Statistical Modeling of Discrete Percentage Measurements With Application to Construction of Acceptance Bounds for Wood Failure in Structural Adhesive Testing

Abstract The goals of this paper are: (1) to provide a statistical analysis approach that is appropriate for data from an interlaboratory study where responses are measured in discrete percentages and are subject to multiple sources of random variability, and (2) to apply this model to data on wood-failure percentages from block-shear tests on structural wood adhesives. We treat percentage responses measured in 5-point intervals as having arisen from observing 20 independent binary responses on different parts of the observed wood blocks. The overdispersion that is likely to result from the practical inadequacy of this assumption is overcome empirically by the inclusion of a random effect for blocks. We propose an analysis based on a parametric bootstrap to provide sampling distributions for statistics that regulators might wish to use in setting standards for acceptance of wood adhesives. Similar computational methods are developed to assess the fit of the model. This model is shown to provide a reasonably good fit for actual data in many of the cases to which it was applied.