VIEWPOINTS. Slavica Jovetic* s comment on Correlation analysis of indicators of regional competitiveness: The case of the Republic of Serbia (2013)

Transcription

1 Economic Horizons, May - August 2014, Volume 16, Number 2, Faculty of Economics, University of Kragujevac UDC: 33 eissn www. ekfak.kg.ac.rs VIEWPOINTS Slavica Jovetic* s comment on analysis of indicators of regional competitiveness: case of the Republic of Serbia (2013) doi: /ekonhor J This letter is to bring to attention some inaccurate information provided in the article entitled analysis of the indicators of regional competitiveness: case of the Republic of Serbia, published in Economic Horizons Vol. 15, No 3, as an original research paper. research paper applied/used a statistical methodology for data analysis to which I add the following remarks: Hypothesis formulation (p. 198) Concerning the hypotheses testing thecausal relationship based on the simple linear correlation coefficient, the null hypothesis (H 0 ) assumes: there is no quantitative agreement between the occurrences, i.e. the simple linear correlation coefficient in the population equals zero, while the alternative hypothesis is a rival hypothesis stating quite the opposite from the zero hypothesis. In the relevant literature, which concerns hypotheses testing, if hypotheses are related to a statistical methodology, the null and alternative hypotheses are always given. correlation analysis does not examine dependence, but rather a quantitative agreement please note that, on p. 198, in the second paragraph, the author(s) state that the paper does not address the issues of indicator values... but rather their correlational dependence. correlation analysis does not examine the frequency of relationships, but rather a quantitative *Correspodence to: S. Jovetic, Faculty of Economics, University of Kragujevac; D. Pucara 3, Kragujevac, Serbia; sjovetic@kg.ac.rs agreement between the occurrences; to this end, please note that, on p. 201, the second paragraph states the following: correlation analysis..., but only on the existence and frequency of these relationships. I cannot conclude what the term frequency implies in the mentioned paper; however, a correlation analysis is a static analysis and it can also be a dynamic one, if a sample is selected at certain times where for each of the samples (time series t 1, t 2,...) simple linear correlation coefficients (R 1, R 2,..., etc.) are determined for two random variables, which is normally used in determining a lag length when choosing lagged variables in a regression analysis. Please note that, on p. 201, the second paragraph states that acorrelation analysis is the most complex analysis. On the contrary, a correlation analysis is not 100% reliable and is only used with some other analyses, i.e.: Regression analysis Firstly, concerning the selection of independent variables that will be used in a regression analysis model, a simple linear correlation coefficient can be used. In that case, one should be careful because all variables in a regression model, which do not have aneffect on a dependent variable, must be eliminated from the model (significance p > α). Furthermore, it can also be used in calculating a coefficient of determination (a coefficient of determination is a ratio of the explained variation to the total variation, where as a simple linear correlation coefficient is the positive square root of the R squared, i.e., a coefficient of determination), which holds an important place/plays an important role in aregression analysis. It shows how much % of the variability of the dependent variable is explained by variations of independent variables which remained in the selected regression model.

2 162 Economic Horizons (2014) 16(2), Factor Analysis - One of the conditions of a factor analysis requires that there should be a statistically significant correlation between the independent variables in the model. foregoing requirement at the beginning of a factor analysisis first checked by using three methods: a correlation coefficient and its statistical significance, Bartlett s test and the KMO (Kaiser-Mayer-Olkin) measure of sampling adequacy and their statistical significance. condition that must be fulfilled is that all the three tests show the same level of statistical significance. reader is informed that the SPSS software package used for the statistical analysis was used for the purposes of the research in the paper; however, the exact version of the mentioned software package is not provided, regardless the fact that this is a mandatory requirement for all scientific papers. Concerning the entire text of the paper, whenever Spearman s correlation coefficient is mentioned, the word rank must be mentioned, i.e. the correct wording is: Spearman s rank correlation coefficient. It is indicative that the formula for calculating Spearman s rank correlation coefficientis given in the paper although this coefficient is not calculated in the paper, while the formula for s coefficient, i.e. a simple linear correlation coefficient, is not given in the paper although this coefficient was used in the paper. formula used for the calculation of s coefficient is as follows: n ( ŷ i y ) 2 i=1 R = n ( y i y ) 2 or R = i=1 cov ( x i y i ) s x s y, ȳ - the average of the observed y i values, ŷ i - the estimated values, cov(x i y i ) - the covariance of the sample observations x i y i, i=1, 2,...n i s x s y - standard deviationsof the sampe observations x i y i, i=1,2,...,n. denotations used in the formula are incorrect. following denotations are considered to be the standard ones: a correlation coefficient concerning a sample is marked with an R s / r s, while when applied to a population it is commonly represented by the Greek letter ρ s. Greek letter σ is reserved for apopulation standard deviation. Furthermore, the paper uses the letter n to denote the number of elementary units in the sample, which means that the letters used to denote the sample and the population are not used as prescribed by the standard and this may cause vagueness. In addition, letters x and y (lowercase) are used to mark variables. Random variables are marked in capital letters (X and Y), while lowercase is reserved for the realizations in the sample (x i and y i, i = 1,2,..., n). Please, also note that it is stated in the paper that, if a piece of information is given on an ordinal scale, only Spearman s rank correlation coefficient can then be applied. inaccuracy of this statement is further confirmed by the results of the indicators used in the paper. Some qualitative data were obtained by a survey; such data must be encrypted (e.g. 1 the lowest value,... 5 the highest value or vice versa) and only then can the simple linear correlation coefficient, i.e. s coefficient (the paper uses only s coefficient), be calculated. Finally, the most significant remark concerning this paper is that the hypothesis on the statistical significance of the simple linear correlation coefficient is not tested by using p-empirical probability. SPSS statistical software package does this automatically, and gives the following outputs: s coefficients, Spearman s rank correlation coefficients and statistical significance (p statistics). results accounted forin the tables indicate that the SPSS software was not used, as the aforementioned outputs would have been included in these tables. Tables 1, 2 and 3 show the results of a hypothetical example contained in the SPSS 15.0 for Windows. Table 1 Descriptive Statistics Mean Std. Deviation N X 62, , Y 27, ,

3 Viewpoints 163 X Y Table 2 s 1,812(**),812(**) 1 ** is significant at the 0.01 level (2-tailed). Table 3 s Spearman s Coefficient 1,000,809(**) rho X Sig. (2-tailed).,001 Coefficient,809(**) 1,000 Y. ** is significant at the 0.01 level (2-tailed). X X Y Y Since p < α, including a possible risk of an error of α = 0.01 and α = 0.05, the alternative hypothesis is confirmed, which means that there is a high statistical significance in terms of a quantitative agreement between the observed variables ( s coefficient) in the population and the high statistical significance of the linear interdependence of the ranks of the observed variables in the population (Spearman s rank correlation coefficient). Based on the scale given in the paper, valid conclusions on the statistical significance of the coefficients in the population cannot be derived. It is an imperative that a hypothesis for statistical significance should be tested. conclusion should not contain the following statement: s coefficient shows that these indicators...do not have any effect on.... Let me emphasize once more that the simple linear correlation coefficient indicates an agreement/interactive relationship while a regression analysis, which is not used in the paper, makes it possible to measure an impact. Received on 28 th March 2014, after revision, accepted for publication on 19 th August Darko B. Vukovic* s response to the comment on: analysis of indicators of regional competitiveness: case of Republic of Serbia (2013) doi: /ekonhor V After the suggested criticisms on the article analysis of indicators of regional competitiveness: * Correspondence to: D. B. Vukovic, Geographical Institute Jovan Cvijic of the Serbian Academy of Sciences and Arts, Djure Jaksica 9/3, Belgrade, Serbia; d.vukovic@gi.sanu.ac.rs Case of the Republic of Serbia, which was published in the journal Economic Horizons, Volume 15, Number 3, in 2013, this text contains the answers to the remarks, with certain corrections. article analysis of indicators of regional competitiveness: Case of the Republic of Serbia belongs to the narrower area of the regional economy, where the statistical analysis only is used as a method of the studied problem. refore, the primary and largest part of the paper is devoted to the regional economy which has affected that some of the statistical procedures are excluded (bearing in mind that the statistics in this paper have a lower theoretical significance). In this text, I am going to present the

4 164 Economic Horizons (2014) 16(2), omitted explanations or the results of the analysis (testing the significance of the correlation of the researched indicators). re are also some errors, which will be corrected. remark stating that the correlation analysis does not examine the frequency of the connections but rather a quantitative agreement between the phenomena is accepted. remark for p. 201 in the second paragraph is rejected. This was about the complexity of the analysis rather than about how reliable or unreliable it is. correlation coefficient is an often used statistical method which determines the existence of quantitative stacking as well as the strength of stacking between variables. In the case of the existence of a linear correlation between two phenomena, it is a simple linear correlation. s coefficient of simple linear correlation is the best-known measure that expresses the degree of linear quantitative stacking between two phenomena. During the testing of the significance of this coefficient, it is assumed that the common layout of researched variables is normal. expression of Spearman s correlation coefficient is shown in the article analysis of indicators of regional competitiveness: Case of the Republic of Serbia, which is an error. refore, this remark is accepted. following formula is used for the computation of s coefficient of the sample (which is omitted in the operation): r = n xy x y n x 2 ( x ) 2 n y 2 ( y ) 2 testing of s linear coefficient of correlation was carried out by using the IBM SPSS Statistics software. Version 20, which is available on the Internet ( download_manager=true) was used. This computational operation is exercised by all the versions of the SPSS, so it was not considered necessary to mention which version was used. Moreover, for the purpose of this analysis, Microsoft Excel 2010 is also sufficient, which can provide an adequate testing of s linear correlation coefficient. At the end of the article (in the Apendix), the values obtained through the survey are shown. Surveys may not include the Likert scale (the encryption of 1 to 5, although the Likert scale may include 7 modalities of answers); they, however, may also offer a different system of answers. In this case, the survey offers a possibility of an index evaluation, as a subjective (qualitative) assessment of participants. further processing of the data I do not want to explain since it was used for the purposes of another analysis, which is not the subject of this paper. Further in the text, the testing of the significance of the correlation of the investigated indicators will be displayed, which testing indicates a statistically significant correlation among the greatest number of indicators. As a relative measure of quantitative stacking between the gross domestic product () of the region and the number of companies, s correlation coefficient was used. On the basis of the obtained values of this coefficient, it was concluded that there is a high degree of direct linear correlation in the sample. In testing the significance of the obtained correlation, the obtained value is less than This indicates that at the respective level of significance between these variables there is a statistically significant correlation (Table 1). Table 1 correlation of the in the region with the number of companies of companies s of companies 1,998** Sig. (2-tailed),002,998** 1 Sig. (2-tailed),002 ** is significant at the 0.01 level (2-tailed) A similar conclusion comes up with testing the significance of the obtained correlations in the sample

5 Viewpoints 165 between indicators of the number and regional (Table 2). analysis showed that there is a high correlation between regional and the number in a certa. further testing of the sample showed that investment in capital assets have a medium positive correlation (r = 0.726). growth of investments is positively correlated with growth, but not to the extent that they have companies and the number. indicator related to the number of entrepreneurs in the region is slightly correlated with regional (r = 0.391). This means that there is less quantitative stacking between these indicators. analysis of these indicators showed logical and expected results. By testing the significance of correlations in the employment sample, the conclusion is that there is a statistically significant positive correlation with indicator budgetary expenditures (Table 3). This relationship indicates that there is a high statistical significance of the quantitative stacking between employment (the number in region) and government invests (budgetary expenditures ). Table 3 correlation of the number and budgetary expenditures Budgetary expenditures s Budgetary expenditures 1,988* Sig. (2-tailed),012,988* 1 Sig. (2-tailed),012 ** is significant at the 0.05 level (2-tailed) On the other hand, there was a slightly positive correlation between an investment and employment growth (r = 0.631); by testing this correlation, however, it was confirmed that it is not statistically significant - p > 0.05 (Table 4). Table 2 correlation of the in the region with the number in the region s 1,981* Sig. (2-tailed),019,981* 1 Sig. (2-tailed),019 ** is significant at the 0.05 level (2-tailed) Table 4 correlation of investments and the number s 1,631 Sig. (2-tailed),369,631 1 Sig. (2-tailed),369

6 166 Economic Horizons (2014) 16(2), By analyzing the quantitative stacking in the sample between the indicators of employment with indicators of working age population (r = ) and population with higher education (r = ), it has been shown that coefficients were strongly negative. Tables 5, 6 and 7 show that the correlation between the business indicators indicates the expected results. In fact, with the significance level of 0.01, statistically significant quantitative stackings between the extent of the and the quality of the state services as well as between the quality of the state services and the of the business have been proven. Table 5 correlation of the the extent of and quality of state services quality of state services s quality of state services 1,994** Sig. (2-tailed),006,994** 1 Sig. (2-tailed),006 ** is significant at the 0.01 level (2-tailed) same conclusion is reached in the case of the analysis of correlation between the of the business and the extent of (Table 7). Table 6 correlation of the quality of the state services and the of the business quality of state services of the business s quality of state services of the business 1,996** Sig. (2-tailed),004,996** 1 Sig. (2-tailed),004 ** is significant at the 0.01 level (2-tailed) Table 7 correlation of the of the business and the extent of of the business s of the business extent of 1 1,000** Sig. (2-tailed),000 1,000** 1 Sig. (2-tailed),000 ** is significant at the 0.01 level (2-tailed)

7 Viewpoints 167 high value of the coefficient in the observed sample also indicate connectivity of air transportation with foreign countries and the independence of the judiciary, but testing has shown that the correlation was not statistically significant - p > Almost all innovation indicators showed high positive values of the coefficient of the sample (over 0.9), except indicators the number of registered patents and published scientific research papers, which have weak positive correlation. high degree of positive correlation between regional BDP and the extent of is confirmed as statistically significant (Table 8). Table 8 correlation of the in the region with the extent of the s 1,999**,999** 1 ** is significant at the 0.05 level (2-tailed). Finally, the significance of the correlation between tourism and the specific indicators of the infrastructure is tested. In this sense, no statistically significant correlation between tourism and the largest number of the indicators of the infrastructure has been proven. only statistically significant correlation, based on the sample data, has been proven to exist among the indicators of investments in water supply, investments in water supply and waste water management and the amount of hazardous waste in the region (Table 9). Table 9 correlation of investments in water supply and waste water management with the amount of hazardous waste in the region in water supply and waste water management amount of hazardous waste in the region s in water supply and waste water management amount of hazardous waste in the region 1,975** Sig. (2-tailed),003,975** 1 Sig. (2-tailed),003 ** is significant at the 0.05 level (2-tailed). Based on the results of testing the significance of the correlation of the researched indicators, the validity of the article analysis of indicators of regional competitiveness: Case of the Republic of Serbia, which was published in the journal Economic Horizons, Volume 15, Number 3, in 2013, can be verified. Received on 10 th April 2014, after two revisions, accepted for publication on 19 th August 2014.