Directional nature of Goodman–Kruskal gamma and some consequences: identity of Goodman–Kruskal gamma and Somers delta, and their connection to Jonckheere–Terpstra test statistic

Although usually taken as a symmetric measure, G is shown to be a directional coefficient of association. The direction in G is not related to rows or columns of the cross-table nor the identity of the variables to be a predictor or a criterion variable but, instead, to the number of categories in the scales. Under the conditions where there are no tied pairs in the dataset, G equals Somers’ D so directed that the variable with a wider scale (X) explains the response pattern in the variable with a narrower scale (g), that is, D(g│X). Hence, G = G(g│X) = D(g│X) but G ≠ D(X│g) and G ≠ D(symmetric). If there are tied pairs, the estimates by G = G(g│X) are more liberal in comparison with those by D(g│X). Algebraic relation of G and D with Jonckheere–Terpstra test statistic (JT) is derived. Because of the connection to JT, G = G(g│X) and D = D(g│X) indicate the proportion of logically ordered test-takers in the item after they are ordered by the score. It is strongly recommendable that gamma should not be used as a symmetric measure, and it should be used directionally only when willing to explain the behaviour of a variable with a narrower scale by the variable with a wider scale. This fits well with the measurement modelling settings.

An Investigation of Factors Responsible for Conflicts Among the University Students

This study was conducted through quantitative study approach. The purpose of this study was to investigate the need of peace education in context of conflict management at university level. Major objectives of the study were to know about the prevailing situation of interpersonal and intra-personal conflicts among the teaching faculty and teachers of BS level in the university and to investigate the factors which are responsible for conflicts among the students and teachers. Research findings are based on questionnaire responses from the faculty members and students. Kindall's Tau B and Tau C were utilized for analysis of collected data. The study revealed that 81.1 % of the faculty members and 83.4% students agreed about the exciting conflicts among the students and teachers at university level. Their responses on symmetric measure also testified the fact that the result was found significant which means that conflicts exist and reflected the factors in their responses. Findings show that students have more interpersonal conflicts and there are many factors included political and academic reasons.

The Duality of Entropy/Extropy, and Completion of the Kullback Information Complex

The refinement axiom for entropy has been provocative in providing foundations of information theory, recognised as thoughtworthy in the writings of both Shannon and Jaynes. A resolution to their concerns has been provided recently by the discovery that the entropy measure of a probability distribution has a dual measure, a complementary companion designated as “extropy”. We report here the main results that identify this fact, specifying the dual equations and exhibiting some of their structure. The duality extends beyond a simple assessment of entropy, to the formulation of relative entropy and the Kullback symmetric distance between two forecasting distributions. This is defined by the sum of a pair of directed divergences. Examining the defining equation, we notice that this symmetric measure can be generated by two other explicable pairs of functions as well, neither of which is a Bregman divergence. The Kullback information complex is constituted by the symmetric measure of entropy/extropy along with one of each of these three function pairs. It is intimately related to the total logarithmic score of two distinct forecasting distributions for a quantity under consideration, this being a complete proper score. The information complex is isomorphic to the expectations that the two forecasting distributions assess for their achieved scores, each for its own score and for the score achieved by the other. Analysis of the scoring problem exposes a Pareto optimal exchange of the forecasters’ scores that both are willing to engage. Both would support its evaluation for assessing the relative quality of the information they provide regarding the observation of an unknown quantity of interest. We present our results without proofs, as these appear in source articles that are referenced. The focus here is on their content, unhindered. The mathematical syntax of probability we employ relies upon the operational subjective constructions of Bruno de Finetti.

Brain Tumor Detection and Classification in Magnetic Resonance Imaging (MRI) using Region Growing, Fuzzy Symmetric Measure, and Artificial Neural Network Backpropagation

<p>Brain tumor is one type of malignant tumors that occurs because there is an abnormal and uncontrolled cell division activity. There are several ways to diagnose brain tumors, for example use MRI images. Through the MRI images, the radiologist can see the brain anatomy without performing surgery. However, this process is still done manually and could lead to misdiagnose. In addition, the different characteristics of brain tumor makes the diagnose more difficult. Therefore, we need a system of Computer-Aided Diagnostic (CAD) that will help radiologist in identifying brain tumors. </p><p>In general, the CAD system consists of two major processes, namely image segmentation and feature extraction and classification. One example of segmentation is Region Growing that will classify the pixels based on certain criteria. However, the manual selection of seed point is a drawback of this method. The examples of feature extraction methods are Fuzzy Symmetric Measure (FSM), and First and Second Order Statistics. FSM values can be used to calculate the symmetry of the image brain, while the first and second order to represent feature in the image. As for the classification process, Artificial Neural Network Backpropagation method is widely used for its ability to resolve nonlinear dan complex problems.</p><p>This research implements CAD system that uses Region Growing, Symmetric Fuzzy Measure, and Backpropagation Neural Network for detecting and classifying the brain tumors. In addition, the modification of converging square is conducted to select a seed point automatically. After testing, the system generates a 100% accuracy and BER is 0 in the case of distinguishing between normal and tumor brain. Besides, the average accuracy in classifying the types of brain tumors achieved 89.72% , the BER 0.1 for training data, and the average accuracy of 84.44%, BER 0.16 for the testing data.</p>