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The Methodology of the Assessment of Profitability of Business Models Adopted by Polish HighGrowth EnterprisesIn order to solve the presented problem, the method of the multidimensional statistical analysis was used. A synthetic indicator of the development of HGEs in a given voivodeship which takes into account financial data proving the profitability of the adopted business model was built. The estimated synthetic development indicators made it possible to rank HGEs located in individual voivodeships according to their financial condition to conclude on the profitability of the business models adopted in them. Also, the stability of the position occupied in the ranking for the analyzed groups of HGEs was assessed, which made it possible to indicate Polish voivodeships which were conducive to the development of enterprises in the analyzed period. "Die following variables were analyzed:
The performance indicator was considered to be a stimulus due to the fact that it reflects the rationality of the operation of the business entity. Rational action is an action that leads to a surplus of revenue over costs. Revenues are perceived as effects obtained as a result of conducted activity, costs, on the other hand, as expenditures necessary to obtain these effects. The gross turnover profitability index determines the ability of a business entity to generate profit. The high level of the indicator means a good financial condition of the entity and the likelihood of its further development. The gross value of fixed assets was considered to be a stimulus due to the fact that every economic activity requires the possession of fixed assets necessary to conduct the activity. The size and structure of the assets used in the production process determine the economic efficiency (Wasilewski and Zabadala, 2011). In addition, the value of fixed assets is the result of investment outlays of enterprises which have an impact on regional development (Zygmunt, 2015). In the study it was assumed that shortterm investments can be undertaken by entities that are experienced investors, characterized by high security funds and income. HGEs are characterized by a high average annual revenue growth. Therefore, they are looking for investments generating income in short term. The average monthly gross salary was treated in the analysis as a measure of the value of intellectual capital. Intellectual capital is the basic resource of an economic entity, which is why it is the main factor of its development and market competitiveness. Therefore, the structure of broadly understood remuneration should support the creation and impact of intellectual capital on the development of an enterprise. Modern remuneration policy should encourage employees to achieve strategic goals of business entities, which even requires treating remuneration as an investment in human capital, and not only as a cost (Sokolowski, 2011). The share of HGEs in the population of active enterprises is desirable because these enterprises contribute to the development of entrepreneurship. They take advantage of market opportunities to start their activities. Research carried out by Polish Agency for Enterprise Development (PAED) showed that there were two main reasons for the emergence of HGEs:
HGEs are able to survive adverse conditions and even achieve growth in the conditions of economic fluctuations. In many cases, this is due to the specifics of their activities such as offering niche products, diversifying prices, customers, or doing the opposite  focusing on a fixed group of customers (Niec and Zakrzewski, 2016). hie share of HGEs employment in general employment was treated as a stimulus for new jobs in the market. The data necessary to estimate the value of diagnostic variables describing the financial condition of HGEs and their importance for the development of individual voivodeships in Poland come from the survey of entrepreneurship indicators conducted by the Central Statistical Office (CSO) (Statistics Poland, 2019). The survey covered active nonfinancial enterprises keeping accounting books in 20132017, which employed at least ten people (in 2017, the size of the surveyed statistical sample was 38,059 enterprises). HGEs whose cumulative growth rate of net revenues from sales of products, goods, and materials was at least 72.8% over the period of three consecutive years (3,940 entities) were separated from this group. This means that HGEs were characterized by at least 20% annual growth of net revenues over a threeyear period (CSO, 2019, pp. 2930). The choice of years and variables for the analysis was dictated by the availability and completeness of data in the database of the CSO. The analyses were carried out for voivodeships constituting the basic administrative units in Poland. Treating voivodeships as objects in the analysis is due to the fact that regional policy is becoming more and more important in increasing the effectiveness of innovation policy (Pachura et al., 2014). It is assumed that the results of the analysis can constitute the basis for undertaking actions aimed at stimulating or strengthening the investment environment for HGEs in individual voivodeships, which should contribute to the increase of their competitiveness. In empirical analyses, the development pattern method was used. It is one of the methods of linear ordering and makes it possible to replace the description of objects using a number of features with one synthetic feature (Ostasiewicz, 1998). Tie development pattern method assumes that there is a model object (the socalled pattern) for which each of the diagnostic features assumes the best values. Then the distances of individual objects (Of, i— 1, 2, ..., n) from the model object (Ow) are determined with the use of a binary function with real values, which should meet the following conditions (Kolenda, 2006): a. d(Oj,0_{2}) > 0 (the distance between objects is always nonnegative). b. d(Oj,0_{2}) = d(0_{2},Oi) (the distance between objects meets the condition of symmetry). c. d(Oj,0_{2}) < d(0_{1;}0_{3}) + d(0_{3},0_{2}) (the distance between objects meets the condition of triangle inequality). d. d(Oj, 0_{3}) = 0 Oj  O2 . Each binary function which meets the conditions (ad) is called a metric and is used to determine the similarity between objects. The notation d(Oj,0_{2}) < d(O_{l;}0_{3}) means that object O, is more similar to object O, than to object 0_{3}. Different types of metrics are used to measure similarity between objects, with Euclidean metrics being the most popular. All diagnostic variables included in the analysis should be classified into one of the three categories of variables: stimulants, destimulants, or neutral variables. Neutral variables measured on the quotient scale should be replaced with stimulants using the following transformation:
where xy is the value of ay'th neutral variable for an zth object, nonij is the nominal value of a уthe variable. Then the value of each diagnostic variable measured at least on the interval scale is standardized according to the following formula:
where Xj are the values of a y’th diagnostic value Xj describing an zth object О,; лу is the arithmetic mean of the diagnostic variable X, Sj is the standard deviation of the diagnostic variable X, z_{:/} are the standardized values of the variable for an zth object; m is the number of diagnostic variables; n is the number of objects. The Z, variable with an average equals to 0, and a standard deviation is already measured on the interval scale, so the transformation of diagnostic variables checked their orders of magnitude to the state of comparability (Walesiak, 2011). In the development pattern method, the key step is to define the reference object (O.J and the antipattern (O,,) whose geometric representation is respective points z_{w}—{z_{w}j)j_{e}^_{2}.....,„} and z_{a} — (z„_{7} )_{je}{_{t}2.....»;} which has the following coordinates: "Die synthetic measure of development (SMD) (m) for an z’th object is determined according to the relation of Equations (5.5) and (5.6): where d{z_{t}p z_{WJ}) is the distance between the z’th object and the model object measured using Euclidean metric; d{z_{aj}, z_{WJ}) is the distance between the development pattern and the antipattern. "Die synthetic measure of development has values in the range (0,1), and the closer its values are to unity, the more the zth object is similar to the model object, and at the same time less similar to the antipattern (Ostasiewicz, 1998). In order to check whether the SMDs estimated in different units of time for the same statistical population are similar to the Friedman rank test was used, the following set of hypotheses was formulated:
where F)' (я) is a distribution function of the SMD for the examined group of objects in the yth unit of time; r is the number of rankings; and n is the number of examined objects. "Die test statistics has the following form (Domariski and Pruska, 2000):
where R) — X''_{=1}z;y is the sum of ranks assigned to objects according to the value of the synthetic measure of development in ayth time unit (J — 1, 2, ..., r). Assuming that the null hypothesis is true, the statistics in the Friedman test have an asymptotic distribution of chisquare with k1 degrees of freedom. In a situation where the Friedman rank test results indicate the occurrence of significant differences in the total distribution of the values of the SMD for the examined group of objects, it is also worth checking in which time units the greatest differences in the formation of this measure occurred. To this end, the Wilcoxon rank test can be used in which the following hypotheses are made:
The Wilcoxon test determines the differences between the values of the SMD in two different time units (SMD_{)Vf}  SMD^), for each tested object {k — 1, 2, ..., n). The modules of these differences are given ranks for which the rank test is defined (Domanski and Pruska, 2000):
where
and
where SDM^ is a variable describing the value of the synthetic measure of development in the z’th period for the /£th object. The set of critical values of the Wilcoxon test is defined by the following relation: P(T < T_{a}) = a (Domanski and Pruska, 2000). For a sample sizes above 25 (n > 25), the following test statistics are used (Domanski and Pruska, 2000): which has an asymptotically normal distribution N (0,1) with the assumption about the truth of the null hypothesis. The last stage of the analysis is ranking objects according to the decreasing values of the synthetic measure of development in each tested unit of time. Based on the rankings, the values of Spearman and Kendall tau rank correlation coefficients will be determined, for which nonpara metric tests will be carried out to verify their statistical significance. On the basis of this conclusion about the stability in the time of ranking, objects in subsequent rankings will be drawn. To verify the null hypothesis about the independence of positioning of objects according to the value of the synthetic measure of development in two selected years:
the following statistics needs to be estimated (Pilatowska, 2006): and
where p, is the Spearman rank correlation coefficient for a population; U_{s} is the test statistics, which for a number of observations higher than 10 (n > 10) has an asymptotically normal distribution N (0,1); r_{s} is the Spearman rank correlation coefficient estimator; and d_{t} is the difference between the positioning of an z’th object in the rankings for the periods t and к. When examining the difference between the probability that the positions of the examined objects in the rankings relative to the synthetic measure of development in two arbitrary units of time are in the same order, and the probability that their order will be different, the Kendall tau correlation coefficient should be estimated (Szajt, 2014): where x_{K} is the Kendall tau coefficient; P is the number of observation pairs for which the relations between positions occupied by any two objects in both rankings are compatible (i.e., if in the first ranking the position occupied by the гth object is higher than the position occupied by the y'th object, in the second ranking the position of the 2th object will be higher than the position of the yth object as well); and О is the number of pairs of not compatible observations for which the relations are opposite. When verifying the null hypothesis about the irrelevance of the Kendall tau correlation coefficient in the context of the alternative hypothesis indicating the significance of the difference between the probabilities of the appearance of consistent and opposite object arrangements in the rankings:
the following statistics should be estimated (Szajt, 2014):
where U_{K}is the test statistics, which for the number of observations higher than 10 (n > 10) has an asymptotically normal distribution iV (0,1). 
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