Water quality surveys: A statistical method based on determinism, quantiles and the binomial distribution

A statistical method for surveying water quality and analysing the results in terms of quantiles is described. The value of a water quality variable in a grab-sample is taken as a deterministic function of the temporal and spatial coordinates of the sampling point. Quantiles can then be defined for any specified region in time and space as unique, fixed values, and randomly located grab-samples may be used to estimate them for the purposes of describing or regulating water quality. Robust statistical inferences are possible using the binomial distribution. Properties of the quantiles, confidence limits, comparisons with fixed values or between regions, assessment of trends, simultaneous inferences and estimation of sample sizes are discussed. Two examples of water quality surveys, one of Port Phillip Bay, the other of the Maribyrnong River, Victoria, are used to illustrate the theory, paying particular attention to practical problems which arose. The proposed method is compared with others based on stochastic models, and is claimed to be simpler and more reliable.