Three methodological approaches were applied to understand the role of interest and self-efficacy in reading and/or writing in students without and with persisting specific learning disabilities (SLDs) in literacy. For each approach students in grades 4 to 9 completed a survey in which they rated 10 reading items and 10 writing items on a Scale 1 to 5; all items were the same but domain varied. The first approach applied Principal Component Analysis with Varimax Rotation to a sample that varied in specific kinds of literacy achievement. The second approach applied bidirectional multiple regressions in a sample of students with diagnosed SLDs-WL to (a) predict literacy achievement from ratings on interest and self-efficacy survey items; and (b) predict ratings on interest and self-efficacy survey items from literacy achievement. The third approach correlated ratings on the surveys with BOLD activation on an fMRI word reading/spelling task in a brain region associated with approach/avoidance and affect in a sample with diagnosed SLDs-WL. The first approach identified two components for the reading items (each correlated differently with reading skills) and two components for the writing items (each correlated differently with writing skills), but the components were not the same for both domains. Multiple regressions supported predicting interest and self-efficacy ratings from current reading achievement, rather than predicting reading achievement from interest and self-efficacy ratings, but also bidirectional relationships between interest or self-efficacy in writing and writing achievement.  The third approach found negative correlations with amygdala connectivity for 2 reading items, but 5 positive and 2 negative correlations with amygdala connectivity for writing items; negative correlations may reflect avoidance and positive correlations approach. Collectively results show the relevance and domain-specificity of interest and self-efficacy in reading and writing for students with persisting SLDs in literacy.

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.