A modified and improved inductive inferential approach to evaluate item discriminations in a conditional maximum likelihood and Rasch modeling framework is suggested. The new approach involves the derivation of four hypothesis tests. It implies a linear restriction of the assumed set of probability distributions in the classical approach that…

BASIE is a framework for interpreting impact estimates from evaluations. It is an alternative to null hypothesis significance testing. This guide walks researchers through the key steps of applying BASIE, including selecting prior evidence, reporting impact estimates, interpreting impact estimates, and conducting sensitivity analyses. The guide…

This paper introduces a dataset and associated analysis of the scores of National Football League (NFL) games over the 2012, 2013, and first five weeks of the 2014 season. In the face of current media attention to "lopsided" scores in Thursday night games in the early part of the 2014 season, t-test results indicate no statistically…

The statistical output of interest to most elementary statistics students is the p-value, outputted in computer programs like SPSS, Minitab and SAS. Statistical decisions are sometimes made using these values without understanding the meaning or how these values are calculated. Most elementary statistics textbooks calculates p-values for z-tests…

Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

Following an exploratory factor analysis, factor scores may be computed and used in subsequent analyses. Factor scores are composite variables which provide information about an individual's placement on the factor(s). This article discusses popular methods to create factor scores under two different classes: refined and non-refined. Strengths and…

This comment offers three descriptions of "p[subscript rep]" that start with a frequentist account of confidence intervals, draw on R. A. Fisher's fiducial argument, and do not make Bayesian assumptions. Links are described among "p[subscript rep]," "p" values, and the probability a confidence interval will capture…

This study compared two approximations for normalizing noncentral F distributions: one based on the square root of the chi-square distribution (SRA), the other derived from a cube root of the chi-square distribution (CRA). The CRA was superior, and generally provided an excellent approximation for noncentral F. (Author/BW)

A sampling subspace in hypothesis testing where Type II error is made for completely illogical reasons from the standpoint of probability is described. The case of unequal probabilities of populations or conditions is also considered. (Author/BS)

Comparing variability of test scores across alternate forms, test conditions, or subpopulations is a fundamental problem in psychometrics. A confidence interval for a ratio of standard deviations is proposed that performs as well as the classic method with normal distributions and performs dramatically better with nonnormal distributions. A simple…

This paper explains how to combine probabilities from discrete distributions, such as probability distributions for nonparametric tests. (Author/BW)

The observed probability "p" is the social scientist's primary tool for evaluating the outcome of statistical hypothesis tests. The small-sample accuracy of nonnull asymptotic distributions of several functions of "p" was studied. Implications for use of the approximations are discussed. (SLD)

Modifications are proposed to the recently developed method of comparing one-step M-estimators of location corresponding to two independent groups that provides good control over the probability of Type I error even for unequal sample size, unequal variances, and different shaped distributions. Simulation results reveal cautions required. (SLD)