MARKOV CHAIN MONTE CARLO APPROACH TO ESTIMATION OF MCDONALD’S OMEGA-HIERARCHICAL COEFFICIENT FOR INTERNAL CONSISTENCY RELIABILITY MEASUREMENT OF PHYSICS ACADEMIC SELFCONCEPT INVENTORY: A DIDACTIC

The use of Cronbach's alpha (α) to estimate the overall internal consistency (OIC) of polytomously scored (PS) items with hierarchical structure has been a common practice among researchers for decades, despite advances in algorithm and software technologies. The use of coefficient alpha is hinged on the assumption that the indicators of an inventory should have equal factor loadings, uncorrelated measurement errors and that the items should measure only one latent construct. The assumptions appear to be violated by many researchers in practice. To avert apparent danger of either underestimation or overestimation of OIC reliability using α in a scientific study for an inventory that contains more than one latent construct, McDonald's (1999) omegahierarchical coefficient was adopted. Data collected were analyzed with eigen values, regression weights, error variances, polygon and trace plots available in factor analysis. The result indicated that ten items of Physics selfconcept inventory showed approximate OIC reliability of .75 based on the Markov Chain Monte Carlo sample size of 100,000. Physics teachers should utilize the inventory to assess their students' academic self-concept. Researchers should also adopt the procedure to measure the OIC reliability of PS inventory with hierarchical structure.