**4. Results**

This is a summary of the results obtained at various stages of the research. The results are divided into two parts: cluster of SMEs analysis and comparison SMEs index of VPi4 with large enterprises.

#### *4.1. Cluster Analysis of Small- and Medium-Sized Enterprises*

The aim of the cluster analysis was to categorize and categorize SMEs based on three levels of the Industry 4.0 index (VPi4). First, the procedure of selecting variables (factors) for clustering is summarized, and then the optimal number of clusters is found, using Elbow a Silhouette methods. The next part presents the results of k-means cluster analysis, including the description of the clusters. Finally, the results of the cluster analysis are validated.

#### 4.1.1. Variables Selection and Principal Component Analysis

Before performing the cluster analysis, it was necessary to choose the variables to be used in clustering. Based on the results of the questionnaire survey, the VPi4 index was calculated for the SMEs. The index consists of three factors (levels): VPi4 Level 1, VPi4 Level 2, and VPi4 Level 3. These factors should not correlate with each other, so it was advisable to use three levels of the VPi4 index. Principal Component Analysis (PCA) was performed to check the independence of these factors. The results are summarized in Table 2. All three dimensions have very similar % of total variance explained.


**Table 2.** Principal Component Analysis.

\* Note: variables are Industry 4.0 index values (VPi4) at different levels.

#### 4.1.2. Optimal Number of Clusters Determination

In this step, the goal is to determine the optimal number of clusters suitable for k-means cluster analysis. It is advisable to use more methods for this purpose, i.e., the Elbow and Silhouette methods in particular (Figure 1). The procedure consists in performing decompositions for di fferent numbers of k-clusters. A value of total within sum of square is calculated for each decomposition (in Elbow method Equation (3)) and Silhouette coe fficient (Equation (1)). Using the k-means algorithm, we divide the data sequentially into two to ten clusters and construct the corresponding function of the number of the clusters. In this case, there is a steep bending in four clusters (Figure 1a). In the case of the Silhouette method, the analysis is performed similarly, obtaining the optimal number of clusters based

on the maximum value of the coefficient (Figure 1b). Both methods choose four clusters as the best solution for k-means clustering.

**Figure 1.** Optimal number of clusters methods results: (**a**) Elbow method and (**b**) Silhouette method.

#### 4.1.3. Results of Cluster Analysis

Based on the performed PCA to select the clustering variables and to determine the optimal number of analysis clusters, a k-means cluster analysis was performed. The calculations were performed in software R, using factoextra and cluster packages. The results are summarized in Table 3, which shows that four rather consistent clusters with 32 to 65 elements were created. Table 3 reports the values within sum of squares (WSS), maximum within cluster distances as diameter, average distance within clusters (which should be as small as possible), and separation with minimum distances of a point in the cluster to a point to another cluster reported for each cluster.


The graphical depiction of the cluster analysis is shown in Figure 2, which shows the results of the cluster analysis in relation to factor variables (VPi4 Level 1, Level 2, and Level 3) in 3D and then in 2D space. It is also evident from Figure 2b that the dimensions of the variables have different directions, confirming their independence. However, it is also evident that there is some overlap in the clusters. This overlap is also explained by the fact that the factor variables are partly complementary and reflect the levels of Industry 4.0. Achieving the second level is conditional by the first level; the achievement of the third level is partly conditional by reaching the first and second levels.

**Figure 2.** K-means and PCA analysis results: (**a**) clusters based on three factors (i.e., F1, F2, and F3) in 3D space; (**b**) biplot—PCA combined with cluster analysis (relations of the clusters and factors).

Table 4 shows results of k-means clustering according to the centroids average characteristics of the Industry 4.0 levels in individual clusters. Cluster 1 is strongly represented by the first and second levels of the VPi4 index. This means that Cluster 1 contains the enterprises with the highest industry implementation rate of 4.0 on average. Cluster 2 only shows a high rate for Factor 3, which is a certain extension of the implementation of Industry 4.0 technologies. Cluster 3 achieves positive values only for the first level of the VPi4 index. So far, its average enterprise achieves only a certain initial industry-leading implementation level of 4.0. The latest cluster, Cluster 4, contains the lowest average values at almost all levels. On average, it is an enterprise with a very low implementation rate of Industry 4.0.



#### 4.1.4. Comprehensive Description of the Clusters

The next part describes the characteristics of clusters in details, based on the characteristics of the enterprises that make them up. It is mainly the relation of the clusters to VPi4 index, its levels, the technologies used by the enterprises, the existence of Industry 4.0 strategies, subjective perception of Industry 4.0 levels by the managers, composition in terms of size, and technological demands of the enterprises in the clusters and others. Based on the prevailing tendencies, the clusters are named as follows:


First, the characteristics related to the VPi4 index are defined: It is clear from Figure 3a that the clusters differ in the level (0−100%) achieved by the VPi4 index values. Cluster 4 enterprises ("noobs enterprises") account for more than 80% of the very low 0−25% index. On the other hand, Cluster 1 ("top technological enterprises") and Cluster 2 ("advances enterprises") have the largest share of the 50−100% index. Both of these categories of the enterprises thus achieve a relatively significant index value. Cluster 3 ("start enterprises") contains mainly the enterprises with an index of 25−50%.

**Figure 3.** Characteristics of clusters based on the VPi4 index: (**a**) VPi4 index results of enterprises (0−25% minimum, over 75% maximum of VPi4 index level) and (**b**) VPi4 index levels 1−3 (Factors 1−3) results.

Figure 3b shows a more detailed resolution of each index level. Cluster 4 has low VPi4 index value at all levels; Cluster 3 has low VPi4 index value at the first two levels, in particular; and Clusters 1 and 2 have a decent rating at all the levels of the index. The distinction between Cluster 1 and Cluster 2 is subjected to further analysis with regard to the similarity of the VPi4 index level.

Other criteria in describing the characteristics of the clusters are related to a subjective evaluation of VPi4 level by the managers and the existence of Industry 4 strategy. Figure 4a summarizes the results of the subjective evaluation of Industry 4 level by the managers on a scale of 1 (low) to 5 (high). From the results, it is clear that, even in the case of Cluster 4, the managers perceived the level of Industry 4.0 at most companies at a low level. A relatively large proportion of managers reported their ranking to be low, similarly, in Cluster 3. The enterprises in Clusters 3 and 4 (mostly 80% of them) have no Industry 4.0 strategy (Figure 4b). The best subjective perception of the implementation of Industry 4.0 was in Clusters 1 and 2. The enterprises in these clusters (approximately 50% of them) also have an Industry 4.0 strategy. These characteristics divide the clusters into two groups (Figure 4b).

**Figure 4.** Characteristics of clusters, based on subjective assessment of Industry 4.0 (I4): (**a**) subjective assessment of Industry 4.0 implementation by enterprises (very low, low, medium, high, or very high implementation of I4) and (**b**) clusters according to the existence of I4 strategy in enterprises.

#### 4.1.5. Description of Each Cluster

Further, the clusters are described separately for better clarity of the differences in the use of the technologies and characteristics of the enterprises. Following four clusters are described:

1. Top Industry 4.0 Technological Enterprises (Cluster 1)

There are 32 enterprises in the cluster. In terms of size, these are medium-sized enterprises (40.65%). Cluster 1 is characterized by 53.13% enterprises that implement the strategy of Industry 4.0. Mostly, there are the enterprises (56.25%) with high-tech and medium high-tech intensity (HTI), mostly electro and engineering (53.13%). These enterprises use a large variety of I4 technologies (Figure 5a). Technological enterprises have a very high value of variables at the first level of the VPi4, such as people, data, cloud, and analysis. These enterprises have a high value of variables as mobile platforms and IT and an average value of sensors and M2M at the second level of the VPi4. At the third level of the VPi4, these enterprises have an average value of VR, sharing data, and learning software. Some enterprises already use nanotechnologies and 3D printers. In general, the technology is the largest in these enterprises, especially at the first and second levels of the index. Due to this, they are called "I4 top technological enterprises".

2. Industry 4.0 Advances Enterprises (Cluster 2)

> The second cluster comprises 49 enterprises, of which 65.31% are the medium-sized enterprises. A total of 46.94% of the enterprises in this cluster have an Industry 4.0 strategy. Similar to the first cluster, there are predominantly (65.31%) high-tech and medium-high intensity (HTI) enterprises in the electro and engineering sector (63.27%). The cluster is characterized by the enterprises with a high rating for some technologies (Figure 5b). These enterprises have average values of variables at first VPi4 level, such as analysis, data, and people. However, most of them still have not using cloud. At the second VPi4 level, they use a high level of IT and IS (ERP and MES). They already introduced some technologies as sharing data and learning software from the third VPi4 level. Some companies use, to a lesser extent, other Industry 4.0 applications, such as nanotechnologies, 3D printers, or auto-vehicles. Overall, enterprises in this cluster use technologies that are supported mainly by IT and infrastructure at the second level of the index. However, some higher-level technologies are used. Due to this, they are called "Advances I4 enterprises".

**Figure 5.** Clusters' characteristics: (**a**) Cluster 1—I4 technological enterprises; (**b**) Cluster 2—I4 advances enterprises.

#### 3. Iindustry 4.0 Starting Enterprises (Cluster 3)

The third cluster consists of a total of 65 enterprises. The vast majority of these enterprises is small (47.69%). However, only 21.54% of them developed an Industry 4.0 strategy. In terms of technological intensity, there are mostly the (61.54%) enterprises with low-tech and medium low-tech intensity (LTI), predominantly the electro and engineering enterprises (38.47%). This cluster includes enterprises which have started implementing Industry 4.0 technologies (Figure 6a). These enterprises have a very high value of variables at the first level of VPi4, such as in people, data, and analysis and average value of cloud. They already have IT infrastructure and, at the average level, have IS and sensors. These enterprises did not use robots, M2M, or mobile technologies. The third level value of VPi4 is very low, as compared to other applications of Industry 4.0. In general, these enterprises are characterized by the introduction of technology only at the first level of the index. Due to this, they are called "I4 starting enterprises".

**Figure 6.** Clusters characteristics: (**a**) Cluster 3—I4 starting enterprises; (**b**) Cluster 4—I4 noobs enterprises.

#### 4. Industry 4.0 Noobs Enterprises (Cluster 4)

The fourth cluster consists of 40 enterprises of a very low level of technology. Of the total, 40% are the small enterprises, and 30% are the micro-enterprises. Only 20% of them have an Industry 4.0 strategy. These are mostly (60%) the enterprises with low-tech and medium low-tech intensity (LTI). Almost 32.5% of them produce the products for domestic market, so that they probably do not require high technology use. These enterprises have very low values of almost all technologies of Industry 4.0 (Figure 6b). They are usually without new technologies or they are using only basic IT infrastructure. Second or third level of VPi4 and other applications of Industry 4.0 are not presented yet. Due to this, they are called "I4 noobs".

#### 4.1.6. Validation of Cluster Analysis

The validity of the cluster analysis results was verified by one-way ANOVA F-tests for each clustered factor (VPi4 Level 1, Level 2, and Level 3). The results of this analysis should verify whether there are statistically significant di fferences between the clusters. In the one-way ANOVA test, we used a *p*-value significance level 0.05, but some of the cluster means are di fferent. If the *p*-value for all four variables is greater than 0.05 (labeled by '\*' in Table 5), excluding them from the analysis should be

considered. The results of the factor ANOVA are shown in Table 5. The results show that, for all variables, there are some di fferences among the clusters.


**Table 5.** Results of ANOVA test.

1 Significance codes: '\*\*\*' 0.001, '\*\*' 0.01, and '\*' 0.05.

However, the ANOVA results cannot be interpreted unambiguously, as it is not clear which pairs of clusters are di fferent. It is advisable to use the Tukey Honest Significant Di fference (HSD) test (for multiple pairwise comparison) to find out if there is a statistically significant di fference between the means of certain cluster pairs. The results of this analysis are summarized in Table 6. In most cases, the di fferences between the clusters are statistically significant. However, there were no di fferences between Cluster 3 and Cluster 1 for VPi4 Level 1; there were no the di fferences between Clusters 4 and 2 for VPi4 level 2, and three di fferences for VPi4 level 3. This means that there are some overlaps between the clusters, especially for VPi4 Level 3 factor variables. Such lack of di fferences in the clusters may partly be due to the fact that all factors are considered follow-up levels of the VPi4 index. In the case of the small- and medium-sized enterprises, it is typical that most of these enterprises do not reach the high third level of the index. Therefore, their values are rather lower, and this causes the similarity of the clusters. Therefore, the di fferences in clusters of VPi4 Level 3 are not so significant. However, such conclusion should not diminish the significance of the cluster analysis and the fact that the clusters are di fferent. The di fferences are also reported by Table 3 (see within sum of squares, diameter, average distance, separation, etc.).


**Table 6.** Results of the Tukey Honest Significant Di fference (HSD) test.

1 Significant codes: '\*\*\*' 0.001, '\*\*' 0.01, and '\*' 0.05. 2 The lower and the upper end point of the confidence interval at 95% (default).

Another method of cluster analysis validation is related to the abovementioned methods, to determining the optimal number of clusters, the Silhouette and Elbow method. The methods were used to determine the parameters of the cluster analysis in order to achieve the most accurate results. However, it should be noted that the average value of Silhouette coe fficient is only 0.32. The reason for this is the overlap of the factor VPi4 Level 3. Another way to verify the validity of a cluster analysis is, for example, the Dunn index, calculated as the ratio of minimum separation/maximum diameter [73,74], 0.06623, in the paper. The higher the Dunn index value, the better the clustering is.

#### *4.2. Comparison SMEs Index of VPi4 with Large Enterprises*

Subsequently, the large enterprises (90 enterprises) and the SMEs were compared in terms of VPi4%. After the Mann–Whitney–Wilcox test was used to test the statistics, at a significance level of 0.05, the differences between the two groups of the enterprises were tested in the overall VPi4% index and also at the different levels (Levels 1−3). In all cases, the null hypothesis (H10) on the agreemen<sup>t</sup> of both groups) was rejected in favor of the alternative hypothesis (H1A, claiming that the large enterprises reach a higher VPi4% level). The results in Table 7 show that the VPi4 index of small- and medium-sized enterprises (SMEs) and VPi4 index of large enterprises (LEs) is different populations.

**Table 7.** Industry 4.0 index (VPi4) distribution, using Mann–Whitney–Wilcox test.


1 Note: differences between VPi4 index median of large enterprises (LEs) and small- and medium-sized enterprises (SMEs).

The normalization of the data of both variables was verified by the Shapiro–Wilk tests, with the *p*-value of VPi4% = 0.002 and the perception of Industry 4.0 by the enterprises *p*-value = 0.000, assuming the normality of the data, as also shown by both histograms. After that, the VPi4% and the subjective perception rate of Industry 4.0 were compared by using both Pearson and Spearman correlation coefficients. The Table 8 below shows the values of the tested statistics for both samples. It is apparent from *p*-values close to zero that, in both large and small enterprises, VPi4% correlates with the subjective perception of enterprises. In both cases, the correlation rate is very similar. Results show that there is dependency between the perception of Industry 4.0 in the enterprises and the VPi4 index of the smalland medium-sized enterprises. The H20 hypothesis was rejected in favor of H2A (Hypothesis 2A) at a significance level of 0.05.


**Table 8.** Relation to subjective perception of Industry 4.0, based on Pearson and Spearman coefficients.

1 Note: Research was conducted between large enterprises (LEs) and small- and medium-sized enterprises (SMEs).

Overall, the results show that these small- and medium-sized enterprise groups differ statistically significantly from large enterprises in their implementation and use of Industry 4.0 technologies.
