![]() This study aimed to test the association between domains of perfectionism to both positive (self-esteem, wellbeing) and negative mental health indices (narcissism and psychological distress) while testing the structural validity of the Short Multidimensional Perfectionism Scale in a large non-English speaking community-based sample in Hungary. However, past studies tended to focus only on one covariate at a time. Different components of perfectionism might be associated in different ways with positive and negative aspects of mental health. Perfectionism is a multidimensional personality trait that may covary with both negative and positive indices of mental health. Selecting wisely the linking coefficient, DCERs may give significant advance in estimating the true reliability and true standard error related to the test score. Instead of Rit, DCERs use other estimators of correlation as the linking factor between the item and the score variable that are less prone to deflation. Within achievement testing, deflation-corrected estimators or reliability (DCER) would be better options. Because Rit is embedded in the traditional estimators of reliability, this causes deflation in the estimates of reliability, and the magnitude of deflation may be remarkable: 0.40-0.60 units of reliability have been reported in some cases. This is a typical pattern where the traditional Pearson's point-biserial and point-polyserial coefficient of correlation between items and score (Rit) may be radically deflated. These kinds of tests are common when testing educational achievement because the tests are often structured by incremental difficulty levels including both very easy tasks, tasks with medium difficulty level, as well as very demanding tasks. Traditional estimators of reliability such as coefficients alpha, theta, omega, and rho (maximal reliability) are prone to give radically underestimated or deflated estimates of reliability for the test score when individual test items have extreme difficulty level in the target population. Based on a simulation, an initial typology of the families of DCERs is presented: some estimators are better with binary items and some with polytomous items some are better with small sample sizes and some with larger ones. The empirical section is a study of the characteristics of combinations of DCERs formed by different bases for the estimators (alpha, theta, omega, and rho), different alternative estimators of correlation as the linking factor between item and the score variable, and different conditions. ![]() A short-cut method to reach estimates closer the true magnitude, new types of estimators, deflation-corrected estimators of reliability (DCER) are studied in the article. ![]() The reason for this radical deflation lies in the item–score correlation (Rit) embedded in these estimators: because the estimates by Rit are deflated when the number of categories in scales are far from each other, as is the case always with item and score, estimates of reliability are deflated as well. Empirical cases have shown that estimates by the widely used estimators such as alpha, theta, omega, and rho may be deflated up to 0.60 units of reliability, or even more, with certain types of datasets. Many widely used estimators are known to underestimate reliability. Reliability of a test score is discussed from the viewpoint of underestimation of and, specifically, deflation in the estimates or reliability.
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