Differentiate orthogonal dimensions from item clusters based on eight methods of determining dimensions of binary data: the case is mathematic test of University's entrance exam in the field of mathematic-physic in 2012-13(1391-92)

Determining dimensions (factors) of tests has a significant importance for other testing purposes. The issue has more importance in binary data and is associated with greater challenges. The object of present study is differentiating of orthogonal dimensions from item clusters basedcomparison of eight methods of determining dimensions of binary data. the methods are: DIMTEST nonparametric method، DETECT nonparametric method، Content analysis of items based on expert judgment and review their answers. Full information factor analysis، cluster analysis based on angle between item vectors، parallel analysis، MAP test and confirmatory factor analysis. First the methods are briefly described and then based on 55 items math test are compared. The results are a confirmation to the subject that a distinction must be made between the number of clusters and orthogonal dimension. Since the number of clusters is an upper limit to the number of dimensions and most methods of determining of dimensions reflect clusters than orthogonal dimensions، then it is better Depending on the desired target، along with content and logical consideration، several methods be used for this purpose.