Evaluation of Censored Data Methods To Allow Statistical Comparisons among Very Small Samples with Below Detection Limit Observations

A simulation and verification study assessing the performance of 10 censored data reconstitution methods was conducted to develop guidance for statistical comparisons among very small samples ( n < 10) with below detection limit observations in dredged sediment testing. Censored data methods were evaluated for preservation of power and nominal type I error rate in subsequent statistical comparisons. Method performance was influenced by amount of censoring, data transformation, population distribution, and variance characteristics. For nearly all situations examined, substitution of a constant such as one-half the detection limit equaled or outperformed more complicated methods. Regression order statistics and maximum likelihood techniques previously recommended for estimating population parameters from censored environmental samples generally performed poorly in very small-sample statistical hypothesis testing with more than minimal censoring, due to their inability to accurately infer distributional properties and their consequent low power or high type I error rates.