Statistical methodology and calculations planned for the project PD Dr. habil. Steffen Uhlig Freie Universität Berlin 04.04.2000

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). 04.04.2000 Page no. 2

Ultimate goal Specification of an appropriate method for assessing the chemical status and of trend detection methods according to WFD requirements. 04.04.2000 Page no. 3

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. 04.04.2000 Page no. 4

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 04.04.2000 Page no. 5

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) 04.04.2000 Page no. 6

Detection of monotonic trends Nonparametric MK-Test Time series: 34 29 33 30 20 22 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, 22-30. S = 12-3 = 9 > critical value, i.e. there is downward trend 04.04.2000 Page no. 7

Detection of non-linear trends Proposal: Apply MK-Test to the series of differences Time series: 22 24 23 26 20 13 Series of differences: 22-24, 23-24, 26-23, 20-26, 13-20 -2 –1 3 –6 -7 3 positive backward differences 7 negative backward differences S = 7-3 = 4 < critical value, i.e. not significant. 04.04.2000 Page no. 8

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. 04.04.2000 Page no. 9

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). 04.04.2000 Page no. 10

Detection of trend reversal Idea no 3: Calculate smoother and use corresponding confidence band (Tibshirani/Hastie or Cleveland) 04.04.2000 Page no. 11

Some aspects of methodology Smoother: Hastie and Tibshirani (without outliers) 04.04.2000 Page no. 12

Some aspects of methodology The determination of the area may affect the outcome of trend analysis considerably 04.04.2000 Page no. 13

Some aspects of methodology Autocorrelation (=short term fluctuation) may cause statistical problems. 04.04.2000 Page no. 14

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. 04.04.2000 Page no. 15

Further effects to be investigated Seasonality Temporal aggregation or modelling of season Autocorrelation Temporal aggregation or specification of ACF 04.04.2000 Page no. 16

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) 04.04.2000 Page no. 17

Power analyses * Power of detecting 10% reduction within 5 years, under the assumption of independency. 04.04.2000 Page no. 18

Power function Depends on trend detection method sampling scheme (frequency and sites) homogenity of area under investigation 04.04.2000 Page no. 19