Researchers in the single-case design tradition have debated the size and importance of the observed autocorrelations in those designs. All of the past estimates of the autocorrelation in that literature have taken the observed autocorrelation estimates as the data to be used in the debate. However, estimates of the autocorrelation are subject to…

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

We describe the calculation of the distribution of the sum of signed ranks and develop an exact recursive algorithm for the distribution as well as an approximation of the distribution using the normal. The results have applications to the non-parametric Wilcoxon signed-rank test.

Endress and Mehler (2009) reported that when adult subjects are exposed to an unsegmented artificial language composed from trisyllabic words such as ABX, YBC, and AZC, they are unable to distinguish between these words and what they coined as the "phantom-word" ABC in a subsequent test. This suggests that statistical learning generates knowledge…

A crossflow reverse osmosis (RO) system was built for a senior-level chemical engineering unit operations laboratory course. Intended to teach students mass transfer fundamentals related to membrane separations, students tested several commercial desalination membranes, measuring water flux and salt rejections at various pressures, flow rates, and…

In most research, linear regression analyses are performed without taking into account published results (i.e., reported summary statistics) of similar previous studies. Although the prior density in Bayesian linear regression could accommodate such prior knowledge, formal models for doing so are absent from the literature. The goal of this…

The Rasch rating (or partial credit) model is a widely applied item response model that is used to model ordinal observed variables that are assumed to collectively reflect a common latent variable. In the application of the model there is considerable controversy surrounding the assessment of fit. This controversy is most notable when the set of…

A latent variable modeling approach that permits estimation of propensity scores in observational studies containing fallible independent variables is outlined, with subsequent examination of treatment effect. When at least one covariate is measured with error, it is indicated that the conventional propensity score need not possess the desirable…

Vertical scaling is necessary to facilitate comparison of scores from test forms of different difficulty levels. It is widely used to enable the tracking of student growth in academic performance over time. Most previous studies on vertical scaling methods assume relatively long tests and large samples. Little is known about their performance when…

The PROC NLMIXED procedure in Statistical Analysis System can be used to estimate parameters of item response theory (IRT) models. The data for this procedure are set up in a particular format called the "long format." The long format takes a substantial amount of time to execute the program. This article describes a format called the "wide…

Every day, the sun showers the Earth with millions of times more energy than its people use. The only problem is that energy is spread out over the entire Earth's surface and must be harvested. Engineers are learning to capture and use some of this energy to make electricity for homes. Solar panels make up the heart of a solar system. They can be…

It is well known that the length and orientation of a shadow cast by a vertical gnomon depends on the time of the day and on the season of the year. But it also depends on the latitude of the site of observation. During the equinoxes, the temporal sequence of the shadows cast by each of the points that form any object follows a straight line from…

catcher is a software program designed to compute the [omega] index, a common statistical index for the identification of collusions (cheating) among examinees taking an educational or psychological test. It requires (a) responses and (b) ability estimations of individuals, and (c) item parameters to make computations and outputs the results of…

Starting with Kenny and Judd ("Psychol. Bull." 96:201-210, 1984) several methods have been introduced for analyzing models with interaction terms. In all these methods more information from the data than just means and covariances is required. In this paper we also use more than just first- and second-order moments; however, we are aiming to…

In the absence of a randomized control trial, regression discontinuity (RD) designs can produce plausible estimates of the treatment effect on an outcome for individuals near a cutoff score. In the standard RD design, individuals with rating scores higher than some exogenously determined cutoff score are assigned to one treatment condition; those…