Beyond "Treatment Versus Control": How Bayesian Analysis Makes Factorial Experiments Feasible in Education Research.

BACKGROUND: Researchers often wish to test a large set of related interventions or approaches to implementation. A factorial experiment accomplishes this by examining not only basic treatment-control comparisons but also the effects of multiple implementation "factors" such as different dosages or implementation strategies and the interactions between these factor levels. However, traditional methods of statistical inference may require prohibitively large sample sizes to perform complex factorial experiments. OBJECTIVES: We present a Bayesian approach to factorial design. Through the use of hierarchical priors and partial pooling, we show how Bayesian analysis substantially increases the precision of estimates in complex experiments with many factors and factor levels, while controlling the risk of false positives from multiple comparisons. RESEARCH DESIGN: Using an experiment we performed for the U.S. Department of Education as a motivating example, we perform power calculations for both classical and Bayesian methods. We repeatedly simulate factorial experiments with a variety of sample sizes and numbers of treatment arms to estimate the minimum detectable effect (MDE) for each combination. RESULTS: The Bayesian approach yields substantially lower MDEs when compared with classical methods for complex factorial experiments. For example, to test 72 treatment arms (five factors with two or three levels each), a classical experiment requires nearly twice the sample size as a Bayesian experiment to obtain a given MDE. CONCLUSIONS: Bayesian methods are a valuable tool for researchers interested in studying complex interventions. They make factorial experiments with many treatment arms vastly more feasible.

(1,6,7,12-Tetra-aza-perylene-κ(2) N,N')bis-(4,4',5,5'-tetra-methyl-2,2'-bipyridyl-κ(2) N,N')ruthenium(II) bis-(hexa-fluorido-phosphate) aceto-nitrile tris-olvate.

In the title compound, rac-[Ru(C14H16N2)2(C16H8N4)](PF6)2·3C2H3N, discrete dimers of complex cations, [Ru(tmbpy)2-tape](2+), of opposite chirality are formed (tmbpy = tetra-methyl-bipyridine; tape = tetraazaperylene), held together by π-π stacking inter-actions between the tetra-aza-perylene moieties with centroid-centroid distances in the range 3.563 (3)-3.837 (3) Å. These inter-actions exhibit a parallel displaced π-π stacking mode. Additional weak C-H⋯π-ring and C-H⋯N and C-H⋯F inter-actions are found, leading to a three-dimensional architecture. The Ru(II) atom is coordinated in a distorted octa-hedral geometry. The counter-charge is provided by two hexa-fluorido-phosphate anions and the asymmetric unit is completed by three aceto-nitrile solvent mol-ecules of crystallization. Four F atoms of one PF6 (-) anion are disordered over three sets of sites with occupancies of 0.517 (3):0.244 (3):0.239 (3). Two aceto-nitrile solvent mol-ecules are highly disordered and their estimated scattering contribution was subtracted from the observed diffraction data using the SQUEEZE option in PLATON [Spek (2009 ▶). Acta Cryst. D65, 148-155].

µ-1,6,7,12-Tetra-aza-perylene-κ(4) N (1),N (12):N (6),N (7)-bis-[chlorido-(η(6)-p-cymene)ruthenium(II)] bis-(hexa-fluorido-phosphate) acetone disolvate.

In the title compound, [Ru2(C10H14)2Cl2(C16H8N4)](PF6)2·2C3H6O, the binuclear Ru(II) complex dication, [{RuCl(η(6)-cym)}2(µ-tape)](2+), built up by a planar 1,6,7,12-tetra-aza-perylene (tape) bridge, two η(6)-bound cymene (cym) ligands and two chloride ligands, includes an inversion center. The Ru(II) atom shows the typical piano-stool motif for arene coordination. The counter-charge is provided by a hexa-fluorido-phosphate anion and the asymmetric unit is completed by an acetone mol-ecule of crystallization. The components of the structure are connected into a three-dimensional architecture by C-H⋯O/F/Cl inter-actions.