Factors influencing the performance of the Mantel-Haenszel procedure in identifying differential item functioning.

The Mantel-Haenszel (MH) procedure has emerged as one of the methods of choice for identification of differentially functioning test items (DIF). Although there has been considerable research examining its performance in this context, important gaps remain in the knowledge base for effectively applying this procedure. This investigation is an attempt to fill these gaps with the results of five simulation studies. The first study is an examination of the utility of the two-step procedure recommended by Holland and Thayer in which the matching criterion used in the second step is refined by removing items identified in the first step. The results showed that using the two-step procedure is associated with a reduction in the Type II error rate. In the second study, the capability of the MH procedure to identify uniform DIF was examined. The statistic was used to identify simulated DIF in items with varying levels of difficulty and discrimination and with differing levels of difference in difficulty between groups. The results indicated that when difference in difficulty was held constant, poorly discriminating items and items that were very difficult were less likely to be identified by the procedure. In the third study, the effects of sample size were considered. In spite of the fact that the MH procedure has been repeatedly recommended for use with small samples, the results of this study suggest that samples below 200 per group may be inadequate. Performance with larger samples was satisfactory and improved as samples increased. The fourth study is an examination of the effects of score group width on the statistic. Holland and Thayer recommended that n + 1 score groups should be used for matching (where n is the number of items). Since then, various authors have suggested that there may be utility in using fewer (wider) score groups. It was shown that use of this variation on the MH procedure could result in dramatically increased type I error rates. In the final study, a simple variation on the MH statistic which may allow it to identify non-uniform DIF was examined. The MH statistic\u27s inability to identify certain types of non-uniform DIF items has been noted as a major shortcoming. Use of the variation resulted in identification of many of the simulated non-uniform DIF items with little or no increase in the type I error rate

Is Quantum Mechanics Compatible with a Deterministic Universe? Two Interpretations of Quantum Probabilities

Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the Aspect-type EPR experiment. It will be shown that the quantum mechanical probabilities appearing in this experiment can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies in the Aspect experiment that quantum theory is incompatible with a deterministic universe.Comment: REVISED VERSION! ONLY SMALL CHANGES IN THE TEXT! compressed and uuencoded postscript, a uuencoded version of a demo program file (epr.exe for DOS) is attached as a "Figure

Weight, volume, and center of mass of segments of the human body

Weight, volume, and center of mass of segments of human bod

General criterion for the entanglement of two indistinguishable particles

We relate the notion of entanglement for quantum systems composed of two identical constituents to the impossibility of attributing a complete set of properties to both particles. This implies definite constraints on the mathematical form of the state vector associated with the whole system. We then analyze separately the cases of fermion and boson systems, and we show how the consideration of both the Slater-Schmidt number of the fermionic and bosonic analog of the Schmidt decomposition of the global state vector and the von Neumann entropy of the one-particle reduced density operators can supply us with a consistent criterion for detecting entanglement. In particular, the consideration of the von Neumann entropy is particularly useful in deciding whether the correlations of the considered states are simply due to the indistinguishability of the particles involved or are a genuine manifestation of the entanglement. The treatment leads to a full clarification of the subtle aspects of entanglement of two identical constituents which have been a source of embarrassment and of serious misunderstandings in the recent literature.Comment: 18 pages, Latex; revised version: Section 3.2 rewritten, new Theorems added, reference [1] corrected. To appear on Phys.Rev.A 70, (2004

Atomic vapor-based high efficiency optical detectors with photon number resolution

We propose a novel approach to the important fundamental problem of detecting weak optical fields at the few photon level. The ability to detect with high efficiency (>99%), and to distinguish the number of photons in a given time interval is a very challenging technical problem with enormous potential pay-offs in quantum communications and information processing. Our proposal diverges from standard solid-state photo-detector technology by employing an atomic vapor as the active medium, prepared in a specific quantum state using laser radiation. The absorption of a photon will be aided by a dressing laser, and the presence or absence of an excited atom will be detected using the ``cycling transition'' approach perfected for ion traps. By first incorporating an appropriate upconversion scheme, our method can be applied to a wide variety of optical wavelengths.Comment: 4 pages, 2 figure

An experimental test of non-local realism

Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned.Comment: Minor corrections to the manuscript, the final inequality and all its conclusions do not change; description of corrections (Corrigendum) added as new Appendix III; Appendix II replaced by a shorter derivatio

Entropy inequalities and Bell inequalities for two-qubit systems

Sufficient conditions for (the non-violation of) the Bell-CHSH inequalities in a mixed state of a two-qubit system are: 1) The linear entropy of the state is not smaller than 0.5, 2) The sum of the conditional linear entropies is non-negative, 3) The von Neumann entropy is not smaller than 0.833, 4) The sum of the conditional von Neumann entropies is not smaller than 0.280.Comment: Errors corrected. See L. Jakobcyk, quant-ph/040908

Comment on "Nonlocality of a Single Photon"

A Comment on the Letter by S. M. Tan, D. F. Walls, and M. J. Collett, Phys. Rev. Lett. 66, 252 (1991)

Quantum Holography

We propose to make use of quantum entanglement for extracting holographic information about a remote 3-D object in a confined space which light enters, but from which it cannot escape. Light scattered from the object is detected in this confined space entirely without the benefit of spatial resolution. Quantum holography offers this possibility by virtue of the fourth-order quantum coherence inherent in entangled beams.Comment: 7 pages, submitted to Optics Expres

Qubits from Number States and Bell Inequalities for Number Measurements

Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate optical parametric amplifier.Comment: revtex4, 7 pages, v2: results identical but extended presentation, v3: published versio