AN OPTIMAL TRANSFORMATION FOR MILK N-ACETYL-BETA-D-GLUCOSAMINIDASE ACTIVITY

A family of power transformations was examined to improve effectivenes s of mastitis diagnosis and sensitivity of hypothesis tests. The famil y of transformations considered included square root, logarithmic, rec iprocal and reciprocal of square root. N-acetyl-beta-D-glucosaminidase activity was assayed on foremilk samples collected as composites of a ll quarters from each of 488 cows in ten commercial herds. Herds were sampled three times at monthly intervals. The frequency distribution o f the observed assay results was extremely fight skewed. Although the optimal transformation was reciprocal of the square root, the logarith mic transformation was only slightly inferior and is recommended for p ractical application. After transformation by logarithm, skewness was greatly reduced (1.35 vs. 0.13), coefficient of determination increase d (0.81 vs. 0.86), F value for the full model increased (3.36 vs. 4.80 ), and the contrast in standard deviation units between samples with m ajor pathogen and no infection was increased by 65%. Choice of base fo r logarithmic transformation is immaterial because the frequency distr ibutions of standard unit deviations from means are invariant to the b ase.