Research Journal of Mathematcs and Statstcs 6(3): 3-34, 14 ISSN: 4-4, e-issn: 4-755 Maxwell Scentfc Organzaton, 14 Submtted: June 8, 14 Accepted: August 19, 14 Publshed: August 5, 14 Mean Vector Analyses of the Votng Patterns of Ghanaans for Three Consecutve Perods: A Case Study of the Greater Accra Regon R. Opou-Sarode, S. Amponsah Gymah, F. Gardner and T. Manu Methodst Unversty College Ghana, Dansoman, Accra, Ghana Abstract: The am of ths paper was to fnd out whether the outcome of future electons n the Greater Accra regon could be predcted based on emprcal data. The votng patterns of the presdental electons n Ghana deserve notce, not because of ther poltcal sgnfcance but because of the theoretcal weght they carry. The shfts n electoral fortunes between the two man poltcal partes n the country, especally n the greater Accra regon provde a unque leverage for assessng theores of votng behavor. The paper uses statstcal tools to examne the electoral performance of the four major poltcal partes n Accra and the Hotellng s T Statstc to test whether a predcton could be made to predct future outcomes of electons. Our results revealed that there was not enough statstcal evdence to predct future outcomes of electons n the greater Accra dstrct. Keywords: Mean vector, multvarate analyss, votng patterns INTRODUCTION There are four man poltcal partes n Ghana, namely: Natonal Democratc Congress (NDC), New Patrotc Party (NPP), People s Natonal Conventon (PNC) and the Conventon s Peoples Party (CPP) (Damnyag, 13). There are also ten regons n Ghana. There are certan regons that are consdered strong hold for certan promnent poltcal partes where as other regons are consdered swngng regons. The strong hold regons are those that are always won by one poltcal party durng electons, whereas the swngng regons can be won by any poltcal party. One of the swngng regons s the Greater Accra regon where the research focused on. The votng pattern n the Greater Accra regon does not appear to have any relatonshp wth the performance of the ncumbent, that s to say that the ncumbent can stll wn though they may have performed poorly durng ther tenure of offce. We therefore set out to study the votng patterns of Ghanaans n the Greater Accra regon. An ntrgung characterstc of electoral poltcs n Ghana and Afrca as a whole s that the ncumbents, however bad, tend to wn electons. Key and Anebo () asserted that people may not really govern themselves, but they can str up a deafenng commoton f they dsle the way they are governed. The commoton could be n the form of votng out that poltcal party whch s not performng well out of power to mae way for a new one. However, the results of electons n Ghana do not appear to agree wth the above asserton. Some of the reasons for the poltcal partes that wn swngng regons have been attrbuted to ethncty, maretng strategy and hstory of the area. Some also do assert that, wnnng n the swngng regons do not follow any specal pattern. Alab and Alab (8) analyzed the effects of ethncty on poltcal maretng n Ghana usng vote data. The analyss made t evdent that poltcal partes wth very strong ethnc support bases are those that have stood that test of tme no matter what maretng tools or approaches are employed. Ntow-Ababo (1) wored on settler communtes, votng patterns and natonal ntegraton: A case study of the Dormaa East consttuency. The study found that even though members of settler communtes n the Dormaa East Consttuency may be nfluenced by ther ethnc bacground when t comes to votng, ther votng pattern does not follow any specal pattern and hence explanng ther votng pattern becomes very dffcult especally n terms of ethncty. The study also showed that there s no sgnfcant dfference between the votng behavor of settler communtes and that of the ndgenous people. Ths mn paper sees to address the most basc and standard statstcal problem about analyzng the trend of presdental votng patterns n Ghana. we ntend to apply the varous multvarate data analyss tools to explore the data gathered from the Electoral Commsson on the votng patterns of Ghana s one of the most swngng regons-the Greater Accra Regon. That s: we see to mae nferences about the varous characterstcs of the populaton under study. Some of these characterstcs are the mean, the varance, the covarance, the standard devaton and so on. The study captures the trend of analyss of the results of the four Correspondng Author: R. Opou-Sarode, Methodst Unversty College Ghana, Dansoman, Accra, Ghana 3
major poltcal partes n Ghana- The rulng Natonal Democratc Congress (NDC), strongest opposton party, the New Patrotc Party (NPP), the People s Natonal Conventon (PNC) and Ghana s frst presdent s party, the Conventon s Peoples Party (CPP). A thorough nowledge of the votng patterns of each regon s essental for every poltcal party, the regstered voters and the general publc as a whole. The Greater Accra Regon whch has been descrbed as one of the most swngng regons n Ghana electons wll be analyzed. Aluagba (13) studed the votng behavor of Ngerans. In hs study he found that the votng behavor of Ngerans has reflected relgous nstnct such that n vrtually all the electons conducted n the country, the votng pattern has often towed along relgous lnes. Durng the 11 general electons, the two major presdental canddates that contested, Presdent Good luc Jonathan of the Peoples Democratc Party (PDP), a Chrstan and General Mohammadu Buhar of the Congress for Progressve Change (CPC), a Moslem, practcally ptched the relgous cleavages wthn the Ngeran electorate aganst each other. The research whch was conducted n Fagge Local Government Area (LGA) of Kano State Ngera found that Ngeran voters resdent n Fagge LGA have the propensty to vote along relgous lnes but ths tendency s more prevalent among Muslms than Chrstans. It further revealed that, even though the electorate n Fagge overtly denounces the consderaton of relgous bacground of canddates durng electon; on Electon Day, votes were cast to reflect relgous prejudces of the voters. It recommends extensve poltcal educaton, good poltcal leadershp and transparent electons for Ngera to overcome the nfluence of relgon on her electoral process. Whle much has been wrtten on the electoral strength of Islamsts n Egypt, most analyss has been done at the natonal level, gnorng regonal dvdes wthn the country. As a means of helpng U.S. polcymaers and Mddle East watchers better understand votng patterns n Egypt snce the 11 revoluton. Worman and Martn (13) conducted a study to dentfy the areas where Islamst partes run strongest and the areas where non-islamsts are most compettve. They found that whle Islamsts perform well across the whole of the country, they draw ther strongest electoral support n Upper Egypt, North Sna and sparsely populated governorates n the west, whle non-islamst partes fare best n Caro and ts mmedate envrons, Port Sad, South Sna and the sparsely populated governorates abuttng the Red Sea. The votng pattern studed over a perod of tme reveals a narrowng of the gap between Islamst partes and ther non-islamst rvals. Bader (1) studed the trends and patterns n the prevalence of electoral malpractce n the post-sovet 31 area. The study explored the relatonshp between electoral malpractce and three varables: the type of electons (presdental or parlamentary), the presence of electoral competton (present n compettve electons, absent n hegemonc electons) and the advance of tme. The fndngs suggest that electoral malpractce does not sgnfcantly decrease over tme, s as wdespread n parlamentary as n presdental electons, but, n lne wth expectatons, s more severe n hegemonc electons than n compettve electons. These fndngs contrbute to nsghts about the nature of authortaran electons and are mportant for consderatons about the future of electon observaton n the regon. General objectves: The man am of ths paper s to provde comprehensve statstcal analyses for the Presdental electons votng pattern of the Greater Accra Regon, whch has been descrbed as one the most swngng regons n Ghana as far as Presdental and Parlamentary votng s concerned. The specfc objectves are as follows: Assessng whether the data set s normally dstrbuted to enable us use the varous multvarate tools/analyses Performng prelmnary analyses of the data to obtan a summary of the statstcs Mang Statstcal Inferences about the mean vectors MATERIALS AND METHODS Quanttatve methods were employed n ths study. Data on the votng patterns of the four most recent perods were analyzed. That s the perods: 4, 8 and 1 from the electoral commsson. The data focuses exclusvely on the Greater Accra Regon Presdental electons. Ths s justfable as more than a 1-year span data s enough to predct or forecast a trend that exst n the data. The results of all the total votes cast that were recorded n the experment years, for the varous consttuences were used. The Greater Accra Regon had consttuences I 1996, 7 consttuences n 4 and 8 and 34 consttuences n 1. It can be seen that 7 consttuences s common n all the years beng consdered. So we are gong to use the data from the 7 consttuences that s common to all the years. The man statstcal software applcatons were the Excel and the SPSS and the statstcal tool used was the multvarate data analyss tools. Assessng the normalty of the data: In ths secton, we present the descrptve statstcs of the ndcators for the votng patterns of the varous consttuences consdered. The ndcators are defned below:
Table 1: Table of descrptve statstcs for the results obtaned for 4, 8 and 1 presdental electons 1 3 4 Mean 3, 443.58 3, 43.17 86.94 437.6 Standard error 1, 38.11 1, 87.3 4.1 44.41 Medan 31, 43. 3,1. 148. 35. Mode #N/A #N/A 17. 9. Standard devaton 11, 77.95 16,848.3 361.89 399.7 Sample varance 138,6,43.5 83, 865, 9.44 13, 964.3 159, 779.57 Kurtoss -.63 -.13 8.3.56 Sewness.7.7.4 1.15 Range 47, 745. 75, 365., 149. 1,57. Mnmum 1, 433., 17. 11. 3. Maxmum 6, 178. 77, 38., 16. 1, 6. Sum, 67, 93., 67, 6. 3, 4. 35, 446. Count 81 81 81 81 Confdence nterval (95%), 63.1 3, 75.47 8. 88.39 Table : Covarance matrx for votng pattern 1 3 4 1 1368918.49 135988.4 133795.1 58734.8 135988.4 83678.69 41549.36 1736.88 3 1337955.1 41549.36 19347.39 3498.58 4 58734.8 1736.88 3498.58 15786.98 1 = Results of the Natonal Democratc Congress (NDC) = Results of the New Patrotc Party (NPP) 3 = Results of the People s Natonal Conventon = Results of the Conventon People s Party 4 The table presented n Table 1 above gves mportant nformaton about the normalty that s needed to perform a parametrc data analyss. Comparatvely, the small standard error values ndcate that the data collected, s good enough to be used n nferental analyss n statstcs. It can be seen that the dfference n errors between the populaton taen and the sample statstcs would be very small and ths s mperatve for the sample statstc to provde a good estmate for the actual populaton parameter. The mode for 1 and whch represents the NDC and the NPP respectvely does not ext over the perod beng studed. Ths means a partcular total votes cast for any of these poltcal partes for the perod studed dd not occur more than once. It can also be seen that the medan and the mean are qute close wth a relatvely small Sewness values for both NPP and NDC. Ths shows how the votes are always spread between these two poltcal partes. It can be concluded the data appears not too far from beng normal, wth closeness n ther medans and means and a relatvely small standard error and small Sewness for NDC and NPP. Ths also llustrates that the votng patterns of Ghanaans has always followed a normal pattern wth NPP and NDC sharng the major total votes cast. The other two poltcal partes, the PNC and the CPP has been qute abnormal, Judgng from the respectve Sewness. normal dstrbuton expressed as: N 4 (μ, Σ) where μ s the sample mean vector and Σ s the covarance matrx. From Table 1, the sample mean vector collected s gven by: 1 3443.58 343.17 = 4 = 86.94 4 437.6 The sample covarance matrx s gven above n Table. Inferences about the mean vector: In ths secton, our am s to perform an nferental statstcs about the mean total votes cast for the varous poltcal partes. That s we see to test at a sgnfcant level of α =.5, whether the mean total votes cast for the 7 consttuences could exceed, μ = (35 35 3 45). The Hypothess that would be tested are as follows: For the Null Hypothess, we have H : µ > µ : aganst the Alternate Hypothess H 1: µ µ. Hotellng s T statstc: We now consder the problem of testng whether the x1 vector as a plausble value for the populaton mean vector μ. A natural generalzaton of the squared dstance s ts multvarate analog: 1 1 ' 1 ' ( µ ) ( µ ) ( µ ) ( µ ) T = S = n S n The Statstcs T s called Hotellng s T. Ths has an approxmate central ch-square wth degrees of freedom. In the expresson above: 1 =, 1 S = ( )( ) ' n n 1 Calculatons for the analyses of the data to obtan summary statstcs: The votng pattern of Ghanaans for the 7 consttuences beng studed s a multvarate If the observed T value s too large -that s, f x s too far from µ, the hypothess H : µ = µ s 3
rejected and to decde how large s large, we need the samplng dstrbuton of T when the hypotheszed mean vector s correct: The crtcal value s gven by: ( n1) Fn, ( ) ( n ) α. We reject the null hypothess H: μ = μ for the - dmensonal vector μ at level α when: T > ( n1) ( n ) where, F ( α ) n, F n, ( α ). s the upper α percentle of the central F dstrbuton wth and n- degrees of freedom. As noted earler: 1 1 1 ( µ ) ' ( µ ) ( µ ) ' ( µ ) T = S = n S n has an approxmate central ch-square dstrbuton wth degrees of freedom and when μ s correct for large n, or when Σ s nown n whch case the dstrbuton s exact then we have normalty. The exact F-dstrbuton reles on the normalty assumpton and we also note that ( n 1 ) n, ( ) ( ) ( ) F x α > α, but these quanttes n are nearly equal for large values of n-. By the use of Mcrosoft Excel, the test statstc for the votng pattern s found as follows: Now, TT = nn(xx μμ oo ) (SS) 1 (xx μμ oo ) =.765 (nn1) nn FF,nn,(αα) = 4(811) 814 FF 4,77(.5) = 4 8 77 FF 4,77(.5) = 4.1558.49 = 1.35 not enough statstcal evdence to nfer that the mean performances of the varous four poltcal partes n the 7 consttuences are greater than hypotheszed means stated. The mean vote for NDC for the presdental electons for the four consecutve years s 3443.58. The result after the analyss revealed that there was not enough evdence to support that the mean can exceed 35. Ths means that the NDC party cannot predct that they can obtan votes exceedng 35 n any electon based on the evdence avalable. The NPP also have a mean vote of 343.17 and the results from Hotellng s T test also revealed that, based on the evdence avalable, the mean cannot exceed 35 n any electon. The mean vote for PNC and CPP are 86.94 and 437.6, smlarly, the test revealed that based on the evdence avalable, the mean for these two poltcal partes cannot exceed 3 and 45, respectvely. In a nutshell, the results further affrms the asserton that, based on the evdence avalable, each of the four poltcal partes cannot obtan votes whch far exceeds what ther mean votes n Table 1 stpulates. CONCLUSION The votng patterns analyzed, revealed there was not enough statstcal evdence to justfy that the votes wll exceed the assumed mean values. Ths further mples that the votes for subsequent electons could not be predcted wth a greater amount of certanty because of the result of the hypothess testng usng Hotellng s T statstc. The test further showed why the greater Accra regon s popularly nown as the swngng regon and can be won by any poltcal party. There may be perhaps other factors that affect the votng patterns n these regons and as a result one cannot depend on emprcal evdence to wn the electons. REFERENCES Snce TT s less than the crtcal value, we fal to reject the null hypothess. Ths mples that there s not enough statstcal evdence to nfer that the mean performances of the varous four poltcal partes n the 7 consttuences are greater than hypotheszed means stated n the votng pattern. RESULTS AND DISCUSSION We faled to reject the null hypothess, whch stated that the mean votes can exceed a hypotheszed values of 35, 35, 3 and 45 for NDC, NPP, PNC and CPP respectvely. Ths mples that there s 33 Alab, G. and J. Alab, 8. Analyses of the effects of ethncty on poltcal maretng n Ghana. Int. Bus. Econ. Res. J., 6(4): 39-5. Aluagba, M.T., 13. The Influence of Relgon on Votng Pattern Durng the 11 Presdental Electon n Fagge Local Government Area of Kano State, Ngera. Socal Scence Research Networ, Bayero Unversty Kano. Bader, M., 1. Trends and patterns n electoral malpractce n post-sovet Eurasa. J. Eurasan Stud., 3(3): 49-57. Damnyag, K.J.B., 13. Votng Pattern of Ghanaans. Nab Publshers. Accra, Ghana.
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