Abstract
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.
Highlights
Quality of a Multiple choice questions (MCQ) type test depends on qualities of the constituent items, assessed in terms of item reliability, item difficulty value, item discriminating value, etc
The quality of assessment depends on a host of factors including quality of a MCQ type test which are derived from quality of the constituent items/ Item qualities are assessed in terms of item difficulty value (Diffi), item discriminating value (Disci) etc
Considering increasing use of MCQs in assessment, suggestion of [4] to find effectiveness of MCQ items, the present study aims at proposing measures of Diffi, Disci, Difficulty value of a test (DiffT), Discriminating value of a test (DiscT) etc. without sacrificing any portion of data and making no assumption of continuous nature or linearity or normality for the observed variables or the underlying variable being measured and provide satisfactory answers to the above said gaps
Summary
Test containing of Multiple choice questions (MCQ) are increasingly used in assessment of Medical education in various context like admission. monitoring of knowledge, path of learning, etc. Discriminating value of an item (Disci) traditionally considers top 27% and bottom 27% of the data. Equation (5) gives relationship between DiffT and Diffi′s Discriminating value of test: Discriminating value of a test is a measure of dissimilarity between the vectors X and I and can be given as DiscT =. Relationship between test reliability and DiscT: Variance of the i-th item SX2i = Xi2. I.e. product of test reliability and square of test discriminating value is equal to square of CV of true scores Both (12) and (13) indicate that DiscT has a negative non-linear relationship with rtt Equation (13) can be verified by computing rtt as per theoretical definition, by the method given by [13]. Empirical illustration: Real life data on MCQ type test with 50 items (m), 911 persons (n) resulted in: 1.DiffT = 0.40990; DiscT= 0.16872.
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