Three measures of internal consistency – Kuder-Richardson Formula 20 (KR20), Cronbach’s alpha (α), and person separation reliability (R) – are considered. KR20 and α are common measures in classical test theory, whereas R is developed in modern test theory and, more precisely, in Rasch measurement. These three measures specify the observed variance as the sum of true variance and error variance. However, they differ for the way in which these quantities are obtained. KR20 uses the error variance of an “average” respondent from the sample, which overestimates the error variance of respondents with high or low scores. Conversely, R uses the actual average error variance of the sample. KR20 and α use respondents’ test scores in calculating the observed variance. This is potentially misleading because test scores are not linear representations of the underlying variable, whereas calculation of variance requires linearity. Contrariwise, if the data fit the Rasch model, the measures estimated for each respondent are on a linear scale, thus being numerically suitable for calculating the observed variance. Given these differences, R is expected to be a better index of internal consistency than KR20 and α. The present work compares the three measures on simulated data sets with dichotomous and polytomous items. It is shown that all the estimates of internal consistency decrease with the increasing of the skewness of the score distribution, with R decreasing to a larger extent. Thus, R is more conservative than KR20 and α, and prevents test users from believing a test has better measurement characteristics than it actually has. In addition, it is shown that Rasch-based infit and outfit person statistics can be used for handling data sets with random responses. Two options are described. The first one implies computing a more conservative estimate of internal consistency. The second one implies detecting individuals with random responses. When there are a few individuals with a consistent number of random responses, infit and outfit allow for correctly detecting almost all of them. Once these individuals are removed, a “cleaned” data set is obtained that can be used for computing a less biased estimate of internal consistency.

The traditional approach to the measurement of change presents important drawbacks (no information at individual level, ordinal scores, variance of the measurement instrument across time points), which Rasch models overcome. The article aims to illustrate the features of the measurement of change with Rasch models. To illustrate the measurement of change using Rasch models, the quantitative data of a longitudinal study of heart-surgery patients (N = 98) were used. The scale “Perception of Positive Change” was used as an example of measurement instrument. All patients underwent cardiac rehabilitation, individual psychological intervention, and educational intervention. Nineteen patients also attended progressive muscle relaxation group trainings. The scale was administered before and after the interventions. Three Rasch approaches were used. Two separate analyses were run on the data from the two time points to test the invariance of the instrument. An analysis was run on the stacked data from both time points to measure change in a common frame of reference. Results of the latter analysis were compared with those of an analysis that removed the influence of local dependency on patient measures. Statistics t, χ2 and F were used for comparing the patient and item measures estimated in the Rasch analyses (a-priori α = .05). Infit, Outfit, R and item Strata were used for investigating Rasch model fit, reliability, and validity of the instrument. Data of all 98 patients were included in the analyses. The instrument was reliable, valid, and substantively unidimensional (Infit, Outfit < 2 for all items, R = .84, item Strata range = 3.93-6.07). Changes in the functioning of the instrument occurred across the two time, which prevented the use of the two separate analyses to unambiguously measure change. Local dependency had a negligible effect on patient measures (p ≥ .8674). Thirteen patients improved, whereas 3 worsened. The patients who attended the relaxation group trainings did not report greater improvement than those who did not (p = .1007). Rasch models represent a valid framework for the measurement of change and a useful complement to traditional approaches.

An intelligent tutoring system for learning basic statistics, called Stat-Knowlab, is presented and analyzed. The algorithms implemented in the system are based on the competence-based knowledge space theory, a mathematical theory developed for the formative assessment of knowledge and learning. The system’s architecture consists of the two assessment and learning modules that interact with each other in a continuous exchange of information about the current knowledge state of a student. This allows the system to personalize the student’s learning, providing only with the learning objects that she is ready to learn. During the browsing of the system, several types of navigation data are recorded. In this work, we analyzed data from two studies that were aimed at examining the learning processes induced by the navigation of the system. The results of both studies highlighted that the system is useful for monitoring the student learning processes during a university course of basic statistics.

Background: Coping with chronic illness can be overwhelming for patients and caregivers, and may be inhibited by the denial mechanism, and therefore, denial represents a critical issue for health professionals. Assessing illness denial is far from easy, and brief tools suitable for medical settings are lacking. In this paper, the development of a short form of the Illness Denial Questionnaire (IDQ) for patients and caregivers is presented. Methods: In study 1, the IDQ was administered to 118 patients and 83 caregivers to examine the internal structure of denial; then the properties of the items (DIF, fit, and difficulty) were evaluated according to the Rasch model in order to select the best items for the Illness Denial Questionnaire-Short Form (IDQ-SF). Study 2 included 202 participants (113 patients and 89 caregivers). The internal structure of the IDQ-SF was tested via confirmatory factor analysis (CFA). Reliability and concurrent validity were also studied using the Anxiety and Depression Questionnaire-Reduced Form (AD-R). Results: The CFA showed a two-factor structure encompassing “Denial of negative emotions” and “Resistance to change”. Results of the Rasch analyses led to the selection of 4 items for each dimension. The resulting IDQ-SF (8 items) showed a two-factor structure as well as good reliability and concurrent validity with AD-R. Conclusion: The IDQ-SF represents a valid tool for quickly evaluating the core of illness denial in patients and caregivers. This brief and easily administrable questionnaire allows health professionals to outline the presence and severity of illness denial in order to set individually tailored interventions.