1. Statistical methodology and calculations planned for the project
PD Dr. habil. Steffen Uhlig
Freie Universität Berlin

2. quo data - quality management and statistics
Statistical methods and software packages for
data bases and statistical analyses of
monitoring programmes
analytical quality assurance (ring tests).
Expertise for
EC, CPCB (India), LAWA, VDLUFA, OSPAR, HELCOM, UNEP, ICES (WGSAEM, ACME).
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3. Ultimate goal
Specification of an appropriate method for assessing the chemical status and of trend detection methods according to WFD requirements.
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4. Procedure Identification of current practise
Preliminary analysis of 120 time series (= determinand/site combinations) as test data sets.
Detailed investigation of methods for assessing the chemical status.
Detailed investigation of methods for trend analysis.
Power analyses
Statistical criteria for defining an area.
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5. Assessing the chemical status 1
70 percentile of station means should not exceed the limit or
the percentage of station means exceeding the limit should be smaller than 30%
Calculation can be performed by Maximum Likelihood or simple replacement methods to deal with „less than“ results.
Criterion: Estimation error
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6. Assessing the chemical status 2
Aggregation by arithmetic or geometric mean, applying Maximum Likelihood or simple replacement methods to deal with „less than“ results.
Criteria:
Relative standard deviation of the level
Bias (eg. artificials trend caused by DL-reduction)
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7. Detection of monotonic trends
Nonparametric MK-Test
Time series:
3 positive backward differences
33-29, 30-29, 22-20
12 negative backward differences:
29-34, 33-34, 30-34, 20-34, 22-34, 20-29,
22-29, 30-33, 20-33, 22-33, 20-30,
S = 12-3 = 9 > critical value, i.e. there is
downward trend
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8. Detection of non-linear trends
Proposal: Apply MK-Test to the
series of differences
Time series:
Series of differences:
22-24, 23-24, 26-23, 20-26, 13-20
– –
3 positive backward differences
7 negative backward differences
S = 7-3 = 4 < critical value,
i.e. not significant.
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9. Detection of trend reversal
Idea no 1: Combine MK-Tests for linear and non-linear trends in order to check whether
level decreases eg. during the last 4 years whereas
in preceding years there was an increase in the level.
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10. Detection of trend reversal
Idea no 2: Apply non-linear regression analysis
Mean level in year t = µ(t) = at2 + bt + c
Determine the year with maximum level: tmax = -b/2a
and compare maximum level µ(tmax) with the current level (applying approximate statistical tests).
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11. Detection of trend reversal
Idea no 3: Calculate smoother and use corresponding confidence band (Tibshirani/Hastie or Cleveland)
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12. Some aspects of methodology
Smoother: Hastie and Tibshirani (without outliers)
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13. Some aspects of methodology
The determination of the area may affect the outcome of trend analysis considerably
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14. Some aspects of methodology
Autocorrelation (=short term fluctuation) may cause statistical problems.
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15. Some aspects of methodology
The choice of the aggregation method (arithmetic or geometric mean, median) may affect the outcome of the trend assessment. The geometric mean downweighs sub populations with higher concentrations.
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16. Further effects to be investigated
Seasonality
Temporal aggregation or modelling of season
Autocorrelation
Temporal aggregation or specification of ACF
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17. Statistical criteria For data given: Is there a significant trend?
For data in future: What is the probability that a given trend or a trend reversal will be significant? (Power function)
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18. Power analyses * Power of detecting 10% reduction within 5 years,
under the assumption of independency.
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19. Power function Depends on trend detection method
sampling scheme (frequency and sites)
homogenity of area under investigation
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