Classification of bathing water quality based on the parametric calculation of percentiles is unsound

Analyses of Irish bathing water quality data sets are reported to investigate whether the parametric calculations proposed in the draft Bathing Water Directive are valid. Faecal coliforms (assumed to be Escherichia coli) and faecal streptococci (assumed to be intestinal enterococci) have been analysed separately. It was noted that classifications based on the parametric 95th percentile calculations disagreed with those based on percentage compliance with the standards on 13.8% of occasions. When these disagreements were studied, it was found that the datasets frequently contained many censored data points (Result < 1). Also, the datasets were not log normally distributed on at least 85% of occasions. Both these findings fatally undermine the validity of using a parametric method for calculating 95th percentiles to classify bathing water quality. By contrast the non-parametric Hazen method is a better estimate of true population 95th percentiles, but essentially gives very similar classifications to the percentage compliance approach, fully agreeing on over 95% of occasions. The same is also true when considering 90th percentiles. A series of Monte Carlo studies were also conducted to determine the impact of small numbers. It was ascertained that small sample sizes are very undependable in determining bathing water classification and the parametric method in particular is particularly unreliable. In conclusion, the parametric method for calculating bathing water compliance is so severely and fatally flawed statistically that it should not form the basis of any legislation. The Hazen method gives a better estimate of true 90th or 95th percentiles, though as the resultant classifications agree with percentage compliance so closely it is doubtful that there is any statistical value in using a percentile approach over the long established and well understood percentage compliance approach.