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

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1 Ecoomic Horizos May - August 2014 Volume 16 Number Faculty of Ecoomics Uiversity of Kragujevac UDC: 33 eissn www. ekfak.kg.ac.rs VIEWPOINTS Slavica Jovetic* s commet o Correlatio aalysis of idicators of regioal competitiveess: The case of the Republic of Serbia (2013) doi: /ekohor J This letter is to brig to attetio some iaccurate iformatio provided i the article etitled Correlatio aalysis of the idicators of regioal competitiveess: The case of the Republic of Serbia published i Ecoomic Horizos Vol. 15 No 3 as a origial research paper. The research paper applied/used a statistical methodology for data aalysis to which I add the followig remarks: Hypothesis formulatio (p. 198) Cocerig the hypotheses testig thecausal relatioship based o the simple liear correlatio coefficiet the ull hypothesis (H 0 ) assumes: there is o quatitative agreemet betwee the occurreces i.e. the simple liear correlatio coefficiet i the populatio equals zero while the alterative hypothesis is a rival hypothesis statig quite the opposite from the zero hypothesis. I the relevat literature which cocers hypotheses testig if hypotheses are related to a statistical methodology the ull ad alterative hypotheses are always give. The correlatio aalysis does ot examie depedece but rather a quatitative agreemet please ote that o p. 198 i the secod paragraph the author(s) state that the paper does ot address the issues of idicator values... but rather their correlatioal depedece. The correlatio aalysis does ot examie the frequecy of relatioships but rather a quatitative *Correspodece to: S. Jovetic Faculty of Ecoomics Uiversity of Kragujevac; D. Pucara Kragujevac Serbia; sjovetic@kg.ac.rs agreemet betwee the occurreces; to this ed please ote that o p. 201 the secod paragraph states the followig: The correlatio aalysis... but oly o the existece ad frequecy of these relatioships. I caot coclude what the term frequecmplies i the metioed paper; however a correlatio aalysis is a static aalysis ad it ca also be a dyamic oe if a sample is selected at certai times where for each of the samples (time series t 1 t 2...) simple liear correlatio coefficiets (R 1 R 2... etc.) are determied for two radom variables which is ormally used i determiig a lag legth whe choosig lagged variables i a regressio aalysis. Please ote that o p. 201 the secod paragraph states that acorrelatio aalysis is the most complex aalysis. O the cotrary a correlatio aalysis is ot 100% reliable ad is oly used with some other aalyses i.e.: Regressio aalysis Firstly cocerig the selectio of idepedet variables that will be used i a regressio aalysis model a simple liear correlatio coefficiet ca be used. I that case oe should be careful because all variables i a regressio model which do ot have aeffect o a depedet variable must be elimiated from the model (sigificace p > α). Furthermore it ca also be used i calculatig a coefficiet of determiatio (a coefficiet of determiatio is a ratio of the explaied variatio to the total variatio where as a simple liear correlatio coefficiet is the positive square root of the R squared i.e. a coefficiet of determiatio) which holds a importat place/plays a importat role i aregressio aalysis. It shows how much % of the variability of the depedet variable is explaied by variatios of idepedet variables which remaied i the selected regressio model.

2 162 Ecoomic Horizos (2014) 16(2) Factor Aalysis - Oe of the coditios of a factor aalysis requires that there should be a statistically sigificat correlatio betwee the idepedet variables i the model. The foregoig requiremet at the begiig of a factor aalysisis first checked by usig three methods: a correlatio coefficiet ad its statistical sigificace Bartlett s test ad the KMO (Kaiser-Mayer-Olki) measure of samplig adequacy ad their statistical sigificace. The coditio that must be fulfilled is that all the three tests show the same level of statistical sigificace. The reader is iformed that the SPSS software package used for the statistical aalysis was used for the purposes of the research i the paper; however the exact versio of the metioed software package is ot provided regardless the fact that this is a madatory requiremet for all scietific papers. Cocerig the etire text of the paper wheever Spearma s correlatio coefficiet is metioed the word rak must be metioed i.e. the correct wordig is: Spearma s rak correlatio coefficiet. It is idicative that the formula for calculatig Spearma s rak correlatio coefficietis give i the paper although this coefficiet is ot calculated i the paper while the formula for Pearso s coefficiet i.e. a simple liear correlatio coefficiet is ot give i the paper although this coefficiet was used i the paper. The formula used for the calculatio of Pearso s coefficiet is as follows: ( ŷ i y ) 2 R = ( y ) 2 or R = cov ( x i ) s x s y ȳ - the average of the observed values ŷ i - the estimated values cov(x i ) - the covariace of the sample observatios x i 2... i s x s y - stadard deviatiosof the sampe observatios x i 2... The deotatios used i the formula are icorrect. The followig deotatios are cosidered to be the stadard oes: a correlatio coefficiet cocerig a sample is marked with a R s / r s while whe applied to a populatio it is commoly represeted by the Greek letter ρ s. The Greek letter σ is reserved for apopulatio stadard deviatio. Furthermore the paper uses the letter to deote the umber of elemetary uits i the sample which meas that the letters used to deote the sample ad the populatio are ot used as prescribed by the stadard ad this may cause vagueess. I additio letters x ad y (lowercase) are used to mark variables. Radom variables are marked i capital letters (X ad Y) while lowercase is reserved for the realizatios i the sample (x i ad i = ). Please also ote that it is stated i the paper that if a piece of iformatio is give o a ordial scale oly Spearma s rak correlatio coefficiet ca the be applied. The iaccuracy of this statemet is further cofirmed by the results of the idicators used i the paper. Some qualitative data were obtaied by a survey; such data must be ecrypted (e.g. 1 the lowest value... 5 the highest value or vice versa) ad oly the ca the simple liear correlatio coefficiet i.e. Pearso s coefficiet (the paper uses oly Pearso s coefficiet) be calculated. Fially the most sigificat remark cocerig this paper is that the hypothesis o the statistical sigificace of the simple liear correlatio coefficiet is ot tested by usig p-empirical probability. The SPSS statistical software package does this automatically ad gives the followig outputs: Pearso s coefficiets Spearma s rak correlatio coefficiets ad statistical sigificace (p statistics). The results accouted fori the tables idicate that the SPSS software was ot used as the aforemetioed outputs would have bee icluded i these tables. Tables 1 2 ad 3 show the results of a hypothetical example cotaied i the SPSS 15.0 for Widows. Table 1 Descriptive Statistics Mea Std. Deviatio N X Y

3 Viewpoits 163 X Y Table 2 Correlatios Pearso Correlatio 1 812(**) Sig. (2-tailed) 001 Pearso Correlatio 812(**) 1 Sig. (2-tailed) 001 ** Correlatio is sigificat at the 0.01 level (2-tailed). Table 3 Correlatios Spearma s Correlatio Coefficiet (**) rho X Sig. (2-tailed). 001 Correlatio Coefficiet 809(**) 1000 Y Sig. (2-tailed) 001. ** Correlatio is sigificat at the 0.01 level (2-tailed). X X Y Y Sice p < α icludig a possible risk of a error of α = 0.01 ad α = 0.05 the alterative hypothesis is cofirmed which meas that there is a high statistical sigificace i terms of a quatitative agreemet betwee the observed variables (Pearso s coefficiet) i the populatio ad the high statistical sigificace of the liear iterdepedece of the raks of the observed variables i the populatio (Spearma s rak correlatio coefficiet). Based o the scale give i the paper valid coclusios o the statistical sigificace of the coefficiets i the populatio caot be derived. It is a imperative that a hypothesis for statistical sigificace should be tested. The coclusio should ot cotai the followig statemet: Pearso s coefficiet shows that these idicators...do ot have ay effect o.... Let me emphasize oce more that the simple liear correlatio coefficiet idicates a agreemet/iteractive relatioship while a regressio aalysis which is ot used i the paper makes it possible to measure a impact. Received o 28 th March 2014 after revisio accepted for publicatio o 19 th August 2014.

4 Ekoomski horizoti Maj - Avgust 2014 Volume 16 Sveska Ekoomski fakultet Uiverziteta u Kragujevcu UDC: 33 ISSN: X www. ekfak.kg.ac.rs GLEDIŠTA Kometar Slavice Jovetić* člaka: Korelacioa aaliza idikatora regioale kokuretosti: Primer Republike Srbije autora Darka B. Vukovića (2013) doi: /ekohor J U časopisu Ekoomski horizoti Volume 15 Sveska 3 Godište 2013 publikova je člaak: Korelacioa aaliza idikatora regioale kokuretosti: Primer Republike Srbije kao izvori auči člaak. U člaku je primejea/korišćea statistička metodologija za aalizu podataka/problema a koju stavljam sledeće primedbe: Defiisaje hipoteze (a str. 198) - U slučaju testiraja hipoteze o korelaciooj vezi a osovu koeficijeta proste lieare korelacije ulta hipoteza (H 0 ) je: e postoji kvatitativo slagaje između pojava ili koeficijet proste lieare korelacije u populaciji jedak je uli a alterativa hipoteza je suproto tvrđeje. U relevatoj literaturi u kojoj se avode hipoteze ako su iste vezae za statističku metodologiju avode se ulta i alterativa. Korelacioa aaliza e ispituje zavisost već kvatitativo slagaje - a str. 198 drugi pasus avedeo je da se rad e bavi pitajima vredosti idikatora... već jihovom korelacioom zavisošću. Korelacioa aaliza e ispituje učestalost veza već kvatitativo slagaje između pojava - a str. 201 drugi pasus avedeo je: Korelacioa aaliza... već samo o postojaju i učestalosti tih veza. Ne zam šta se mislilo u radu pod pojmom učestalost ali *Korespodecija: S. Jovetić Ekoomski fakultet Uiverziteta u Kragujevcu Đ. Pucara Kragujevac Srbija; sjovetic@kg.ac.rs korelacioa aaliza je statiča aaliza i mogla bi da bude diamička aaliza ukoliko bi se uzorak birao u određeim vremeskim periodima i za svaki taj uzorak (u vremeu t 1 t 2...) za dve slučaje promeljive određivali koeficijeti proste lieare korelacije (R 1 R 2... itd.) što se iače koristi za određivaje dužie zaostajaja kod biraja promeljivih sa zaostajajem u regresiooj aalizi. Na str. 201 drugi pasus avedeo je da je korelacioa aaliza ajsložeija aaliza. Naprotiv korelacioa aaliza je epouzdaa aaliza i koristi se samo uz eku drugu aalizu i to: Regresioa aaliza - U prvom koraku kod izbora ezaviso promeljivih koje će ući u model regresioe aalize može se koristiti koeficijet proste lieare korelacije. I u tom slučaju treba biti opreza jer sve promeljive u regresioom modelu koje emaju uticaj a zaviso promeljivu moraju da apuste model (sigifikatost p > α). Dalje još se koristi za izračuavaje koeficijeta determiacije (koeficijet determiacije je odos između objašjee i ukupe varijase a koeficijet proste lieare korelacije je pozitiva kvadrati kore iz koeficijeta determiacije) koji ima svoje začajo mesto/tumačeje u regresiooj aalizi. O pokazuje koliko je % varijabiliteta zaviso promeljive objašjeo varijacijama ezaviso promeljivih koje su ostale u odabraom regresioom modelu. Faktorska aaliza - Jeda od uslova u faktorskoj aalizi je da postoji statistički začaja korelacija između ezaviso promeljivih u modelu. U prvom koraku faktorske aalize se proverava ovaj uslov pomoću tri metoda: koeficijeta korelacije i jegove statističke začajosti Bartletovog i КМО

5 166 Ekoomski horizoti (2014) 16(2) (Kaiser-Mayer-Olki) testa i jihove statističke začajosti. Uslov je da sva tri testa pokažu istu statističku začajost. U radu je avedeo da je korišće SPSS statistički softver mada se e avodi verzija istog što je obavezo u svim aučim radovima. U celom radu gde se avodi Spirmaov koeficijet korelacije mora da stoji reč raga odoso Spirmaov koeficijet korelacije raga/ragova. Idikativo je da je avede obrazac za izračuavaje Spirmaovog koeficijeta korelacije raga a da o ije račuat u radu a ije avede obrazac za Pirsoov koeficijet koeficijet proste lieare korelacije koji je korišće u radu. Obrazac za Pirsoov koeficijet je: ( ŷ i y ) 2 cov ( x i ) R = ili R = ( y ) 2 s x s y gde su ȳ - aritmetička sredia posmatraih vredosti ŷ i - ocejee vredosti cov(x i ) - kovarijasa opservacija a osovu uzorka x i 2... i s x s y - stadarde devijacije opservacija x i 2... a osovu uzorka. Obrazac ima pogreše ozake. U stadardu je prihvaćeo da se u uzorku koeficijet korelacije obeležava sa R s /r s a u populaciji sa ρ s. Ozaka σ rezervisaa je za stadardu devijaciju populacije. Dalje se u radu koristi ozaka -broj elemetarih jediica u uzorku što zači da se mešaju stadardizovae ozake za uzorak i populaciju. Takođe se sa x i y (mala slova) obeležavaju promeljive. Slučaje promeljive se obeležavaju velikim slovima (X i Y) a realizacije u uzorku malim slovima (x i i 2 ). Dalje se u radu avodi da ako su podaci dati a ordialoj skali može se primeiti samo Spirmaov koeficijet korelacije raga. Da to ije tačo potvrđuju i rezultati istraživaja idikatora u radu. Neki kvalitativi podaci dobijei su aketom; ti podaci moraju da se šifriraju (a primer 1 - ajiža vredost ajviša vredost ili obruto) i oda da se izračua koeficijet proste lieare korelacije Pirsoov koeficijet (u radu su prikazai samo Pirsoovi koeficijeti). Na kraju oo što je ajveća zamerka ovom radu to je da ije testiraa hipoteze o statističkoj začajosti koeficijeta proste lieare korelacije pomoću statistike p-empirijske verovatoće. SPSS statistički program to radi automatski a kao rezultati se prikazuju: Pirsoovi koeficijeti Spirmaovi i statistička začajost koeficijeta (statistika p). Prikaz rezultata u tabelama ukazuje da ije korišće SPSS program jer bi bilo prikazao sve avedeo. U tabelama 1 2 i 3 prikazai su rezultati hipotetičkog primera u SPSS 15.0 for Widows. Tabela 1 Descriptive Statistics Mea Std. Deviatio N X Y Tabela 2 Correlatios X Y X Pearso Correlatio 1 812(**) Sig. (2-tailed) 001 Y Pearso Correlatio 812(**) 1 Sig. (2-tailed) 001 ** Correlatio is sigificat at the 0.01 level (2-tailed). Tabela 3 Correlatios X Y Spearma s X Correlatio Coefficiet (**) rho Sig. (2-tailed). 001 Y Correlatio Coefficiet 809(**) 1000 Sig. (2-tailed) 001. **Correlatio is sigificat at the 0.01 level (2-tailed).

6 Gledišta 167 Pošto je p < α to se uz rizik greške α = 001 i α = 005 prihvata alterativa hipoteza a to zači da postoji visoka statistička začajost kvatitativog slagaja između posmatraih promeljivih (Pearso-ov koeficijet) u populaciji i visoka statistička začajost lieare međuzavisosti ragova posmatraih promeljivih u populaciji (Spearma-ov koeficijet). Na osovu prikazae skale u radu e mogu se izvoditi validi zaključci o statističkoj začajost koeficijeata u populaciji. Neophodo je testirati hipotezu o jihovoj statističkoj začajosti. U zaključku e sme da se avede tvrdja: Pirsoov koeficijet pokazuje da ovi idikatori... emaju uticaj a.... Još jedom aglašavam da koeficijet proste lieare korelacije pokazuje slagaje/iterakcijski odos a regresioa aaliza koja ije korišćea u radu omogućuje mereje uticaja. Primljeo 28. marta 2014 ako revizije prihvaćeo za publikovaje 19. avgusta 2014.