Evaluation of whole effluent toxicity data characteristics and use of Welch's T-test in the test of significant toxicity analysis.

The U.S. Environmental Protection Agency (U.S. EPA) and state agencies evaluate the toxicity of effluent and surface water samples based on statistical endpoints derived from multiconcentration tests (e.g., no observed effect concentration, EC25). The test of significant toxicity (TST) analysis is a two-sample comparison test that uses Welch's t test to compare organism responses in a sample (effluent or surface water) with responses in a control or site sample. In general, any form of t test (Welch's t included) is appropriate only if the data meet assumptions of normality and homogeneous variances. Otherwise, nonparametric tests are recommended. TST was designed to use Welch's t as the statistical test for all whole effluent toxicity (WET) test data. The authors evaluated the suitability of using Welch's t test for analyzing two-sample toxicity (WET) data, and within the TST approach, by examining the distribution and variances of data from over 2,000 WET tests and by conducting multiple simulations of WET test data. Simulated data were generated having variances and nonnormal distributions similar to observed WET test data for control and the effluent treatment groups. The authors demonstrate that (1) moderately unequal variances (similar to WET data) have little effect on coverage of the t test or Welch t test (for normally distributed data), and (2) for nonnormally distributed data (similar in distribution to WET data) TST, using Welch's t test, has close to nominal coverage on the basis of simulations with up to a ninefold difference in variance between the effluent and control groups (∼95th percentile based on observed WET test data).