Evaluation of Psychometric Properties of Tests used in Educational Research

It is imperative to assess psychometric parameters of tests and items by methodologically sound approaches and finding relationships among the psychometric qualities. The paper describes methods of computations of psychometric parameters of MCQ test and items under classical test theory, finds relationships among theoretically defined test reliability with factorial validity (FV) and separately with discriminating and difficulty values of test and items considering the entire data. Finding r_(tt(theoretical)) from a single administration offers significant benefits like computation of test error variance; testingH_0: r_(tt(theoretical))=1; finding battery reliability, estimation of true scores and its confidence interval. Relationships of r_(tt(theoretical)) derived with FV of standardized scores (〖FV〗_(Z-scores)), test discriminating value (〖Disc〗_T), Cronbach alpha in terms of item discriminating value 〖(Disc〗_i) and 〖Disc〗_T, Item reliability as function of 〖Diff〗_i and 〖Disc〗_T, alpha using PCA results (α_PCA) with 〖FV〗_(Z-scores). The point of inflection of the negatively slopped reliability - discriminating value curve gives 〖Disc〗_T for which test reliability is optimal; Common point of 〖Disc〗_iand 〖Diff〗_i curves could be used in item deletions to improve test reliability.