Compliance with criteria limiting the discharge of pollutants or standards of water quality in the reveiving water body are assessed by monitoring. In order to set limits or standards, the features of the discharge or the water body to be monitored must be characterized. This generally involves the fitting of a probability distribution to historical data or data from preliminary sampling and the choice of a statistic for the limit or standard. Monitoring data collected to assess compliance are assumed to follow data will help to ensure that the assumption is met. Statistical methods which either assume a distribution for the quality variable or involve a transformation to a binary variable are compared. The validity of the underlying assumptions in the application of the methods to water or effluent quality data is discussed.