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This transformation has been used to enable the geometric mean and the log standard deviation to be calculated, given that three of the values are below the limit of detection, i.e. < 1 cfu per 100 ml 3


Calculated as s = {[Σx2 - (Σx)2/n]/(n - 1)}

Ranking method

The ranking method (WHO/UNEP, 1994b) is a very simple method because it involves ordering and multiplication operations, making the use of any complex formulae or laborious graphical analysis unnecessary. The interim UNEP/WHO Mediterranean criteria for recreational waters specify that thermotolerant coliform counts in at least ten samples taken during the bathing season must not exceed 100 cfu per 100 ml in 50 per cent of samples and 1,000 cfu per 100 ml in 90 per cent of samples (UNEP/WHO, 1985). The “n” values obtained are first ranked in ascending order of concentration (by definition, the order number, “i”, takes values of 1 to n) (Table 8.9). Then the appropriate order numbers for a given percentage, P (i.e. 50 and 90 per cent) are calculated as i = nxP/100. If ten samples have been taken, then the 50 per cent is measured directly against the fifth value of cfu per 100 ml in the ranking and the 90 per cent against the ninth value. If the number of samples taken does not give a whole number value, the result should be rounded to the nearest whole number to obtain the order. This concentration has to be lower than or equal to the specified standards to comply with the interim criteria. The order point in the rank for the 50 per cent criterion of 12 samples (examples of Table 8.8 and 8.9) is 50 × 12/100 = 600/100 = 6. The order point for the 90 per cent criterion is 90 × 12/100 = 1,080/100 = 10.8 = 11th position. Thus for bathing area A, the sixth point in rank order corresponds to a concentration of 590 cfu per 100 ml while the eleventh corresponds to a concentration of 3,390 cfu per 100 ml. For bathing area B, the corresponding values are 8 and 140 respectively. Whereas A fails both standards, B complies with both (Table 8.8).

Geometric mean

The other systems of interpreting water quality, i.e. the geometric mean with confidence intervals (US EPA, 1986) and the log-normal distribution method (WHO/UNEP, 1994b), are based on the fact that sets of microbiological data from sampling a recreational area are found to conform to a skewed positive distribution, because normally there are many low values and only a few high values.

The transformation of the microbiological counts obtained into decimal logarithms often produces a more symmetrical distribution. The proper descriptive statistic for central tendency is the geometric mean (equal to the median in the case of a normal distribution) with two associated measures of dispersion: the standard deviation of the logarithms of the values (the log standard deviation) and the 95 per cent confidence interval of the geometric mean.

The geometric mean is equal to the antilogarithm of the arithmetic mean of the logarithms of individual concentrations. In the USA it is considered to be the best estimate of the central tendency and the preferred statistic for summarising microbiological results (APHA/AWWA/WPCF, 1995). If there are values less than 1 cfu per 100 ml (i.e. 0 cfu per 100 ml) in the data set it will be impossible to calculate the

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