The statistical implications of autocorrelation for detection in environmental health assessment

Abstract

Many environmental health and risk assessment techniques and models aim at estimating the fluctuations of selected biological endpoints through the time domain as a means of assessing changes in the environment or the probability of a particular measurement level occurring. In either case, estimates of the sample variance and mean of the sample variance are crucial to making appropriate statistical inferences. The commonly employed statistical techniques for estimating both measures presume the data were generated by a covariance stationary process. In such cases, the observations are treated as independently and identically distributed and classical statistical testing methods are applied. However, if the assumption of covariance stationarity is violated, the resulting sample variance and variance of the sample mean estimates are biased. The bias compromises statistical testing procedures by increasing the probability of detecting significance in tests of mean and variance differences. This can lead to inappropriate decisions being made about the severity of environmental damage. Accordingly, it is argued that data sets be examined for correlation in the time domain and appropriate adjustments be made to the required estimators before they are used in statistical hypothesis testing. Only then can credible and scientifically defensible decisions be made by environmental decision makers and regulators.