Interlaboratory studies in measurement science, including key comparisons, and meta-analyses in several fields, including medicine, serve to intercompare measurement results obtained independently, and typically produce a consensus value for the common measurand that blends the values measured by the participants.Since interlaboratory studies and meta-analyses reveal and quantify differences between measured values, regardless of the underlying causes for such differences, they also provide so-called 'top-down' evaluations of measurement uncertainty.Measured values are often substantially over-dispersed by comparison with their individual, stated uncertainties, thus suggesting the existence of yet unrecognized sources of uncertainty (dark uncertainty). We contrast two different approaches to take dark uncertainty into account both in the computation of consensus values and in the evaluation of the associated uncertainty, which have traditionally been preferred by different scientific communities. One inflates the stated uncertainties by a multiplicative factor. The other adds laboratory-specific 'effects' to the value of the measurand.After distinguishing what we call recipe-based and model-based approaches to data reductions in interlaboratory studies, we state six guiding principles that should inform such reductions. These principles favor model-based approaches that expose and facilitate the critical assessment of validating assumptions, and give preeminence to substantive criteria to determine which measurement results to include, and which to exclude, as opposed to purely statistical considerations, and also how to weigh them.Following an overview of maximum likelihood methods, three general purpose procedures for data reduction are described in detail, including explanations of how the consensus value and degrees of equivalence are computed, and the associated uncertainty evaluated: the DerSimonian-Laird procedure; a hierarchical Bayesian procedure; and the Linear Pool. These three procedures have been implemented and made widely accessible in a Web-based application (NIST Consensus Builder).We illustrate principles, statistical models, and data reduction procedures in four examples: (i) the measurement of the Newtonian constant of gravitation; (ii) the measurement of the halflives of radioactive isotopes of caesium and strontium; (iii) the comparison of two alternative treatments for carotid artery stenosis; and (iv) a key comparison where the measurand was the calibration factor of a radio-frequency power sensor.

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This work presents the implementation in R of the α-shape of a finite set of points in the three-dimensional space R 3. This geometric structure generalizes the convex hull and allows to recover the shape of non-convex and even non-connected sets in 3D, given a random sample of points taken into it. Besides the computation of the α-shape, the R package alphashape3d provides users with tools to facilitate the three-dimensional graphical visualization of the estimated set as well as the computation of important characteristics such as the connected components or the volume, among others.

We present the experimental scattering matrix as a function of the scattering angle of the lunar soil simulant JSC-1A. The measurements were performed at 488 nm, 520 nm and 647 nm, covering the range of scattering angles from 3 • to 177 •. The effect of sub-micron size particles on the measured phase function and degree of linear polarization has been studied. After removing particles smaller than 1 µm radius the forward scattering peak becomes steeper. Further, the maximum of the degree of linear polarization increases, moving toward smaller scattering angles. Interestingly, the negative branch at backward direction disappears as the small particles are removed from the sample. As multiple scattering calculations with polarization included require single scattering matrices in the whole scattering range (from 0 • to 180 •), we computed the corresponding synthetic scattering matrix through an extrapolation method, considering theoretical boundary conditions. From the extrapolated results, the asymmetry parameter g and the back-scattering linear depolarization factor δ L were computed.