Anders Bignert, Dep. of Contaminant Research 06.10.27

Randomization and stratification Randomization and stratification — — a model analysis at different a model analysis at different

variation scenariosvariation scenarios

Swedish Museum of Natural History

TidsserierCB-153, ug/g lipid w., guillemot egg

St Karlson(tot)=148,n(yrs)=15

0

2

4

6

8

10

12

14

16

18

88 90 92 94 96 98 00 02

m=5.15 (4.18,6.35)slope=-8.0%(-9.7,-6.3)SD(lr)=.13,2.4%,10 yrpower=1.0/.86/4.7%y(02)=2.95 (2.57,3.38)r2=.89, p<.001 *tao=-.87, p<.001 *SD(sm)=.18, n.s.

pia - 03.11.26 09:27, 153u

Timeseries

Pow

er

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

slope %

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

pia - 03.09.15 18:05, cur035a

SD(lr) = 0.35

Power as a function of slope (annual change in %) at log-linear regression analysis at a residual standard deviation on a log-scale of 0.35, assuming normally distributed residuals. The graphs, from left to right, represent sampling every, every-second, third and fourth year, respectively based on Monte Carlo simulations at 10,000 runs.

Sampling frequency

Sampling period = 12 years

Spatial monitoring

Objectives?

• Estimate mean and variance

• Regional differences

• Spatial trends

• Level in relation to class limit

Figur II. Variogram som visar hur skillnaden mellan prov (CB-118, pg/g färskvikt i strömmings muskel från Bottenhavet) ökar med ökande avstånd.

Sem

ivar

ainc

e (%

)

.0

.5

1.0

1.5

2.0

2.5

Distance (km) 0 25 50 75 100 125 150 175 200 225 250 275

pia - 06.10.21 20:13, pol

Sample variogram

< 2.5

2.5 - 5.0

5.0 - 7.5

7.5 - 10

10 - 15

Pb ug/g dry wt.

Lead, 2000

TISS - 02.09.26 13:11, pbm00

< 2.5

2.5 - 5.0

5.0 - 7.5

7.5 - 10

10 - 15

> 15

Pb ug/g dry wt.

Lead, 1990

TISS - 02.09.26 13:14, pbm90

2003, NB64P

n of

sp

ecie

s

0

2

4

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16

18

n of stations

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

pia - 04.02.29 00:13, ks1

N of species – n of samples (nets)

Randomization technique

Sampling design

TISS - 05.03.20 00:58, 090100

Random design

TISS - 06.08.18 08:54, fig1b

Unaligned square lattice design

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23

24

25

TISS - 02.03.16 22:51, 6aln

Sobol sequence

TISS - 06.08.17 16:06, m111

CV = 10%

1 1 1

0

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100

0 5 10 15 20 25 30 35 0

5

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20

25

0 5 10 15 20 25 30 35

pia - 06.08.17 14:48, p111

Distance to class limit:

25, 15, 10 , 5%

TISS - 06.08.17 17:10, ts111_20

CV=20%, normal distributed

CV = 20%

0

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60

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80

90

100

0 5 10 15 20 25 30 35 40 45 0

5

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15

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25

30

0 5 10 15 20 25 30 35

pia - 06.08.17 17:20, p111_20

Distance to class limit:

30, 25, 20, 15, 10%

10 > 34

TISS - 06.08.18 10:40, ts121_20

CV=20%, Log-normal distribution

CV = 20%, log-normal distr.

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100

0 5 10 15 20 25 30 35 40 45 50 0

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0 5 10 15 20 25 30 35 40 45 50

pia - 06.08.18 10:54, p121_20

Distance to class limit:

30, 25, 20, 15, 10%

34 > 50

TISS - 06.04.01 17:14, 090603

TISS - 06.04.10 07:24, ts1

75 > 53

N of samples vs chance to go below limit2 1 1

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70

pia - 06.04.11 17:03, p211

random sampling

N of samples vs chance to go below limit2 1 3

0

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20

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60

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80

90

100

0 10 20 30 40 50 60

pia - 06.04.11 16:56, p213

Sobol sequence

TISS - 06.04.11 00:56, ts101TISS - 06.04.11 13:35, ts311

N of samples vs chance to go below limit3 1 1

0

10

20

30

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50

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80

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100

0 20 40 60 80 100

pia - 06.04.11 16:44, p311

random sampling

N of samples vs chance to go below limit3 1 3

0

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80

90

100

0 10 20 30 40 50 60

pia - 06.04.11 16:30, p313

”Stratified” sampling

100 > 65

PCBTCDD eqv.

100 km

< 2

2 - 2.5

2.5 - 3

3 - 3.5

> 3.5

pg/g w.w.

TISS - 05.05.04 16:36, 1pqsmpol

PCBTCDD eqv.

100 km

< 2

2 - 2.5

2.5 - 3

3 - 3.5

pg/g w.w.

TISS - 06.08.18 14:11, ts411_10

0

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0 5 10 15 20 25 30 35 0

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35

0 5 10 15 20

pia - 06.08.18 15:33, p411

35% (normally distributed) variation were added (> total variation = 39 %)

True mean = 2.5 pg/g. Distance to 4.0, 3.5 and 3.0 pg/g (37.5%, 28%, 17%)

Tolerance limit

91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

121 122 123 124 125 126 127 128 129 130 131 132 133 134 135

136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

151 152 153 154 155 156 157 158 159 160 161 162 163 164 165

166 167 168 169 170 171 172 173 174 175 176 177 178 179 180

TISS - 04.09.23 18:50, 0502b

Afla-toxines in figs

TISS - 02.12.02 09:40, cl3dax05

PCDD/DF - TEQ

Herring, geometric mean

Muscle

TISS - 02.12.02 09:45, cl3dbx05

PCDD/DF- TEQ Herring, 95% conf. int.

Muscle

TISS - 02.12.02 09:55, cl3dcx05

PCDD/DF- TEQ Herring, 95% pop int.Muscle