In order to detect a wide range of aberrant behaviors, it can be useful to incorporate information beyond the dichotomous item scores. In this paper, we extend the l[subscript z] and l*[subscript z] person-fit statistics so that unusual behavior in item scores and unusual behavior in item distractors can be used as indicators of aberrance. Through…

Estimates of various variance components, universe score variance, measurement error variances, and generalizability coefficients, like all statistics, are subject to sampling variability, particularly in small samples. Such variability is quantified traditionally through estimated standard errors and/or confidence intervals. The paper derived new…

This article discusses the basics of the "4 scales of measurement" and how they are applicable to research or everyday tools of life. To do this you will be able to list and describe the four types of scales of measurement used in quantitative research; provide examples of uses of the four scales of measurement; and determine the…

In psychological and survey research, the prevalence and serious consequences of careless responses from unmotivated participants are well known. In this study, we propose to iteratively detect careless responders and cleanse the data by removing their responses. The careless responders are detected using person-fit statistics. In two simulation…

Head Start is a national program that helps young children from families with low income get ready to succeed in school. It does this by working to promote their early learning and health and their families' well-being. The Head Start Family and Child Experiences Survey (FACES) provides national information about Head Start programs and…

Increasingly students, particularly those in the social sciences, work with survey data collected through a more complex sampling method than a simple random sample. Failing to understand how to properly approach survey data can lead to inaccurate results. In this article, we describe a series of online data visualization applications and…

This technical report describes the results of analyses performed on data collected from 2013 to 2017, using the IDEA Feedback System for Administrators (FSA). The FSA is used to gather impressions from core constituents about an administrator's performance of relevant administrative roles, as well as her/his leadership style, interpersonal…

Power analysis is a fundamental prerequisite for conducting scientific research. Without power analysis the researcher has no way of knowing whether the sample size is large enough to detect the effect he or she is looking for. This paper demonstrates how psychometric factors such as measurement error and equating error affect the power of…

Statistical information pervades everyday life in the twenty-first century. Research shows, however, that the skills needed to be able to understand and critically evaluate statistical information must be specifically taught. In 2013, an externally assessed National Certificate in Educational Achievement standard in statistical literacy was…

In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and…

An IRT-based sequential procedure is developed to monitor items for enhancing test security. The procedure uses a series of statistical hypothesis tests to examine whether the statistical characteristics of each item under inspection have changed significantly during CAT administration. This procedure is compared with a previously developed…

We investigated methods of including covariates in two-level models for cluster randomized trials to increase power to detect the treatment effect. We compared multilevel models that included either an observed cluster mean or a latent cluster mean as a covariate, as well as the effect of including Level 1 deviation scores in the model. A Monte…