Quantifying natural variability as a method to detect environmental change: Definitions of the normal range for a single observation and the mean of m observations.

The normal range has been defined as the range that encloses 95% of reference values; in practice this range has been defined as the reference mean ± 2 standard deviations (SD). When sample sizes are small and reference data are not normally distributed, the mean ± 2 SDs do not enclose 95% of data values. Prediction intervals (PI) calculated using sample statistics are used in the present study to define the normal range for a single observation and the mean of m observations. The PIs provide confidence limits for the next randomly selected observation (or mean of m observations) from a population. The PIs are defined using normally distributed reference data; normality can typically be achieved with transformations of the data. Covariates can be used to explain some of the variability in the reference distribution, increasing the ability to detect change. When assumptions of normality are not met, alternative methods of defining the normal range are provided. The normal range can be used to quantify natural variability and assess change from the reference distribution. It can be used as an early warning indicator of change in environmental monitoring to identify the need for further investigation.