In the study The Use of Regression Analysis for Correcting Matrix Effects in the X-Ray Fluorescence Analysis of Pyrotechnic Compositions, published in the Proceedings of the Tenth Conference on the Design of Experiments in Army Research Development and Testing, ARO-D Report 65-3 (1965), an experiment was conducted in which the concentrations of 4 components of a propellant mixture and the weights of fine and coarse particles in the slurry were each allowed to vary. Factors A, B, C, and D, each at two levels, represent the concentrations of the 4 components and factors E and F, also at two levels, represent the weights of the fine and coarse particles present in the slurry. The goal of the analysis was to determine if the X-ray intensity ratios associated with component 1 of the propellant were significantly influenced by varying the concentrations of the various components and the weights of the particle sizes in the mixture. A | fraction of a 26 factorial experiment was used with the defining contrasts being ADE, BCE, and ACF. The following data represent the total of a pair of intensity readings. The pooled mean square error with 8 degrees of freedom is given by 0.02005. Analyze the data using a 0.05 level of significance to determine if the concentrations of the components and the weights of the fine and coarse particles present in the slurry have a significant influence on the intensity ratios associated with component 1. Assume that no interaction exists among the 6factors.

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Intensity Treatment Batch Combination Ratio Total abef cdef (1) 2.2480 1.8570 2.2428 2.3270 1.8830 1.8078 ace bde abcd adf bcf 2.1424 1.9122