The simple average of student growth scores is often used in accountability systems, but it can be problematic for decision making. When computed using a small/moderate number of students, it can be sensitive to the sample, resulting in inaccurate representations of growth of the students, low year-to-year stability, and inequities for…

International survey researchers are increasingly turning to a geospatial sampling approach known as gridded population sampling for finer resolution and a more updated sampling frame than conventional census-based sampling. To date, there have been no direct comparisons of accuracy between survey results derived from the two methods. This…

This paper explores the effect of using multitask learning for abstractive summarization in the context of small training corpora. In particular, we incorporate four different tasks (extractive summarization, language modeling, concept detection, and paraphrase detection) both individually and in combination, with the goal of enhancing the target…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Predictability of behavior is an important characteristic in many fields including biology, medicine, marketing, and education. When a sequence of actions performed by an individual can be modeled as a stationary time-homogeneous Markov chain the predictability of the individual's behavior can be quantified by the entropy rate of the process. This…

In educational research that calls itself empirical, the relationship between validity and reliability is that of trade-off: the stronger the bases for validity, the weaker the bases for reliability (and vice versa). Validity and reliability are widely regarded as basic criteria for evaluating research; however, there are ethical implications of…

When performing a meta-analysis unexplained variation above that predicted by within study variation is usually modeled by a random effect. However, in some cases, this is not sufficient to explain all the variation because of outlier or unusual studies. A previously described method is to define an outlier as a study requiring a higher random…

Early on during word recognition, letter positions are not accurately coded. Evidence for this comes from transposed-letter (TL) priming effects, in which letter strings generated by transposing two adjacent letters (e.g., "jugde") produce large priming effects, more than primes with the letters replaced in the corresponding position (e.g.,…

When a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable, the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the…

This paper discusses the limitations of Classical Test Theory, the purpose of Item Response Theory/Latent Trait Measurement models, and the step-by-step calculations in the Rasch measurement model. The paper explains how Item Response Theory (IRT) transforms person abilities and item difficulties into the same metric for test-independent and…

The article by W. K. Estes marks a turning point in the mathematical learning theory movement. The central constructs were stimulus variability, stimulus sampling, and stimulus response association by contiguity, in a framework enabling prediction of response probability and latency. (SLD)

Large scale surveys usually employ a complex sampling design and as a consequence, no standard methods for estimation of the standard errors associated with the estimates of population means are available. Resampling methods, such as jackknife or bootstrap, are often used, with reference to their properties of robustness and reduction of bias. A…

Analysis of a two-way sample of means is considered when corresponding population means are believed a priori to satisfy a partial order restriction. Simulation and the Gibbs sampler are used to summarize posterior distributions, and the posterior distribution is used to predict GPAs of first-year students at University of Iowa. (SLD)