Comparison of arithmetic and geometric means as measures of a central tendency in cattle nematode populations

Efficacy calculations in anthelmintic studies require estimates of the cent ral tendency for the nematode populations. Confusion exists among practitio ners regarding which measures of central tendency are most appropriate; alt hough the arithmetic mean is frequently used, there are theoretical reasons for preferring the geometric mean. To investigate this controversy, arithm etic and geometric means were compared for their suitability for use in mea suring efficacy. Arithmetic and geometric means were compared as measures o f central tendency for skewed distributions. The following criteria were de veloped to facilitate the comparison: (1) probability around the parameter, (2) influence of extreme values, and (3) proximity to the median. Under lo g-normality, theoretical results demonstrated the superiority of the geomet ric mean. Modified-bootstrap simulations using empirical data from cattle w ere used to confirm theoretical expectations. Simulations on log-normal dat a supported the geometric mean as the better indicator of the central tende ncy. Additionally, for data not confirmed as log-normal, the superiority of geometric means was demonstrated. In a comparison of precision, it was sho wn that mean squared error was always smaller for sample geometric means th an for arithmetic means when n greater than or equal to 2. Simulation resul ts added support to that conclusion. (C) 1999 Elsevier Science B.V. All rig hts reserved.