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Application of Discriminant Analysis to Predict the Institute's Annual World Applied Sciences Journal 33 (2): 213-219, 2015 ISSN 1818-4952 © IDOSI Publications, 2015 DOI: 10.5829/idosi.wasj.2015.33.02.1 Application of Discriminant Analysis to Predict The Institute’s Annual Performance in Sargodha Board 12Humera Razzak, Mehboob Ali and 3Maqsood Ali 1Ex-Lecturer, Department of Statistics, Government College University Faisalabad, Pakistan 2Government Post Graduate College, Jauharabad District Khushab, Pakistan 3Punjab Bureau of Statistics, Lahore, Pakistan Abstract: This study has been carried out on the annual performance of 2nd Year (12th year education) results 2014 of various institutes affiliated with Sargodha board. Discriminant analysis has been used for achieving sharper discrimination between two categories (group 1: institutes having annual results below board average result and group 2: institutes having annual results above board average result) based on disciplines of institutes, gender, status of institutes and geographical area of four districts in Sargodha division. Successful discrimination is made between institutes with results below or above board average. Clustering annual results of institutes under two categories is statistically significant on the basis of discriminant analysis. The data is obtained from managing body of Sargodha board. Analyzing set of seven variables shows five of them significantly help in discriminating between institutes with result below or above board average. Therefore it is suggested to reclassified institutes who were misclassified under results below board average result. Key words: Discriminant analysis Sargodha board Institute annual performance INTRODUCTION into account of individual discipline performance and some other factors that may be more likely to affect its College enrollments have grown rapidly in result. recent years. Concerns about annual performance of The Board of Intermediate & Secondary Education institutes as compared to board results are (BISE) Sargodha was established in 1968 under the West widespread.Since institute annual result rate may not only Pakistan BISE Multan and Sargodha Ordinance. This is 2nd influence student outcome but also effect admission in Punjab in terms of its establishment. At this time process and individual interest toward getting higher Sargodha board authorizes Sargodha, Khushab, Mianwali education [1]. Practically it is very important to predict and Bhakkar districts [3] BISE Sargodha has the authority institutes success with the help of some set of to organize the exams of matric and intermediate. independent variables including gender and some In this research Sargodha board 2nd year results demographical outcomes [2] in order to seek answer to a 2014 has been predicted under two categories institutes question that what was performance of an institute as having annual results below board average result and compared to board annual result? institutes having annual results above board average Prediction about institute success rate in terms of result based on disciplines of institutes, gender, status of whether its annual result is below or above board average institutes and geographical area of four districts. result is actually a process of determining that which Out of total 230 institutes affiliated with group that particular institute belongs. Typically an Sargodha board the annual results of 93 institutes are institute is declared as having result below or above included, other institutes were dropped from the analysis board average result on basis of overall averages of due to unavailability of all four disciplines in these various disciplines percentage scores regardless of taking institutes. Corresponding Author: Humera Razzak, Department of Statistics, Government College University Faisalabad, Pakistan. 213 World Appl. Sci. J., 33 (2): 213-219, 2015 Will an institute is more likely to show result above Sargodha board average result 2014 is 60.88. Two groups board average result due to higher performance in General of dependent variable are made on the basis of board Science group? Demographical characteristics of annual average result. The independent variables are institutes have likelihood to effect institute results as Medical students passed percentage of an institute (X1 ), compared to board average results? Reliable answers to Non-medical students passed percentage of an institute all questions related to problem mentioned above are (X2 ), General Science students passed percentage of an seeked in this research using traditionally discriminant institute (X3 ), Arts students passed percentage of an analysis. institute (X45 ), Gender (X ), Status of institution as public Discriminant analysis is a multivariate statistical and private (X6 ) and Geographical area of four district of technique used in statistics. This technique classifies an Sargodha division which consists on Sargodha, object into one among several groups based on its Khushab, Mianwal and Bhakkar districts (X7 ). The attributes. Discriminant analysis has three main sample/data consists of 93 institutes those have these objectives. First, to identify the attributes that variables and other institutes were dropped from the discriminates among the groups. The second objective is analysis due to unavailability of all four disciplines in to use the identified variables to develop some functions, these institutes. called the discriminant functions, for computing some new Discriminant Analysis finds a set of prediction variables or indices that will parsimoniously represent the equations based on independent variables that are used differences among the groups. The third objective is to to classify individuals into groups [16,17]. In many ways, use the computed scores to develop a rule to classify discriminant analysis parallels multiple regression future observations into one of the several groups analysis. This method formulates linear equation which [4].Classification of various predictive variables has been has been the most recognizable and the simplest already done in many past studies [5-10]. interpretable measure of effect [18]. The main difference Discriminant analysis has been used as major tool for between these two techniques is that regression analysis predicting final results of students/disciplines based on deals with a continuous dependent variable, while various classifications in many researches [11-13]. discriminant analysis must have a discrete dependent A successful discrimination was made between two variable. groups of study by Ogum [14] who applied multivariate The mathematics of discriminant analysis is related analysis on scores of applicants admitted in university of very closely to the one-way MANOVA. In fact, the roles Nigeria medical school in the 1975/1976 academic of the variables are simply reversed. The classification session.Similar work is done by Okoli [15], who (factor) variable in the MANOVA becomes the dependent discriminated two groups based on academic scores and variable in discriminant analysis. The dependent variables found misclassifications of student scores using in the MANOVA become the independent variables in the classification rule. discriminant analysis. This study is carried out to find some of the institutes Suppose you have data for K groups, with Nk misclassified as “having result below board average observations per group. Let N represent the total number result” may fall in “having result above board average of observations. Each observation consists of the result” group. Wrongly classified or misclassified measurements of p variables. The ith observation is institutes will be fish out with the help of discriminant represented by Xki . Let M represent the vector of means function and classification rule. of these variables across all groups and Mk the vector of means of observations in the kth group. MATERIALS AND METHODS Define three sums of squares and cross products matrices, STW , S and S A as follows In this study, the data is obtained from managing body of Sargodha board which consists of Sargodha board 2nd year annual results 2014. The dependent variable is the overall college/higher secondary school (HSS) results (Y) and this result is divided into two categories: if the institute result is above board average result than group one and if the institute result is below board average result than group two. The overall SA = S- TW S 214 World Appl. Sci. J., 33 (2): 213-219, 2015 Next, define two degrees of freedom values, df12 and df : RESULTS AND DISCUSSION df12 = K-1, df = N-K A discriminant function is a weighted average of the The purpose of the present study was to examine the values of the independent variables. The weights are relationship between institute annual academic selected so that the resulting weighted average separates performance under two categories (below/above board the observations into the groups. High values of the average result) and various institutes characteristics. Out average come from one group; low values of the average of 93 institutes included in our analysis we have 62 come from another group. The problem reduces to one of institutes showing result above board average and 31 finding the weights which, when applied to the data, best below board average. discriminate among groups according to some criterion. Mean scores on each variable is listed in group The solution reduces to finding the eigenvectors of means Table 1. Annual result of institutes with four −1 disciplines was high in group 2 on the average with mean SS. The
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