Nevertheless, its limitations are well known ( Lord and Novick, 1968 Cortina, 1993 Yang and Green, 2011), some of the most important being the assumptions of uncorrelated errors, tau-equivalence and normality.
As stated by Sijtsma (2009), its popularity is such that Cronbach (1951) has been cited as a reference more frequently than the article on the discovery of the DNA double helix. The α coefficient is the most widely used procedure for estimating reliability in applied research.
The results show that omega coefficient is always better choice than alpha and in the presence of skew items is preferable to use omega and glb coefficients even in small samples. In this paper, using Monte Carlo simulation, the performance of these reliability coefficients under a one-dimensional model is evaluated in terms of skewness and no tau-equivalence.
This procedure has proved very resistant to the passage of time, even if its limitations are well documented and although there are better options as omega coefficient or the different versions of glb, with obvious advantages especially for applied research in which the ítems differ in quality or have skewed distributions. The Cronbach's alpha is the most widely used method for estimating internal consistency reliability. 3Department of Methodology of the Behavioral Sciences, University Complutense de Madrid, Madrid, Spain.2Department of Social Psychology and Methodology, University Autonoma de Madrid, Madrid, Spain.1Department of Psychology, University of La Frontera, Temuco, Chile.Future studies suggested to enter text.Italo Trizano-Hermosilla 1,2 * and Jesús M. Empirical verifications of proposed measures were undertaken. Relationship derived between test discriminating value and test reliability as per theoretical definition. Cronbach alpha was expressed and computed in terms of discriminating value of test and item. The point of intersection of the two curves can be used for item deletion along with other criteria. With increase in number of correct answer to an item, item difficulty curve increases and item discriminating curve decreases. Each ranges between 0 and 1 like difficulty value of test and an item. Discriminating value of test and an item are taken as coefficient of variation (CV) of test score and item score respectively. Difficulty value of test and item is defined as function of cosine of the angle between the observed score vector and the maximum possible score vector. The paper proposes new measures of difficulty and discriminating values of binary items and test consisting of such items and find their relationships including estimation of test error variance and thereby the test reliability, as per definition using cosine similarities.
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