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Appendix J: Example of Determining Uncertainty Using Replicates

Table A12: Summary of duplicated samples
Sample Concentrations (mg/kg)
Arsenic Copper Lead
A 71 215 183
A2 72 206 182
Mean 71.5 210.5 182.5
B 52 180 181
B2 59 174 204
Mean 55.5 177 192.5
C 17 43 70.1
C2 20 49 73.6
Mean 18.5 46 71.85
D 42 127 84.2
D2 48 137 96.1
Mean 45 132 90.15

 

Table A13: Extracted precision data 11

Sample % of mean of pair
Arsenic Copper Lead
A 99.30 102.14 100.27
A2 100.70 97.86 99.73
B 93.69 101.69 94.03
B2 106.31 98.31 105.97
C 91.89 93.48 97.56
C2 108.11 106.52 102.44
D 93.33 96.21 93.40
D2 106.67 103.79 106.60
Mean (%) 100 100 100
Standard deviation (%) 6.6 4.3 4.9
95% error (%) 12 5.5 3.6 4.1
Guideline value (mg/kg) 30 370 300
Lower than guideline value: any value below (mg/kg) ... 13 28.4 356.7 287.6
Higher than guideline: any value above (mg/kg) ... 31.6 383.3 312.4
Indistinguishable from guideline (mg/kg) 28.4 to 31.6 357 to 383 287 to 312

 11 This method assumes that samples themselves were replicated at each location, so that the variation measured represents the sum of analytical and sampling variation.

12 The samples taken are not the site, but they do represent it. Student's t-test 95% error is the best method to establish whether or not we can say that the underlying population mean for the site (that a given sample was collected from) is distinguishable from the guideline value. Normality can be assumed as data here describe variation between the normalised replicates.

13 Example for arsenic: calculated as 30 mg/kg minus 5.5% of 30 mg/kg.