# Ring Test Data Evaluation

## Abstract

The statistical evaluation of the ring test data (only standard test battery) was performed in a step-wise process. First, the individual test results (EC/LC_{50} values) were recalculated (using probit analysis and the ToxRat program). Secondly, they had to fulfil several acceptance criteria. Data sets which passed these acceptance criteria were evaluated in two different ways in parallel: according to the approach usually used for the validation of chemical and physicochemical methods in environmental analysis (ISO 5725-2 (2002)) and according to the warning limit approach following Environment Canada (2005). However, for the evaluation of the results from ecotoxicological tests, the ISO approach had to be modified. Assuming that EC/LC_{50} values are log-normally distributed, the log-transformed EC/LC_{50} values were used instead of the original EC/LC_{50} values, to calculate means and standard deviations. Hence the re-transformed total means are not arithmetic but geometric means. Since the ecotoxicological test procedures in question are tedious and elaborate compared with trace analytical investigations, replicate determinations within a given laboratory and within short intervals of time were impossible. Thus, repeatability and reproducibility were evaluated using the results of the different laboratories together with the confidence intervals of the results, which were each calculated by application of the same algorithm. In addition, the results of the individual tests were used to calculate warning limits according to Environment Canada (2005). The test results that were identified as statistical outliers (ISO approach) or those outside the warning limits (Environment Canada) were excluded from the calculation of the final geometrical mean EC/LC_{50}. As a measure of robustness, the ratio between reproducibility and repeatability standard deviation, the standard deviations calculated according to the warning limit approach and the factor between minimum and maximum EC/LC_{50} value are presented. Finally, recommendations to improve the statistical evaluation of data from ecotoxicological ring tests are given.

## Keywords

Acceptance criteria Performance data Repeatability Reproducibility Statistical evaluation Validation Warning limits## Notes

## Glossary

(Environment Canada 2005) on an EC_{50} or LC_{50} represent upper and lower concentrations, within which the true endpoint is thought to lie, for a stated level of probability. The 95% confidence limits represent a statement that there is a 19 out of 20 chance that the true endpoint falls within those specified limits.

_{50}

(Environment Canada 2005) is the median effective concentration. It is the concentration of material in water (e.g., mg/L) or soil or sediment (e.g., mg/kg) that is estimated to cause a specific toxic effect to 50% of the test organisms. In most instances the EC50 and its 95% confidence limits are statistically derived by analyzing the percentages of organisms showing the specific effect at various test concentrations, after a fixed period of exposure. The duration of exposure must be specified (e.g., 72-h EC50).

(Environment Canada 2005) is a measure of central tendency for a set of observations. It can be useful because it is less influenced by extreme values than is the more familiar arithmetic mean. For n values in a set, the geometric mean is the nth root of the product of all the values (i.e., multiplied). It can also be calculated as the antilogarithm of the arithmetic mean of the logarithms of the values.

_{50}

(Environment Canada 2005) is the median lethal concentration, i.e., the concentration of material in water, soil or sediment that is estimated to be lethal to 50% of the test organisms. The LC_{50} and its 95% confidence limits are usually derived by statistical analysis of percent mortalities in several test concentrations, after a fixed period of exposure. The duration of exposure must be specified (e.g., 48-h LC_{50}).

(Environment Canada 2005) is a symmetric bell-shaped array of observations. The array relates frequency of occurrence to the magnitude of the item being measured. In a normal distribution, most observations will cluster near the mean value, with progressively fewer observations toward the extremes of a range of values. The shape is determined by the mean and standard deviation, with 68.3%, 95.4%, and 99.7% of the observations included within ±1, ±2, and ±3SD of the mean, respectively.

(Environment Canada 2005) is an extreme observation, a measurement that does not seem to fit the other values from a test.

(Environment Canada 2005) is a unit of divergence from the mean of a normal distribution, expressed in terms of a standard deviation of the distribution. The practical use of probits, in estimating an LC_{50} or EC_{50}, is to straighten the sigmoid curve of the accumulated normal distribution, which shows percent effect as a function of log concentration.

*s*

_{r}

(ISO 5725-1) is a measure of dispersion of the distribution under repeatability conditions, i.e. conditions where independent test results are obtained with the same method on identical test items in the same laboratory by the same operator using the same equipment within short intervals of time.

*s*

_{R}

(ISO 5725-1) is a measure of dispersion of the distribution under reproducibility conditions, i.e. conditions where test results are obtained with the same method on identical test items in different laboratories with different operators using different equipment.

(Environment Canada 2005) is a graph used to follow changes over time, in the endpoints which measure toxicity of a reference toxicant. The date of the test is on the horizontal axis and the effect-concentration is plotted on the vertical logarithmic scale.

(Environment Canada 2005) allow an investigator to evaluate the variation in toxicity tests with a reference toxicant. The limits are ±2SD, calculated logarithmically, from the historic geometric mean of the test endpoints.