The first step towards discussing a phenomenon or a concept in depth and with powerful scientific principles and methodology is to develop, adapt and utilize tools that accurately measure and discover the problem. For this purpose, the present study concentrated on paternalistic leadership, which is a new concept in the field of management, and reliability and validity studies on the scale (PLS) that was used to assess paternalistic leadership by Cheng et al. (2004) were conducted to add the scale to the national literature. The study was conducted on the data collected from 326 (EFA) + 255 (CFA) research assistants to determine the validity of the scale. In a determination of the reliability of the scale, item-total point correlations and Cronbach’s Alpha internal consistency coefficient were used. In order to determine how the scale works in different cultural and qualitative samples, the adaptation version was discussed by comparing with the previous factor analysis studies of the PLS. The analysis showed that adaptation version of the PLS, with the structure of its 3 sub-dimensional and 23-items, will able to be used in studies aiming to determine the characteristics of paternalistic leadership in the organizational structure and management processes of universities for the researchers working in the field of higher education.

Pearson product–moment correlation coefficient between item g and test score X, known as item–test or item–total correlation (Rit), and item–rest correlation (Rir) are two of the most used classical estimators for item discrimination power (IDP). Both Rit and Rir underestimate IDP caused by the mismatch of the scales of the item and the score. Underestimation of IDP may be drastic when the difficulty level of the item is extreme. Based on a simulation, in a binary dataset, a good alternative for Rit and Rir could be the Somers’ D: it reaches the ultimate values +1 and –1, it underestimates IDP remarkably less than Rit and Rir, and, being a robust statistic, it is more stable against the changes in the data structure. Somers’ D has, however, one major disadvantage in a polytomous case: it tends to underestimate the magnitude of the association of item and score more than Rit does when the item scale has four categories or more.

Kelley’s Discrimination Index (DI) is a simple and robust, classical non-parametric short-cut to estimate the item discrimination power (IDP) in the practical educational settings. Unlike item–total correlation, DI can reach the ultimate values of +1 and ‒1, and it is stable against the outliers. Because of the computational easiness, DI is specifically suitable for the rough estimation where the sophisticated tools for item analysis such as IRT modelling are not available as is usual, for example, in the classroom testing. Unlike most of the other traditional indices for IDP, DI uses only the extreme cases of the ordered dataset in the estimation. One deficiency of DI is that it suits only for dichotomous datasets. This article generalizes DI to allow polytomous dataset and flexible cut-offs for selecting the extreme cases. A new algorithm based on the concept of the characteristic vector of the item is introduced to compute the generalized DI (GDI). A new visual method for item analysis, the cut-off curve, is introduced based on the procedure called exhaustive splitting.

A new index of item discrimination power (IDP), dimension-corrected Somers’ D (D2) is proposed. Somers’ D is one of the superior alternatives for item–total- (Rit) and item–rest correlation (Rir) in reflecting the real IDP with items with scales 0/1 and 0/1/2, that is, up to three categories. D also reaches the extreme value +1 and ‒1 correctly while Rit and Rir cannot reach the ultimate values in the real-life testing settings. However, when the item has four categories or more, Somers’ D underestimates IDP more than Pearson correlation. A simple correction to Somers’ D in the polytomous case seems to lead to be effective in item analysis settings.  In the simulation with real-life items, D2 showed very few cases of obvious underestimation and practically no cases of obvious overestimation. With certain restrictions discussed in the article, D2 seems to be a good alternative for these classic estimators not only with dichotomous items but also with the polytomous ones. In general, the magnitudes of the estimates by D2 are higher than those by Rit, Rir, and polychoric correlation and they seem to be close of those of bi- and polyserial correlation coefficients without out-of-range values.

Although Goodman–Kruskal gamma (G) is used relatively rarely it has promising potential as a coefficient of association in educational settings.  Characteristics of G are studied in three sub-studies related to educational measurement settings. G appears to be unexpectedly appealing as an estimator of association between an item and a score because it strictly indicates the probability to get a correct answer in the test item given the score, and it accurately produces perfect latent association irrespective of distributions, degrees of freedom, number of tied pairs and tied values in the variables, or the difficulty levels in the items. However, it underestimates the association in an obvious manner when the number of categories in the item is more than four. Towards this, a dimension-corrected G (G2) is proposed and its characteristics are studied. Both G and G2 appear to be promising alternatives in measurement modelling settings, G with binary items and G2 with binary, polytomous and mixed datasets.