Although the statistical reliability of membrane filter results is higher than that of the MPN procedure, membrane counts are not absolute numbers; 95 per cent confidence limits can be calculated using a normal distribution equation (Fleisher and McFadden, 1980; PHLS, 1994; APHA/AWWA/WPCF, 1995).

# 8.7.3 Statistical procedures

A single water sample from a recreational area gives very little useful information. However, when individual results are accumulated and analysed statistically, then the trend in water quality will become apparent. Statistical analysis also enables evaluation of the improvement of water quality after remedial actions have been applied (e.g. to sewage contamination sources) and enables achievement of comparability between different regions within the same country or across countries. To establish comparability for the concentrations of thermotolerant coliforms from different regions, it is essential to agree what will be analysed (i.e. all the thermotolerant coliforms or only E. coli) otherwise comparison is impossible (Figueras et al., 1994, 1997). The type of data analysis needed depends on the nature of the study (see Chapter 3).

For regulatory monitoring programmes, the objective of data analysis is to demonstrate compliance with a standard. The definition of the standard specifies the type of statistical analysis required. Most recreational water quality standards derive from those of the US EPA (Dufour and Ballentine, 1986), UNEP/WHO (1985) or the European Bathing Water Directive (EEC, 1976). More recently, WHO has published the Guidelines for Safe Recreational Water Environments (WHO, 1998). Microbiological standards typically specify the frequency of analysis and the number or proportion of samples that must not exceed given limiting values of the target organism. The rules for interpreting compliance differ with each standard. For microbiological surveys or epidemiological studies, the type of data analysis is decided at the planning stage. The procedures and statistics that are most often used to assess compliance during or after a bathing season are described below, together with worked examples from two sets of data from the two different bathing areas shown in Table 8.8, with the calculation of their basic statistics in Table 8.9.