Many agronomic experiments with complete factorial treatment designs are conducted in two or more environments. If at least one of the treatment factors is qualitative, the combined analysis may appropriately include pairwise comparisons of various treatment means averaged over environments. Heretofore, however, formulae for estimation of the variances of pairwise mean differences, which are needed for the calculation of least significant differences (or other mean separation procedures), have not been available in either the agronomic or statistical literature. The main purpose of this paper is to provide the formulae for estimation of these variances so that researchers can use them in testing the significance of differences among various treatment means averaged over environments. Emphasis is given to combined analyses of series of experiments in which the effects of experiments are considered to be random; individual experiments are assumed to have complete factorial treatment designs involving either two or three factors of which at least one is qualitative. All treatment effects, including main effects and interactions, are considered to be fixed effects. Formulae applicable to commonly used experimental designs are presented for the estimation of variances for the five categories of pairprise mean differences in two‐factor treatment designs and the 19 categories of pairwise mean differences in three‐factor treatment designs. Experimental design considerations and the implications of assuming random (versus fixed) experiment effects as well as the structure of the treatment × experiment interactions are studied. Pooling portions of the treatment × experiment interaction with error mean squares are considered, and suggestions are given for cases where some of the treatment factors are quantitative rather than qualitative.

The oligosaccharides, raffinose and stachyose, have been implicated as causative factors for the flatulence and uncomfortable feeling often experienced after consuming products containing soybean [Glycine max (L.) Merrill] meal. Soybeans are primarily grown for their oil and protein content. Their value might be enhanced, however, if the oil and protein content remained high and the oligosaccharide content were lowered to make them more acceptable for human consumption. Seeds of 60 selected lines from Maturity Groups 00 through IV were analyzed for protein, oil, total sugar, and individual sugar content. The ranges in values for oil, protein, total sugar, sucrose, raffinose, and stachyose were 14.5 to 23.0, 33.1 to 49.2, 5.6 to 10.9, 2.5 to 8.2, 0.1 to 0.9, and 1.4 to 4.1 g per 100 g seed respectively. Simple correlation analysis revealed that total sugar content and oil content in soybean seeds are positively associated, and each was negatively correlated with protein content. Sucrose and raffinose content were positively correlated with oil content, while stachyose content was positively associated with protein. Even though the correlation between certain sugars and oil or protein was statistically significant, considerable variation in total sugar content was not explained by the coefficient of determination (r2).

A systematic study has been performed to determine how the characteristics of granules prepared by spray drying aqueous alumina slurries are influenced by processing parameters: binder type (PEG Compound 20M or PEG-8000), solids loading (30 or 40 vol%), ammonium polyacrylate deflocculant level (0.35-1.00 wt%), and spray-dryer type. Correlations between slurry rheology and granule characteristics have been made, and a model for granule formation is presented. The packing density of the primary particles within the granules is lower for slurries with higher yield stress and is dependent on the slurry solids loading. Granules prepared using 0.35 wt% deflocculant (0.14 mg/m 2 ), which correspond to high slurry yield stress, are of solid morphology, whereas higher deflocculant levels result in hollow granules that contain a single large open pore or crater. The degree to which particles are able to rearrange during drying influences the final granule density and is determined by the strength of the floc structure, as indicated by the slurry yield stress. When the yield stress is low, a crater may form from the inward collapse of the surface of a forming granule when the particle packing density in a droplet continues to increase after the droplet size becomes fixed by the formation of a rigid shell, leaving an internal void with internal pressure lower than that of the surrounding atmosphere.

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