Statistical analysis of theCeriodaphniatoxicity test: Sample size determination for reproductive effects

An analysis of sample size requirements for the Ceriodaphnia dubia reproduction toxicity test is presented. Sample size requirements for detecting nominally specified biological effect sizes in the presence of different variance models are examined over a range of false positive error rates (α) and false negative error rates (β). Mean total young produced per female from control organisms in 53 separate toxicity tests yields a mean (22.52) and variance (68.25) that are used in sample size determinations. Results from these calculations demonstrate that in tests using the currently accepted sample size of 10 organisms per concentration, hypothesis-testing techniques are capable of detecting a range of 31 to 100% reproductive inhibition relative to controls. This wide range of minimum detectable inhibition values indicates that the ability to detect biologically significant levels of reproductive inhibition in this test is constrained by the statistical properties (i.e., power) associated with the currently accepted test protocol. It is suggested that the design of the Ceriodaphnia toxicity test be based not only on a minimum level of control reproductive output (as currently recommended), but also on the ability to detect a specified level of reproductive inhibition.