The use of digital tools greatly affects the way of doing business, this is reflected in aspects such as the creation, destruction, and modification of jobs [1,2]. The digital transformation for the Colombian tourism subsector has had positive impacts; for example, in the first quarter of 2018, the profits of companies that used digital resources in the development of their activities exceeded by 6.9% the profits of companies that did not use those resources [3].

Despite the above, the progress of the digital transformation is not uniform in the set of companies in the tourism sector, because not all companies can overcome the difficulties, they encounter in the digitization process. Inequalities to access information, knowledge and education through new technologies [4], known as the gap, hinder the design and implementation of policies that guide improvements in the Colombian tourism sector.

From this objectivity, it is not possible to speak of a single digital gap, given that it is multifaceted depending on the context of comparison; thus, there exists a semantic application of digital gaps in plural [5]. For this reason, the relevance of partial ICT indicators for measuring the digital divide (gap) has been recognized [6].

Consequently, a first unavoidable task is the statistical measurement of the digital gap in order to know the situation of digitization in the Colombian tourism sector. For this, a good tool is the index evaluation, which is a synthetic measure that accounts for an abstract definition [7].

In this scenario, the multivariate statistical analysis that mentions the set of techniques used to examine, represent and interpret the associations between multiple variables of an individual or sample of individuals, at the same time [8,9]. It is suitable for the construction of indexes, from the application of different analysis methods.

Among the multivariate techniques most used for the elaboration of indexes or indicators, the Main Components Analysis (PCA) and the Factor Analysis (AF) are efficient, by summarizing a set of original quantitative variables in a few synthetic variables, with minimal loss of information [9,10].

The use of techniques analogous to PCA is also common when dealing with qualitative variables. For this reason, the Main Categorical Components Analysis (CATPCA) is widely used for the construction of indexes that address qualitative original variables, summarizing them in a few synthetic variables with the least possible loss of information [11,12].

Although each multivariate method can be used separately in the construction of indexes. These become more efficient when used together with other data analysis techniques. Indeed, the combined use of the aforementioned multivariate techniques for the transformation of partial indicators (original variables) into a few synthetic variables (indexes) is notable [13,14].

The measurement of the digital gap in the Colombian tourism industry that is proposed in this research is done with an approach from multivariate statistics with the results referring to Information and Communication Technology (ICT) obtained in the Annual Service Survey (EAS) -2017 [15], within the dimensions of ICT Preparation, Use and Impacts.

For the construction of the composite Index of Use, Preparation and Impacts of ICT (IUPITIC) in the PIMES [16], which is a mathematical combination of sub-indexes or partial indicators [9,11], the information of the National Department of Statistics [15] was available through of the EAS. This survey measured the technological component of 5,989 Colombian companies in the service sector in general. Which were distributed according to the economic activity described by the International Standard Industrial Classification-ISIC Revision 4.

Now, in order to obtain the target population, the definition of a tourist industry made by the World Tourism Organization [17] was used, thus framing the ISIC (CIIU)-4 divisions by group, together with their number of companies, to the tourist activities of accommodation, foods and beverages, transportation and equipment rental, and travel agencies and other reservation services. In effect, a target universe of 1,678 companies was obtained. The variables of interest of the EAS- 2017 [15] were selected as stipulated by [18], thus choosing 14 qualitative variables for the Use sub-index, 5 quantitative variables in the Preparation sub-index, and 1 quantitative variable for the Impact sub-index.

The IUPITIC index compromises the use of quantitative and qualitative variables, consequently, in order to elaborate the Use sub-index, the method of Analysis of Main Categorical Components-CATPCA is used, which allows treating qualitative variables, for the construction of the Preparation and Impact sub-indexes is used in Main Components Analysis -ACP, and for the IUPITIC composite index the weighted weights method is applied. Finally, a single factor ANOVA is used in order to measure the gap.

The measurement of the digital gap in the Colombian tourism sector was carried out in this research evaluating a composite index (IUPITIC) defined from the Use (𝑌_𝑖 with i=1,2),, of Preparation n (𝑋_𝑖 with i=1,2), and of Impact (C) of Information and Communication Technology.

In these calculations 𝑌₁- corresponds to the value of the form of business, 𝑌₂ - speed and communication of digital information, 𝑋_1- occupation of internet and computer and X₂ - salary and telework.

The variables considered in the aforementioned sub-indexes (𝑌_𝑖, 𝑋_𝑖, and C) are presented in the following Table 1, also the notations of the variables in this tabulation correspond to those established in the information capture instruments used by DANE (2018).

Table 1

Source: Authors

The values obtained for the subindexes and the composite index are detailed below:

The execution of composite indexes in order to measure the digital gap from the Use, Preparation and Impact of ICTs in companies, is efficient for the construction of public and business policies for the purposes of competitive sector improvement.

The low level of the IUPITIC index shows some important differences in the means by organizational size. Micro and large companies tend to have better Use, Impact and Preparation of ICTs in their activities, while medium sized and small companies are those that least use ICTs in their functions.

The Single Factor Variance Analysis is a good objective tool in order to infer inequalities in the scores of the composite index - IUPITIC. Determining the existence of a digital gap from the combined values of the Use, Preparation and Impact of ICT by company size in the Colombian tourism sector.

The evaluation of the robustness of the elaborated composite index is appropriate in order to know the efficiency of the model. In this context, the synthetic variable - IUPITIC shows a correct adaptation for the measurement of the digital gap in the tourist sector that was studied.

The use of multivariate techniques in order to measure the digital gap is convenient, especially since there is no universal consensus on how digital gaps can be mediated. Therefore, it is necessary to advance in the construction of composite indexes that enable the evaluating of the Use, Preparation and Impacts of the ICTs of the different companies for the productive strengthening.