101 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Multivariate Analysis of Psychometric Variables Affecting Job Satisfaction Among School Teachers: A Case Study at Primary and Secondary Schools in Shashemene Town, Ethiopia Sano Kedir Mohammed * Department of Statistics, Madda Walabu University, Robe, Ethiopia Email: sanokedir@yahoo.com Abstract This study has dealt with factors affecting the level of job satisfaction among school teachers at Shashemene town in 2010/11 academic year. Data were obtained from primary and secondary sources. A cross-sectional survey was conducted on a total of 405 teachers from different government and non-government schools using stratified random sampling technique. In the present study, the relationships between psychometric items (55- items) were examined by the combination of factor analysis and Bayesian logistic regression analysis. Firstly, factor analysis was used to group the items of the same characters as factors or explanatory variables of job satisfaction among teachers. Then, ten factors, having eigen-values greater than 1, were selected as independent variables and the factor scores coefficients were used in the Bayesian logistic regression analysis. It was found that eight unobserved variables had significant effects on job satisfaction. Key words: Psychometric variables; Factor analysis; job satisfaction; eigen-values; teachers. 1. Introduction The teachers’ level of satisfaction has been identified as the critical factor in determining their performance and professional development. The subject has received increasing attention of researchers and scholars around the world since 1950s [1]. Many studies of job satisfaction have been carried out across the economy, education, etc [2]. ------------------------------------------------------------------------ * Corresponding author. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 76, No 1, pp 101-112 102 have defined work satisfaction as an effective response or reaction to a wide range of conditions or aspects of one’s work such as pay, supervision, working conditions and the work itself. Others have defined it as an effective orientation towards anticipated outcome [3] or an employee’s effective reactions to a job based on comparing actual outcomes with desired outcomes [4]. It has been generally recognized as multifaceted construct that includes employees feeling about a variety of both intrinsic and extrinsic job elements [5]. Intrinsic determinants pertain to the nature of activities inherent to, a position or set of tasks such as intellectual stimulation or feeling of accomplishment. Extrinsic determinants focus on external factors such as relation with co-workers or job security. So, job satisfaction is a subjective variable which does not lead itself readily to quantification. It is experienced, when employees have fulfilled, whatever needs or considerations, they deem important in their work. Most people in employment consciously experience a degree of satisfaction or dissatisfaction with their job. Moreover, they tend to be more satisfied with some aspects of their job than others. The relevance of job satisfaction is crucial to the long term growth of any work industry all over the world. This has to do with needs satisfaction which is essential in the lives of workers because it forms the fundamental reason for working [6]. People work because they expect returns or salary which will help to meet their needs in life. The present study is an attempt to find out which facet or dimension affects the job satisfaction of primary and secondary school teachers significantly. The study has taken into account intrinsic and extrinsic factors to find out the level of job satisfaction and to see the effect of age, gender, marital status, educational level, occupational level and length of employment which are called demographic factors on the job satisfaction of academicians. 1.2 Statement of the Problem Teachers’ job satisfaction is a major and current issue of the international communities. Specially, in sub- Saharan countries, education is not up to the standard qualitatively and quantitatively, hence to improve these many factors has to be considered, but from these issues of teachers need to be studied. The questions that this study seeks to probe are as follows: What relationships (correlations) are there among the items of psychometric properties which shows feeling of teachers in many aspects? What are the most significant factors that influence overall job satisfaction of teachers with respect to psychometric variables? The general objective of the study has been to determine or asses factors affecting overall job satisfaction among teachers at Shashemene town. 2. Data and Methodology The study was conducted in Shashemene town, a rapidly growing town in Oromia region of Ethiopia. Shashemene is centrally located, which is 250 km far from the capital city of Ethiopia, i.e. Addis Ababa. Geographically, it lies between Latitude of 7, 2000 (712'0.000"N) and Longitude of 38, 6000 (3836'0.000"E). The altitude of this town ranges from 1500metres to 2300meters above sea level. According to CSA (2007) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 76, No 1, pp 101-112 103 report, the estimated population size of the town was 102,062, of which 51,477 were males and 50,585 were females. Educational institutes in the town, include one governmental TVET college, two non-governmental university college and four private colleges, three governmental high schools and two governmental preparatory schools. In Shashemene town, there were 48 primary schools of which 10 were governmental and 38 were non- governmental schools, having 278 and 501 teachers, respectively. There were also 10 high schools of which seven were non-governmental and three were governmental and there were six preparatory schools of which four were non-governmental and two were governmental. The total numbers of teachers employed in preparatory schools and high schools were 69 and 254, respectively [7]. The target populations for the study have been teachers employed in primary and secondary schools of governmental and non-governmental during 2010/11 at Shashemene town. These teachers were full timer paying tax from their salary. A cross- sectional survey design with stratified random sampling technique was used in this study. 2.1 Multivariate Analysis Multivariate statistical methods have grown increasingly popular over the past twenty-five years. The continued explosion of multivariate statistical procedures can no doubt be attributable to the belief that models of nature and human behavior, must often account for multiple, inter-related variables that are conceptualized simultaneously or over time [8]. 2.1.1 Principal Component Analysis (PCA) According to [8], principal components are defined as linear combinations of random variables when seen analytically. Geometrically, these linear combinations represent the selection of a new coordinate system obtained by rotating the original coordinate system in such a way that the new axes represent directions with maximum variability and provide simpler description of covariance. The general objectives of principal component analysis (PCA) are the reduction of a large number of variables whose inter relationships are complex to a much smaller set of new variables whose interrelationships are simple, but which contain most of the variation in the original variables and ease of interpretation. PCA is a mathematical technique which does not require the user to specify an underlined statistical model to explain the error structure. In particular no assumption is made about the probability distribution of the original variables. PCA is done either using the theoretical covariance matrix Σ, or theoretical correlation matrix ρ of X, where X is a random vector with p dimensions. Usually the covariance matrix (Σ) is used to analyze variables with the same unit of measurement. Since the correlation matrix is the covariance of a standardized variable, the correlation matrix (ρ) has been used to analyze the variables with different unit of measurement. As the unit of measurements of the variables, in this study is the same, it is possible to use either covariance or correlation matrix. The PCA was based on the correlation matrix ρ of X. Algebraically; principal components (PCs) are those uncorrelated linear combinations pYYY ,...,, 21 whose variances are as large as possible. Geometrically; these linear combinations represent the selection of a new coordinate system obtained by rotating the original coordinate axes pXXX ,...,, 21 . Let the covariance matrix associated with the random vector T pXXXX ),...,,( 21 has the eigenvalue-eigenvector pairs (λ1, e1), (λ2, e2), … , (λp, e p) where λ1 λ2 … λp, then the i th principal component is given by American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 76, No 1, pp 101-112 104 piXeXeXeXeY ipii T i ,...,2,1,....21 ……………………….3.3 With this choices pieeXVar i T i ,...,2,1,)( kieeYYCov T k T iki ,0),( The PCA provides a highly parsimonious summary that might be useful in further analysis. So it is necessary to determine the number of components that are needed to provide an adequate summary of a given set of [8]. The Number of Principal Components As a rule of thumb, only those components are retained whose variance λ are greater than unity, or equivalently only those components are retained, which individually explain at least a proportion 1/p of the total variance. Another useful visual aid determining an appropriate number of PCs is the scree plot. It is a plot of i versus i, with eigenvalues ordered from largest to smallest (the magnitude of eigenvalues versus its number). Then, to determine the appropriate number of components, one looks for elbows (bends) in the scree plot. The number of components is taken to be the point at which the remaining eigenvalues are relatively small and all are about the same size. 2.1.2 Factor Analysis Factor analysis is a statistical technique by which one describes (if possible) the covariance relationship among many variables in terms of few underlying unobservable random quantities called factors. The underlying idea in factor analysis is grouping variables that are highly correlated together to form a single underlying factor that is responsible for the observed correlation. The Orthogonal Factor Model Let the observed random vector with p component has mean and covariance matrix . The factor model postulates that is linearly dependent upon a few unobservable random variables m21 ,...,F,FF and p additional source of variation p ,...,, 21 called specific errors where m