Estimation of mean and median particle size of ruminant digesta

An alternative exponential equation with a parameter as an exponent was compared to a recently published exponential procedure for estimating mean and median particle size. Both equations were fit to literature values for particle size distributions of esophageal extrusa, rumen digesta, and feces. In addition, 112 observations of particle-size distributions of esophageal extrusa were fit to both equations for comparison. Both equations gave adequate fits of rumen digesta and feces, but the earlier model was biased by regular deviations from observed data for esophageal extrusa. Use of the previously published model overestimated mean particle size in esophageal extrusa from 4.5 to 10.3%. Median particle size was underestimated from 4.9 to 5.6%. Analytic solutions exist for mean and median particle sizes for the earlier model, but it is necessary to estimate numerically the mean and median particle sizes when using the proposed equation. Even though the solution for the proposed equation must be determined numerically, it will prevent bias between experimental treatments, give more accurate estimates of mean and median particle size, and result in a lower residual sums of squares. In addition, a single equation can be used to model particle size reduction throughout the digestive tract.