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Logarithmic Normal Distribution for Description of Sieved Forage Materials

Animal Science Research Division

E. L. Cox and B. T. Weinland

Biometrical Services, ARS, USDA Beltsville, Maryland 20705

H. L. Lucas, Jr.

Biomathematics Program, North Carolina State University, Raleigh 27607

ABSTRACT

Samples of chopped or pelleted grass hay and resulting rumen contents and feces from feeding cattle in changeover trials were sieved, and adequacy of describing results by the log normal distribution was investigated. Geometric mean particle sizes ranged from 235 µ for dissociated pellets to 4,180 µ for chopped hay or log₁₀ means of 2.37 to 3.62. Fitting the cumulative log normal distribution to data from single sievings yielded residual standard deviations less than .311 corresponding to less than 5.1% of the sum of squares for variation in particle size not explained. Fecal samples showed no statistically significant lack of fit, but fewer data pellets and chopped forage did. Nevertheless, the log normal yielded a good practical description in all cases. Sample coefficients of variation of duplicate determinations were less than 14% for mean particle size and less than 8% for standard deviations of particle size. Experimental errors as coefficients of variation include animal variability and were based on means of quadruplicate determinations for rumen content and means of duplicate determinations for feces. These values were less than 6% for three sets of rumen means but were 34% on the fourth. The corresponding statistics for standard deviations of log particle size were less than 10%. Forage sieve data is fitted adequately by normal distributions so that log means and log standard deviations are useful in summarizing results.

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