Macroalgae and phytoplankton as indicators of ... - Naturstyrelsen

4.3 Evaluation of the precision of the chlorophyll a indicator
described as 'summer mean' and '90 th percentile'
Different indicators have been suggested to characterise phytoplankton
biomass. In the Baltic GIG summer means have been proposed, whereas
the North East Atlantic GIG proposes to use the 90-percentile as indicator.
The rationale behind these selections has not been given careful considerations
with respect to the statistical properties of indicator estimation.
For the usefulness of indicators, two issues should be considered: 1)
the responsiveness of the indicators to the pressure and 2) the precision
of the indicator from sample sizes. In this section we will compare the
two different indicators of phytoplankton biomass by means of their precision
given realistic sample sizes. We will examine these properties assuming
chla to be described by parametric distributions (normal and lognormal)
and non-parametric distribution using data from the national
monitoring database. The precision of the indicator will be assessed by
the standard error of the indicator estimation.
The standard error of the mean is known to be inversely related to the
square root of the sample size but such explicit relationships are more
difficult to derive for percentiles. However, it is known that the variance
of percentiles increases going from statistics describing the median to
minimum and maximum values. Therefore, for different samples sizes (n
= 10, 20, 30, …., 100) a standard normal and lognormal distribution was
simulated 10000 times, and the mean, the median, 60-percentile, 70-
percentile, 80-percentile and 90-percentile were calculated from these
sample distributions. The standard error or the different statistics (indicators)
was estimated as the standard deviation of the 10000 replicates.
The results using the two parametric distributions are in accordance with
the theory of increasing standard error going from the mean over median
to the 90-percentile (Figure 4.7). If data are normal distributed, then
using the mean, estimated by the average of the sampled data, is by far
the most precise indicator of the distribution. For the lognormal distribution
the raw average of data is not the best estimator of the mean and it is
actually more uncertain than the median and 60-percentile. This is due to
the skewness of the lognormal distribution with high observations in the
right tail that have a strong influence on the average. However, logtransforming
the data prior to averaging and back-transforming the
mean to the original scale gives the most precise indicator (Figure 4.7),
because the log-transformation implicitly gives less weight to high observations
and thereby reduce their influence on the mean statistic. Thus,
the mean statistic is the most precise indicator for a sample distribution,
provided that data can be approximated by a parametric distribution.
This is also the reason why the mean is used as parameter, and not the
median or a percentile, for characterising statistical distributions.
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