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…

Researchers have documented many misconceptions students hold about sampling variability. This study takes a different approach--instead of identifying shortcomings, we consider the productive reasoning pieces students construct as they reason about sampling distributions. We interviewed eight undergraduate students newly enrolled in an…

The problem of assessing whether experimental results can be replicated is becoming increasingly important in many areas of science. It is often assumed that assessing replication is straightforward: All one needs to do is repeat the study and see whether the results of the original and replication studies agree. This article shows that the…

Statistical inference involves drawing scientifically-based conclusions describing natural processes or observable phenomena from datasets with intrinsic random variation. We designed, implemented, and validated a new portable randomization-based statistical inference infrastructure (http://socr.umich.edu/HTML5/Resampling_Webapp) that blends…

Respondent-driven sampling (RDS) is a survey method for hidden populations and, as such, it offers a suitable approach for sampling the homeless. Surprisingly, the practical use of RDS in surveying homeless populations has only sporadically been described in the professional literature so far, and the specifics of using RDS for sampling this group…

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators, which, in many but not all cases, are related to asymptotic Normal distributions ensured by central…

As a result of the evidence-based decision-making movement, the number of randomized trials evaluating educational programs and curricula has increased dramatically over the past 20 years. Policy makers and practitioners are encouraged to use the results of these trials to inform their decision making in schools and school districts. At the same…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction; and…

While various studies suggest that informal statistical inference (ISI) can be developed by young students, more research is needed to translate this claim into a well-founded learning trajectory (LT). As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation, and evaluation of the…

This document provides tables underlying figures in "Education, Employment, and Earnings: Expectations of 2009 Ninth-Graders in 2016" and describes the survey methodology, sources of error in estimates, response rates and nonresponse bias, and statistical procedures for the Statistics in Brief report "Education, Employment, and…

This guide describes a five-step collaborative process that educators can use with other educators, researchers, and content experts to write or adapt questions and develop surveys for education contexts. This process allows educators to leverage the expertise of individuals within and outside of their organization to ensure a high-quality survey…

In this paper, we estimate the causal effect of an extra year of schooling on mathematics performance for seven Latin American countries based on PISA 2012. To that end we exploit exogenous variation in students' birthdates around the school entry cut-off date using both sharp and fuzzy Regression Discontinuity designs. We find strong effects of…

The purposes of this manuscript are to identify common statistical mistakes in sport management, and to provide scholars with suggestions on how to develop and improve the quality of quantitative research. We have reviewed articles published from 2001 to 2017 in the "Journal of Sport Management," "Sport Management Review,"…

When an assessment undergoes changes to the administration or instrument, bridge studies are typically used to try to ensure comparability of scores before and after the change. Among the most common and powerful is the common population linking design, with the use of a linear transformation to link scores to the metric of the original…