Bioassays for allelopathy: Measuring treatment responses with independent controls

Abstract

In bioassays for allelopathy, where responses to treatments are determined in conjunction with responses to independent controls, statistical comparisons among treatments require an index which measures each treatment response (T) in relation to its control response (C). The most commonly used index, the treatment-control ratio (T/C), exhibits two analytical problems. First, means ofT/C values are distorted upward when any of the individual values is greater than one, i.e., when stimulation occurs. Second, the distribution ofT/C values may not be normal and homoscedastic. We provide two alternative indices of response whose means do not exhibit the upward distortion ofT/C means. Then, the two indices are compared toT/C values in an empirical test for normality and homoscedasticity on a large bioassay data set. Results indicate that for this data set, one of the alternatives,RI, is clearly superior.RI is defined as 1 — (C/T) ifT≥C and asT/C — 1 ifT <C.