Star graphs induce tetrad correlations: for Gaussian as well as for binary variables

Tetrad correlations were obtained historically for Gaussian distributions when tasks are designed to measure an ability or attitude so that a single unobserved variable may generate the observed, linearly increasing dependences among the tasks. We connect such generating processes to a particular type of directed graph, the star graph, and to the notion of traceable regressions. Tetrad correlation conditions for the existence of a single latent variable are derived. These are needed for positive dependences not only in joint Gaussian but also in joint binary distributions. Three applications with binary items are given.Comment: 21 pages, 2 figures, 5 table

Matrix representations and independencies in directed acyclic graphs

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.Comment: Published in at http://dx.doi.org/10.1214/08-AOS594 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A remark on equidistance in Hilbert spaces

It is shown that in a Hilbert space the only infinite equidistant systems of points are those obtained by translation and scaling from (in the complex case: almost) orthonormal systems

Development and Implementation of an Administrative Internship Program

This article describes the development and implementation of a pilot program to prepare teachers seeking New York State certification as School District Administrators, by assigning them as administrative interns to a school district. The district superintendent of a large urban school district and the college program director partnered to design a pilot experiential course to take the place of an existing internship course for eight candidates. The dual purpose was to provide an authentic learning experience for the candidates, and to provide actionable information for the superintendent for improvement of the district instructional program. The candidates reviewed the New York State District Report Card to identify areas of academic concern, conducted research, and interviewed district personnel to make suggestions and recommendations for academic improvement. Findings and recommendations were presented to the superintendent and his administrative staff to inform district improvement efforts, and for improvement of the existing course. Recommendations are included

2-Carboxy­quinolinium–2,4,6-trinitro­benzene­sulfonate–quinolinium-2-carboxyl­ate (1/1/1)

The structure of the title adduct compound, C10H8NO2 +·C6H2N3O9S−·C10H7NO2, from the reaction of 2,4,6-trinitro­benzene­sulfonic acid (picrylsulfonic acid) with quinoline-2-carboxylic acid (quinaldic acid) in 2-propanol–water, has been determined at 130 (2) K. The cation and the adduct species form a twisted cyclic hydrogen-bonded R 2 2(10) pseudo-dimer which is extended into a one-dimensional chain structure through short head-to-tail carboxylic acid O—H⋯Ocarbox­yl associations [O⋯O = 2.4711 (19) Å]. The picrylsulfonate anions are attached peripherally by single N—H⋯Osulfonate hydrogen bonds [N⋯O = 2.8643 (19) Å]