- The measurements each year are summarised by an annual index.
- A weighted regression model is fitted to the annual indices.
The type of model depends on the number of years of data:
- 1-2 years: no model
- 3-4 years: mean
- 5-6 years: linear trend
- 7+ years: smoother

- The fitted models are used to assess environmental status against available assessment criteria and evidence of temporal change in biological effect levels in the last fifteen years

Each stage is described in more detail below for the case when all the biological measurements are above the detection limit. Other help files describe how the methodology is adapted when there are 'less-than' measurements.

Let *c _{ti}, i = *1

`y_t=text{median}{\c_{ti}, i=1 ...n_t}`

For all other biological effects, the annual index is the median log measurement:

`y_t=text{median}{\log(c_{ti}), i=1 ...n_t}`

The annual indices are modelled as:

`y_t=f(t)+\epsilon_t`

where *y _{t}* is the annual index in year

The form of *f*(*t*) depends on the number of years of data:

- 1-2 years
- no model is fitted as there are too few years for formal statistical analysis
- 3-4 years
- mean model
*f*(*t*) = µ - there are too few years for a formal trend assessment, but the mean level is summarised by µ and is used to assess status
- 5-6 years
- linear model
*f*(*t*) = µ + β*t* - the indices vary linearly with time; the fitted model is used to assess status and evidence of temporal change
- 7+ years
- smooth model
*f*(*t*) = smooth function of time - the indices vary smoothly over time; the fitted model is used to assess status and evidence of temporal change

A loess smoother is used to estimate the smooth function of time. The amount of
smoothing is controlled by the neighbourhood of annual indices that
is used to estimate each *f*(*t*) as *t* runs from 1 to *T*. A neighbourhood of 9,
for example, uses the 9 indices that are closest to *t* to estimate *f*(*t*).
A sequence of neighbourhoods are considered (7, 9, 11 up to *T*, if *T* is odd, or *T* + 1,
if *T* is even) with the final choice based on Akaike's Information Criterion
corrected for small sample size (AICc). However, if there is no evidence of nonlinearity in the data
(i.e. if the AICc of the linear model is lower than that of the best smoother) then the linear model
*f*(*t*) = µ + β*t* is used instead.

Linear regression is described by e.g. Draper & Smith (1998). Loess smoothers were developed by Cleveland (1979). The application of loess smoothers to contaminant time series is described by Fryer & Nicholson (1999).

Cleveland WS, 1979. Robust locally-weighted regression and smoothing scatterplots. Journal of the American Statistical Association 74: 829-836.

Draper NR & Smith H, 1998. Applied regression analysis, 3rd edition. Wiley

Fryer RJ & Nicholson MD, 1999. Using smoothers for comprehensive assessments of contaminant time series in marine biota. ICES Journal of Marine Science 56: 779-790.

Environmental status and temporal trends are assessed using the model fitted to the annual indices.

Environmental status is assessed by comparing a one-sided 95% confidence limit on the fitted value in the most recent monitoring year to the available assessment criteria. The upper confidence limit is used for most biological effects. However, the lower confidence limit is used for biological effects where high values indicate healthy organisms: scope for growth, glutathionine transferase, acetylcholine esterase activity and aminolevulinic acid dehydratase. If, for example, the upper (lower) confidence limit is below (above) the Background Assessment Concentration (BAC), then the mean index in the most recent monitoring year is significantly below (above) the BAC and levels are said to be 'at background'.

No formal assessment of status is made when there are only 1 or 2 years of data. However, an ad-hoc assessment is made by comparing the index (1 year) or the larger (smaller) of the two indices (2 years) to the assessment criteria.

Temporal trends are assessed for all time series with at least five years of data.
When a linear model has been fitted (i.e. when there are 5-6 years of data, or if there are 7+ years of
data and no evidence of nonlinearity), there is evidence of a temporal trend if the slope β of the
linear regression of *y _{t}* on

Fryer RJ & Nicholson MD, 1999. Using smoothers for comprehensive assessments of contaminant time series in marine biota. ICES Journal of Marine Science 56: 779-790.