Lm. Berning et al., AN OPTIMAL TRANSFORMATION FOR MILK N-ACETYL-BETA-D-GLUCOSAMINIDASE ACTIVITY, Preventive veterinary medicine, 17(1-2), 1993, pp. 77-88
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.