 2 score of 95%, and level 3 score of 67% (three dots to the right of the graph). In total, five companies in the first wave achieved absolutely zero values in Vpi4.

Furthermore, the VPi4 index distribution was statistically compared, using the samples from the first wave and the second wave of the research. For this reason, Mann–Whitney–Wilcox test statistics were used to compare the samples. Table 4 shows that, at all levels of the VPi4 index except the third level, the results of the first and second wave research were identical. Di fferences were found only in the third level with a *p*-value = 0.0267. However, the third level of the index is very specific, as higher ranking at this level is often more di fficult for enterprises to achieve after the first two levels are met. The enterprises in the second wave achieved a higher level of the VPi4 index at level 3 than in the first wave. The results also show that there was a di fference in self-perception and self-assessment of the use of Industry 4.0 for the enterprises in the first and second waves.


**Table 4.** Industry 4.0 index (VPi4) distribution, using Mann–Whitney–Wilcox test.

The results of the comparison of the index results in the first and second waves of the research show that hypothesis H10 cannot be rejected, as the results of both surveys showed the same distributions.

4.3.2. Relation of the Index to the Subjective Perception of the Level of Industry 4.0 by the Enterprises

The relation of the index to the subjective perception of the level of Industry 4.0 by the enterprises was carried out in both waves of the research. The correlation between VPi4 index (%) and the scale on which enterprises evaluated themselves in relation to Industry 4.0 from 1–5 was analyzed (1—we do not have Industry 4.0; 5—we fully have Industry 4.0). Pearson and Spearman coe fficients were used for testing. Firstly, a coe fficient of determination of *R<sup>2</sup>* = 0.2784 was calculated; thus, the dependence explained 28% of the variability of the number of points. On average, the enterprises rated themselves 2.1 with Industry 4.0, with an average rating of the recalculated VPi4 index being 45% more similar to the score of 3. One-quarter of enterprises had a VPi4 value below 29%, with the upper quarter having a value above 60%. In terms of their own perception, 50% of the enterprises ranged from 1–3 on a five-point scale. As also reported by the minima and maxima, some of the enterprises did not achieve any points in the VPi4 index. The maximum was 88% and 34 points in VPi4.

The normalization of the data of both variables was verified by the Shapiro–Wilk test, with the *p*-value of VPi4% = 0.09 assuming the normality of the data, as also shown by the histogram. With the perception of Industry 4.0 by the enterprises, the *p*-value test was close to zero; therefore, the normality of the data was not assumed. The results of the correlation of both variables are shown in Table 5. Here, on the basis of a *p*-value = 0.0000, the null hypothesis of independence was rejected in favor of the alternative using the Pearson coe fficient at the significance level of 5%. We proved the existence of a linear dependence, which was also proven by the positive Pearson correlation coe fficient (0.5277). At the same time, in terms of Spearman correlation, where the *p*-value was very close to zero with *R* = 0.5147, the null hypothesis was rejected in favor of H2 A on the dependence of both variables.


Similarly, a second questionnaire survey was used for the second wave of the research (Table 5). The coe fficient of determination was lower than in the first wave of the research ( *R<sup>2</sup>* = 0.1705). Dependence, therefore, explained only 17% of the variability. In the normality verification by the Shapiro–Wilcox test, the values were low to zero in both cases. Therefore, the normality of data, for the VPi4 index and the perception values of Industry 4.0 by the enterprises, was not considered. It was, therefore, better to compare the dependence of the Spearman coe fficient. Its value was 0.4054, i.e., compared to the results in the first wave, the level of dependence was lower. Its value was, however, statistically significant.

Given the proven dependence in both surveys, it was possible to conclude the correct setting of VPi4 by means of factor analysis and the suitability of the questions, as it largely corresponded to the perception of the enterprises in terms of Industry 4.0.

4.3.3. Relation of the Index to Intensity of Technology and Index Weighting

The relation to the intensity of technology in the industry was tested in the first wave of the research only (Table 6). The Mann–Whitney test determined the null hypothesis at the sample significance level of α = 0.05, where X = high-technology sector di fficulty and Y = low-technology sector di fficulty. The hypotheses were tested, providing H30 = *x*0.50 − *y*0.50 = 0 and H3 A = *x*0.50 > *y*0.50, as viewed from VPi4. As shown in the table below, the null hypothesis of both samples was rejected when the *p*-value was close to zero, and a positive *Z* confirmed the alternative hypothesis, claiming that the higher-tech enterprises have a higher level of Industry 4.0 (VPi4).

**Table 6.** Intensity of technology levels (HTI—high-tech intensity; LTI—low-tech intensity), based on Mann–Whitney test.


Interestingly, it was not possible to reject this hypothesis for the perception of the enterprises from the perspective of Industry 4.0, with a *p*-value of 0.2298; therefore, this hypothesis could not be rejected, and we can further assume that the high- and low-tech enterprises saw themselves in a similar way. The hypothesis testing also failed to reject the null H30 hypothesis at levels 1 and 3 of Industry 4.0 implementation, as the *p*-values were greater than α. On the other hand, for the second phase of Industry 4.0 implementation, it was possible to prove the di fferences between the two groups. The enterprises with higher technological demands were often more successful.

The VPi4 index was adjusted for comparing enterprises with di fferent intensities of technology. The Mann–Whitney test was used to compare more independent samples where the *p*-value did not indicate statistically significant sectoral di fferences from the entire sample (Table 7), except for LTS, where a *p*-value (0.0184) indicated a di fference at the 0.05 level of significance. For this reason, it was necessary to adjust the index (index obtained by the median di fference of 0.0899) for LTS companies, so that their results could be compared with the values of other groups. This fact was logical in terms of the lower use of technologies that were included in VPi4 for enterprises belonging to the low-technology sector. After adjusting the index for LTS enterprises, the Mann–Whitney test was re-conducted, where no significant di fference between the whole sample and LTS was found (*p*-value = 0.0967).


**Table 7.** Intensity of technology sectors, based on Mann–Whitney test. M—medium; HT—high-tech; LT—low-tech; S—sector.
