Precision Measurement of the p(e,e ' p)pi(0) Reaction at Threshold

New results are reported from a measurement of $\pi^0$ electroproduction near threshold using the $p(e,e^{\prime} p)\pi^0$ reaction. The experiment was designed to determine precisely the energy dependence of $s-$ and $p-$wave electromagnetic multipoles as a stringent test of the predictions of Chiral Perturbation Theory (ChPT). The data were taken with an electron beam energy of 1192 MeV using a two-spectrometer setup in Hall A at Jefferson Lab. For the first time, complete coverage of the $\phi^*_{\pi}$ and $\theta^*_{\pi}$ angles in the $p \pi^0$ center-of-mass was obtained for invariant energies above threshold from 0.5 MeV up to 15 MeV. The 4-momentum transfer $Q^2$ coverage ranges from 0.05 to 0.155 (GeV/c)$^2$ in fine steps. A simple phenomenological analysis of our data shows strong disagreement with $p-$wave predictions from ChPT for $Q^2>0.07$ (GeV/c)$^2$, while the $s-$wave predictions are in reasonable agreement.Comment: 5 pages, 6 figure

Orthonormal F Contrasts for Factors with Ordered Levels in Two-Factor Fixed-Effects ANOVAs

In multifactor fixed-effects ANOVAs, we show how to construct orthonormal F contrasts for main effects. Our primary focus is the case when the levels of the factor of interest are ordered. Likewise, in multifactor equally replicated fixed-effects ANOVAs, we show how to construct orthonormal F contrasts for interactions. The primary focus here is on interactions when both factors are ordered, although the approach also applies if just one factor is ordered. Interactions with both factors ordered may be interpreted in terms of generalised correlations

Ordinal Cochran-Mantel-Haenszel Testing and Nonparametric Analysis of Variance: Competing Methodologies

The Cochran-Mantel-Haenszel (CMH) and nonparametric analysis of variance (NP ANOVA) methodologies are both sets of tests for categorical response data. The latter are competitor tests for the ordinal CMH tests in which the response variable is necessarily ordinal; the treatment variable may be either ordinal or nominal. The CMH mean score test seeks to detect mean treatment differences, while the CMH correlation test assesses ordinary or (1, 1) generalized correlation. Since the corresponding nonparametric ANOVA tests assess arbitrary univariate and bivariate moments, the ordinal CMH tests have been extended to enable a fuller comparison. The CMH tests are conditional tests, assuming that certain marginal totals in the data table are known. They have been extended to have unconditional analogues. The NP ANOVA tests are unconditional. Here, we give a brief overview of both methodologies to address the question “which methodology is preferable?”