Understanding exam score distributions has implications for item response theory (IRT), grade curving, and downstream modeling tasks such as peer grading. Historically, grades have been assumed to be normally distributed, and to this day the normal is the ubiquitous choice for modeling exam scores. While this is a good assumption for tests…

In this paper, we address the following questions: What misconceptions do high school students exhibit in their first encounter with significance test problems through a repeated sampling approach? Which theory or framework could explain the presence and features of such patterns? With brief prior instruction on the use of Fathom software to…

We study the problem of partitioning a class of N students into k groups of n students each (N = k × n), such that their learning from peer interactions is maximized. In our formalization of the problem, any student is able to increase his score in the subject the class is studying up to the score of the student who is at p-percentile among his…

This conference presentation reviews the authors' work on autocorrelations in single-case designs. The bias-corrected autocorrelation is computed, results are meta-analyzed with 5-level multilevel analysis in SAS Proc Mixed. Results suggest autocorrelations are normally distributed, and that taking into account nesting in outcomes and articles…

People aged 20-39 were stopped in the streets of Victoria (Australia) and Madrid (Spain) to gauge their views on the gendering of mathematics. The findings suggested that for respondents from both countries, if stereotyped beliefs are held they were more strongly associated with the traditional male stereotype, that is, that males are considered…

The purpose of this study was to inform the deliberations of a policymakers' working group by investigating what key actors in the materials' marketplace are doing to align digital and print-based materials with the Australian Curriculum and what steps need to be taken to deliver aligned materials to schools. Content analysis method was used to…

Prior research investigating PSTs' statistical thinking is sparse, yet teacher educators need to know how best to prepare future teachers for their work and given the increasing importance of STEM education we need teachers who are capable of preparing students at an early age to think about data. In this paper we share the results from a study…

Self-efficacy is a personal belief in one's ability to accomplish particular tasks. Academic self-efficacy relates to one's belief in ability to accomplish learning activities. A convenient cluster sample (n = 105) of undergraduate students at a regional university in the midsouth was administered a survey that measured student academic…

The current study examines three regression models: OLS (ordinary least square) linear regression, Poisson regression, and negative binomial regression for analyzing count data. Simulation results show that the OLS regression model performed better than the others, since it did not produce more false statistically significant relationships than…

Many researchers and students assume that the univariate distribution has a single, ubiquitous "bell" shape, perhaps because most books only portray the "standard normal" or normal z-score distribution. This paper shows that the normal curve can have infinitely many appearances. It illustrates that the width to height ratio can…

Many univariate statistical methods assume that dependent variable data have a univariate distribution. Some statistical methods assume that the error scores are normally distributed. It is clear that the concept of data normality is an important one in statistics. This paper explains that, notwithstanding common misconceptions to the contrary,…

Greater understanding and use of confidence intervals is central to changes in statistical practice (G. Cumming and S. Finch, 2001). Reliability coefficients and confidence intervals for reliability coefficients can be computed using a variety of methods. Estimating confidence intervals includes both central and noncentral distribution approaches.…

This paper reviews graphical and nongraphical procedures for evaluating multivariate normality by guiding the reader through univariate and bivariate procedures that are necessary, but insufficient, indications of a multivariate normal distribution. A data set using three dependent variables for two groups provided by D. George and P. Mallery…

This paper provides a brief review of the concepts of confidence intervals, effect sizes, and central and noncentral distributions. The use of confidence intervals around effect sizes is discussed. A demonstration of the Exploratory Software for Confidence Intervals (G. Cuming and S. Finch, 2001; ESCI) is given to illustrate effect size confidence…

While violation of the homogeneity of variance assumption has received considerable attention, violation of the assumption of normally distributed data has not received as much attention. As a result, researchers may have the mistaken impression that as long as the assumptions of independence of observations and homogeneity of variance are…