Improved Quality: Item and Test parameters

Introduction: Quality of a MCQ type test depends on qualities of the constituent items, assessed in terms of item reliability, item difficulty value, item discriminating value, etc. However, quality of a test involving reliability, validity, difficulty and discriminating values of the test etc. requires new approaches. Need is felt to find difficulty and discriminating values of an item and test using entire data and to derive relationships amongst them including relationship with test reliability to see impact of item deletion. Methods: Using angular similarity approach, measures proposed for item difficulty and item discriminating value, difficulty and discriminating value of test. Relationship derived between (i) difficulty value and discriminating value of item; (ii) difficulty value and discriminating value of a test (iii) test discriminating value and test reliability as per theoretical definition. Cronbach alpha was expressed using sum of item difficulty values and test discriminating value Results and Discussion: Each proposed measure ranges between 0 to 1. Discriminating value of test and item as coefficient of variation satisfy desired properties and facilitates population estimations. Intersection of item difficulty and item discriminating curves provides a data driven criterion for item deletion, impact of which on test reliability may be checked. In addition, the proposed measures facilitate testing of statistical hypothesis of departure of test reliability from unity, confidence interval of reliability, etc. Future problems suggested.

Angular similarity in test parameters

Through N-dimensional person space, the article gives measures of test parameters and item statistics, including difficulty/discriminating value of test, correlations between a pair of items, and item-total correlations with binary items using angular similarity between two vectors. Relationships between difficulty value and discriminating value of items and test were derived, including relationship between test reliability and test discriminating value. Reliability of a test as per theoretical definition in terms of length of score vectors of two parallel subtests and angle between such vectors was derived. The method was extended to find reliability of a battery of tests. Reliability and discriminating value of a Likert-type item and scale was found in terms of angular similarity without involving assumptions of continuous nature or linearity or normality for the observed variables, or the underlying variable being measured. The proposed methods also avoid test of unidimensionality or assumption of normality or bivariate normality associated with the polychoric correlations. Thus, the proposed methods are in fact nonparametric and considered as improvement over the existing ones. Reliability as a measure of association of two vectors and discrimination as a measure of distance between the vectors are likely to show a negative relationship.

A Voltage-Based Hierarchical Diagnosis Approach for Open-Circuit Fault of Two-Level Traction Converters

This paper proposes a voltage-based hierarchical diagnosis approach for insulated gate bipolar transistors (IGBTs) open-circuit fault of two-level AC-DC-AC traction converters. The proposed approach can diagnose the open-circuit fault in the single-phase rectifier as well as in the three-phase inverter without extra sensors. Moreover, no mandatory control signal injection is required, which ensures safe operation. In addition, the different levels of diagnostic results are flexibly determined by the presented hierarchical diagnosis architecture, which depends on the market requirements of wide use of IGBT modules. To be specific, firstly, a mixed-logic-dynamic estimation model of DC-link voltage is established. Secondly, the diagnosis characteristic function (DCF) is constructed by way of a residual characteristic analysis under normal and various open-circuit fault cases. Thirdly, the vector angular similarity function (VASF) is calculated for leg-level diagnosis and the control signals switching matching method is used to locate the fault in the device-level. Finally, the experimental results show the effectiveness of the proposed approach.