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A Visual Proof: Convergence of a Hyper Power Sequence -- A Generalisation
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Rajib Mukherjee – International Journal of Mathematical Education in Science and Technology, 2025
I provide a visual proof for the "Convergence of a Hyper power sequence," which generalises a beautiful result; also proved visually by Azarpanah in 2004.
Descriptors: Mathematical Logic, Visualization, Generalization, Equations (Mathematics)
Redefining Item Response Models for Small Samples
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Jean-Paul Fox – Journal of Educational and Behavioral Statistics, 2025
Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…
Descriptors: Sample Size, Item Response Theory, Accuracy, Bayesian Statistics
Hold the Bets! Should Quasi-Experiments Be Preferred to True Experiments When Causal Generalization Is the Goal?
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Andrew P. Jaciw – American Journal of Evaluation, 2025
By design, randomized experiments (XPs) rule out bias from confounded selection of participants into conditions. Quasi-experiments (QEs) are often considered second-best because they do not share this benefit. However, when results from XPs are used to generalize causal impacts, the benefit from unconfounded selection into conditions may be offset…
Descriptors: Elementary School Students, Elementary School Teachers, Generalization, Test Bias