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…

Person-fit assessment may help the researcher to obtain additional information regarding the answering behavior of persons. Although several researchers examined person fit, there is a lack of research on person-fit assessment for mixed-format tests. In this article, the lz statistic and the ?2 statistic, both of which have been used for tests…

As a part of an opening course survey, data on eye color and gender were collected from students enrolled in an introductory statistics course at a large university over a recent four year period. Biologically, eye color and gender are independent traits. However, in the data collected from our students, there is a statistically significant…

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

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…

In this note the Nearest Neighbour Index is investigated in three cases, linear, 2-dimensional and 3-dimensional. In each case the formula is investigated and the numerical values for the data points to be viewed as attracting each other, repelling each other or being randomly distributed are justified. Also, in each of the three cases mentioned…

Minkowski distances are used to indicate similarity of two vectors in an N-dimensional space. How to compute the probability function, the expectation, and the variance for Minkowski distances and the special cases City-block distance and Euclidean distance. Critical values for tests of significance are presented in tables. (SLD)

The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…

Three exact probability tests, counterparts of t tests for single sample, independent samples, and dependent samples, are described for data obtained from ratings on "m" scales by a single rater or on a single scale by "n" raters. (LMO)

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)

The random variable p and its functions figure in several "tests of combined significance," meta-analysis summaries based on sample significance values, and ps have been used singly, as well as in other tests for evaluating the outcomes of individual research studies. In this work, asymptotic distributions of the sample one-sided…

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