THE APPLICATION OF THE TOOLS OF SPATIAL STATISTICS TO EVALUATION REGIONAL DIFFERENTIATION OF POLISH AGRICULTURE

Transkrypt

1 ACTA UNIVERSITATIS LODZIENSIS FOLIA OECONOMICA 285, 2013 Kamńska Ageska * THE APPLICATION OF THE TOOLS OF SPATIAL STATISTICS TO EVALUATION REGIONAL DIFFERENTIATION OF POLISH AGRICULTURE Abstract. The artcle presets the applcato of the spatal autocorrelato aalyss evaluato of regoal dfferetato of agrculture Polad. The study based o the selected data for the sxtee provces from the year I order to estmate the level of agrculture WAP methods were appled. O the bass of the sythetc measure, developed durg the study, a rakg of regos was costructed. Addtoally, the aalyses were broadeed by the use of spatal autocorrelato statstcs whch eabled to cosder the exstg spatal relatos. Key words: spatal autocorrelato, Mora s global statstc, Mora s local statstc, regoal varablty I. INTRODUCTION Membershp structures of Europea Uo ad use of uo fuds have capablty o the level of Polsh agrculture. Aalyses of levels of agrculture developmet ca be mportat strumet creato of effectve regoal rural polcy. These operatos am at lqudato of regoal dffereces. Stuato of polsh agrculture, especally regoal dsparty was aalyed by may researchers [Borkowsk ad Scęsy (2002), Musyńska (2009), Zegar (2003)]. I order to estmate regoal dfferetato methods of multvarate statstcal aalyss usually were appled [Młodak (2006)]. I the paper, o the bass of the sythetc varable, developed durg the study, the regos were classfed ad grouped to clusters, accordg to ts level of developmet. Addtoally, the aalyses were broadeed by the use of spatal autocorrelato statstcs whch eabled to cosder the exstg spatal relatos. * Ph.D., Departamet of Appled Mathematcs ad Computer Scece, Uversty of Lfe Sceces Lubl. [201]

2 202 Kamńska Ageska II. MATERIAL AND METHODS The study used selected data of the Cetral Statstcal Offce (Regoal Data Bak) for the sxtee provces from the year Both essetal ad statstc reasos decded about dagostc features selecto. Moreover mutually strog correlated features were elmated to dspose of duplcate formato. Coeffcets of varato were also cluded statstcal aalyss- quas-costat varables were rejected. Fally chose dagostc varables were: X1- ow reveue of vovodshps budgets PLN per capta; X2- lfestock of cattle heads per 100 ha of agrcultural lad; X3- lfestock of pgs heads per 100 ha of agrcultural lad; X4- harvests of basc cereals per 1 ha of agrcultural lad [t]; X5- procuremet of potatoes t per 1 ha of agrcultural lad; X6- procuremet of sugar beets t per 1 ha of agrcultural lad; X7- procuremet value of vegetables t per 1 ha of agrcultural lad; X8- procuremet of fruts t per 1 ha of agrcultural lad; X9- uemploymet rate rural areas; X10- proporto of agrcultural lads total area; X11- average farm area ha. All of them were cosdered stmulats, except for X9 (destmulat). I order to ormale the features the stadarato was used. I order to estmate the level of agrculture sythetc measure was used, based o Hellwg method [(Hellwg(1968)]. He proposed a cocept of the taxoomc measure of developmet uderstood as the arragemet of uts vestgated depedg o ther dstace from the stadard establshg the developmet patter. I order to determe the degree of smlarty betwee object ad the stadard pot. The developmet measure s determed as follows: d 1, (1) d 0 where: d - eucldea dstace betwee the object ad the stadard pot, 0 d s d, d d 1 d 2 1 1, sd ( d d ) 1 2, 0 1. (2) The more developed the object, the hgher the value of ths dcator.

3 The Applcato of the Tools of Spatal Statstcs 203 O the bass of sythetc measure, mea ad stadard devato admstratve uts were dvded to four typologcal classes represetg dfferet level of the research ssue: I class: s II class: s III class: s IV class: s where: - mea, s - stadard devato Spatal relatoshps were evaluated o the bass of global ad local Mora s I coeffcets [Asel(1995)]. For the sythetc dcator global Mora s I coeffcet was calculated accordg to formula: I 1 1 j1 w j 1 j1 w ( 1 j 1 ( )( ) 2 j ) (3) where: - umber of observatos - value of varable for -th locato j - value of varable for j-th locato - average value of varable w j weght betwee locatos ad j based o cotguty where the defto of eghbor was based o sharg a commo boudary. Cotguty spatal relatoshps were assged a value of 1 to eghborg locatos ad 0 to all other oes. Spatal weghts are stadarded by row. Each weght s dvded by ts row sum. Sgfcat value of I greater tha 0 proves postve autocorrelato. It meas that objects have smlar values of varables (hgh values of the varable locato ted to be clustered wth hgh values of the same varable locatos that are eghbors of, ad vce versa). Value of I less tha 0 proves egatve autocorrelato. Negatve autocorrelato meas, that exst bg dffereces betwee values for eghborg objects (hgh values a varable locato ted to be co-located wth lower values the eghborg locatos).value of I equal to 0 or smlar to 0 meas radom spatal dstrbuto.

4 204 Kamńska Ageska Local Mora s I was calculated for each observato ut accordg to formula: I 1 ( j1 w ( j ) 2 j ) For each locato, values of I allow for the computato of ts smlarty wth ts eghbours ad also to test ts sgfcace. Fve scearos may emerge [Jac (2006)]: Locatos wth hgh values wth smlar eghbors (kow as hot spots ) Locatos wth low values wth smlar eghbors (kow as cold spots ) Locatos wth hgh values wth low-value eghbors (potetal outler) Locatos wth low values wth hgh-value eghbors (potetal outler) Locatos wth o sgfcat local autocorrelato. Sgfcace test for global ad local Mora s I statstcs were preseted Clff ad Ord (1981). Testg of sgfcace of autocorrelato was based o emprcal value of the Z statstc whch follows ormal dstrbuto: I E( I) Z I ~ N(0,1). Var( I ) These specfc cofguratos ca be detfed from a Mora scatterplot. Ths graph depcts a stadarded varable the x-axs versus the spatal lag of that stadarded varable. The spatal lag s a summary of the effects of the eghborg spatal uts. I essece, Mora scatterplot presets the relato of the varable the locato wth respect the values of that varable the eghborg locatos. By costructo the slope of the le the scatter plot s equvalet to the Mora's I coeffcet. The four quadrats the scatterplot box thus represet dfferet types of assocato betwee the values at a gve locato ad ts spatal lag. he upper rght ad lower left quadrats represet postve spatal assocato, the sese that a locato s surrouded by smlar valued locatos. For the upper rght ths s assocato betwee hgh values, whle for the lower left quadrat ths s assocato betwee low values. The upper left ad lower rght quadrats correspod to egatve assocato, low values are surrouded by hgh values (upper left) ad hgh values are surrouded by low values (lower rght). The relatve destes of these quadrats dcate whch of these patters of egatve spatal assocato ( the tradtoal sese) domate [Asel (1993)]. / (4)

5 The Applcato of the Tools of Spatal Statstcs 205 III. RESULTS Table 1 cotas the values of the sythetc measure represetg the level of agrculture developmet. Table 1. Values of sythetc measure Polad vovodshps the year 2010 Vovodshps Class Welkopolske 0,525 Kujawsko-Pomorske 0,372 I Opolske 0,345 Łódke 0,324 Pomorske 0,312 Warmńsko-Maurske 0,277 II Maowecke 0,268 Dolośląske 0,261 Podlaske 0,252 Śląske 0,226 Małopolske 0,175 Zachodopomorske 0,172 III Śwętokryske 0,168 Lubelske 0,124 Lubuske 0,057 Podkarpacke 0,017 IV mea 0,242 Source: ow work. There was a clasterg tred Polad s provcal level developmet (represeted by dcator ). Vovodshps wth the hgh values of sythetc measure were alog the le from Pomorske to Opolske. Low values of was observed the orth-wester ad south-easter corers of Polad [Fgure 1]. Fgure 1. Values of dcator for vovodshps Source: ow work.

6 206 Kamńska Ageska The value of global Mora s I was equal to 0,26 ad proved sgfcat postve spatal autocorrelato (p-value=0,023). Table 2 cotas the values of local Mora s I. Sgfcat postve values of I were obtaed by Kujawsko- Pomorske, Łódke, Opolske ad Podkarpacke. It meas that locatos were surrouded by smlar eghbors. Table 2. Values of local Mora s I vovodshps the year 2010 Vovodshp I p-value Welkopolske 0,341 0,103 Kujawsko-Pomorske 0,812 0,005 Opolske 0,577 0,044 Łódke 0,379 0,018 Pomorske 0,414 0,038 Maowecke 0,019 0,360 Podlaske 0,010 0,416 Warmńsko-Maurske 0,144 0,156 Dolośląske 0,078 0,16 Śląske 0,006 0,433 Zachodopomorske 0,243 0,208 Małopolske 0,452 0,06 Lubelske 0,487 0,094 Śwętokryske 0,234 0,085 Lubuske 0,93 0,12 Podkarpacke 1,24 0,037 Source: ow work. The provces wth sgfcat values for I (usg sgfcace level of 0.05) are depcted Fgure 2. The lght gray shade o the map dcates a spatal claster of vovodshps wth hgh values of ad the dark gray shade correspods wth claster of low values. Fgure 2. Map llustratg sgfcace of Local Mora s I Source: ow work.

7 The Applcato of the Tools of Spatal Statstcs 207 Fgure 3 s the Mora scatterplot for ths data, wth a lear smoother supermposed. Almost all of the assocatos fall the lower left ad upper rght quadrats dcatg presece of clasters. All pots the upper rght quadrat (hgh-hgh assocato) correspodg to claster of hgh values ad ts smlar eghbors (Kujawsko-Pomorske, Opolske, Łódke, Pomorske, Warmńsko- Maurske, Welkopolske, Maowecke Dolośląske). Pots the lower left quadrat (low-low assocato) correspodg to Podkarpacke vovodshp ad all ts eghbors (Lubelske, Śwętokryske Małopolske). Whle the overall tedecy portrayed the scatterplot s oe of postve assocato, oe vovodshp show the opposte: low value surrouded by hgh values for Lubuske. Lubuske was the potetal outler, but the value of I for that rego was t sgfcat. Fgure 3. Mora scatterplot for dcator Source: ow work. IV. CONCLUSIONS The performed aalyses showed regoal dfferetato of agrculture Polad. Vovodshps wth the hgh level of developmet were alog the le from Pomorske to Opolske. Low level of agrculture was observed the orthwester ad south-easter corers of Polad. The best agrcultural stadg was foud for Welkopolske vovodshp ad relatvely the worst for Podkarpacke ad Lubuske. That results are partly cosstet wth those reported prevous studes.

8 208 Kamńska Ageska Addtoally, the comparatve aalyss was broadeed by the use of the tools of spatal autocorrelato statstcs whch eabled to cosder the exstg spatal relatos. Presece of postve spatal autocorrelato for agrculture was proved. It meas clasterg tred Polad s provcal level developmet. Claster of hgh level of agrculture was formed by Pomorske, Opolske, Łódke ad Warmńsko-Maurke. The claster of low values was formed by Podkarpacke. Geeralg, spatal autocorrelato statstcs are very useful tool multvarate regoal aalyses, partcular Polsh agrculture. They form about the kd ad the stregth of spatal depedece, make possble a determato of assocatos amog objects ad establshg spatal structure better tha usg the tradtoal methods. REFERENCES Asel L. (1993), The Mora Scatterplot as a ESDA Tool to Assess Local Istablty Spatal Assocato, Research Paper Asel L. (1995), Local dcators of spatal assocato-lisa. Geographcal Aalyss 27, Clff A., Ord J.K. (1981), Spatal Process: Models ad Applcatos, Po, Lodo. Borkowsk B., Scęsy W. (2002), Metody taksoomce w badaach prestreego różcowaa rolctwa. Rock Nauk Rolcych, sera G., t. 89,.2, Warsawa. Hellwg Z. (1968), Zastosowae metody taksoomcej do typologcego podału krajów e wględu a poom ch rowoju ora asoby strukturę wykwalfkowaych kadr. Pregląd statystycy 15, Jac K. (2006), Zjawsko autokorelacj prestreej a prykłade statystyk I Moraa ora lokalych wskaźków, ależośc prestreej. Idee praktycy uwersalm geograf, r 33, IGPZ PAN, Warsawa. Młodak A. (2006), Aala taksoomca w statystyce regoalej. Df, Warsawa Musyńska A. (2009), Regoale różcowae rolctwa w Polsce w 2007 roku. Rock Naukowe Sera, t.xi,.4. Warsawa. Zegar J. (red). (2003), Zróżcowae regoale rolctwa. GUS, Warsawa. Bak Daych Regoalych: Główy Urąd Statystycy. Kamńska Ageska ZASTOSOWANIE METOD WAP DO OCENY POZIOMU PRZESTRZENNEGO ZRÓŻNICOWANIA ROZWOJU ROLNICTWA W POLSCE Predmotem badań była aala regoalego różcowaa rolctwa w Polsce. Oceę poomu rolctwa jego dyspersj prestreej opracowao a podstawe daych statystycych gromadoych pre Główy Urąd Statystycy, wykorystując aręda Welowymarowej Aaly Porówawcej (WAP). Na podstawe skostruowaej meej sytetycej utworoo rakg wojewódtw. Dodatkowo wykorystao aręda statystyk prestreej w celu detyfkacj prestreych ależośc.