In the discussion of mean square difference (MSD) and standard error of measurement (SEM), Barchard (2012) concluded that the MSD between 2 sets of test scores is greater than 2(SEM)[superscript 2] and SEM underestimates the score difference between 2 tests when the 2 tests are not parallel. This conclusion has limitations for 2 reasons. First,…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

The Bologna Declaration brought reforms into higher education that imply changes in teaching methods, didactic materials and textbooks, infrastructures and laboratories, etc. Statistics and mathematics are disciplines that traditionally have the worst success rates, particularly in non-mathematics core curricula courses. This research project,…

Describes a simplified method for converting raw scores to standard scores and transforming them to "T-scores" for easy comparison of performance. Obtaining letter grades from T-scores is discussed. A reading list is included. (GH)

The extent of error likely to occur with each of several approximations for the standard deviation, internal consistency reliability, and the standard error of measurement is analyzed. Approximations were compared with exact statistics obtained on 85 different classroom tests constructed and administered by professors in a variety of fields. Means…