Methods in Water Science and Technology Scientific research Cross validation of two different COD test kits (Kit with Hg and kit without Hg) Written by: Eric Clayderman CAZOLI December 2014 University of Stavanger Department of Mathematics and Natural Sciences 4036 Stavanger
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Methods in Water Science and Technology
Scientific research
Cross validation of two different COD test kits (Kit with Hg and kit without Hg)
Written by: Eric Clayderman CAZOLI
December 2014
University of Stavanger Department of Mathematics and Natural Sciences
4036 Stavanger
Abstract: COD measurements on COD standard solutions and wastewater samples
were done by using two different COD test kits (kit with Hg and kit without Hg). Data
obtained from both kits were analyzed by looking essentially at statistical parameter
mean X and standard deviation σ. The objective of this work was to compare the
analyzed data in order to check the cross validation of the two kits. Results of this
work showed that the two kits are the same when measuring COD standard
solutions, while they do not really overlap when measuring wastewater samples.
Key words: COD, wastewater, test kits, mean, cross validation
1. Introduction:
Chemical Oxygen Demand (COD) is a term used in both water and
wastewater treatment to measure the amount of a specified oxidant reacting with a
given sample under controlled conditions (Al-‐Momani, 2003). The diochromate ion
(Cr2O72-‐) is the specified oxidant in colorimetric method and its amount is
expressed in terms of its oxygen equivalence.
Under the presence of catalysts (sulphuric acid H2SO4, mercuric sulphate AgSO4 and
sulfamic acid H3NSO3), the dichromate (Cr2O72-‐) oxidizes organic material in a
sample after incubation of 2h at 150°C. This oxidation reduces Cr2O72-‐ (hexavalent)
into Cr3+ (trivalent). Each of these chromium species has a direct relationship with
During the statistical analysis, parameter mean X and standard deviation σ were
calculated. Table 3 and 4 show respectively the mean and the standard deviation of
COD values obtained from the two kits. The average COD concentrations of standard solutions and wastewater samples were subtracted by COD content of blanks.
Table 3: Average COD concentrations of standard solutions (C1, C2, C3) and wastewater samples
COD concentrations ( mgCOD/L)
Blank C1 C2 C3 Wastewater Hg 74 1485 498 128 467
Hg free 26 1510 508 131 439 Table 4: Standard deviation of COD values (σx)
C1 C2 C3 Wastewater Hg 9 3 3 374
Hg free 24 3 3 105
4.2.2. Rejection of data
By looking at the table 2, we can see that some of the COD concentrations of
wastewater samples look specious. The value 1303 mgCOD/L (from kit with Hg) and
the value 637 mgCOD/L (from kit without Hg) seem anomalously large. By applying
the Chauvenet´s criterion, we can decide the rejection of these two values.
Assuming provisionally all COD measurement of wastewater samples is
legitimate.
a. N=6 (1303, 409, 388, 400, 354, 392); the mean X is here 467 and the standard
deviation σx is 374. The difference between the suspect Xsus=1303 and the mean X=
467 is 836, or 2.2 standard deviations; that is,
Tsus= (xsus-‐x)/ σx = (1303-‐467)/374 = 2.2
Referring to the table in Appendix ii, the probability that a measurement will differ
from X by 2.2σx or more is:
Prob(outside 2.2σx) = 1-‐ Prob(inside 2.2σx)
= 1-‐ 0.972 = 0.028
In 6 measurements, I would expect to find 0.168 of one measurement as deviant as
the suspect result. Since 0.168 is less than the 0.5 set by Chauvenet´s criterion, I
should reject the suspect Xsus= 1303 mgCOD/L. So, the new mean and standard
deviation for COD of wastewater, which was measured by kit with Hg, would be
respectively 315 mgCOD/L and 21.
b. N=5 (441, 422, 637, 456, 354); the mean X here is 439 and standard deviation σx is
105. The difference between the suspect Xsus=637 and the mean X= 439 is 198, or
1.88 standard deviations; that is,
Tsus= (xsus-‐x)/ σx = (637-‐439)/105 = 1.88
Referring to the table in Appendix ii, the probability that a measurement will differ
from X by 1.88σx or more is
Prob(outside 1.88σx) = 1-‐ Prob(inside 1.88σx)
= 1-‐ 0.939 = 0.061
In 5 measurements, I would expect to find 0.305 of one measurement as deviant as
the suspect result. Since 0.305 is less than the 0.5 set by Chauvenet´s criterion, I
should reject the suspect Xsus= 637 mgCOD/L. So, the new mean and standard
deviation for COD of wastewater, which was measured by kit without Hg, would be
respectively 421 mgCOD/L and 48.
4.2.3. Correct estimator for all measurements
If we assume 95 % confidence for our measurements, the average COD for
our samples would be:
COD= X ± (σx/√n)*tα/2,n-‐1
where:
x: mean σx : standard deviation
n: number of measurements α: accepted error= 5%= 0.05
For 95% confidence, the real mean of COD (mg/L) for the standard solutions and the
wastewater sample are the following:
Conclusion: By looking at the real mean of COD for standard solutions, we can see
that the two test kits overlap. Therefore, we can say that the two tests are the same.
For the wastewater samples, we can see that the two kits almost overlap. The
reason, why they do not exactly overlap for wastewater samples, could be from the
subtraction of the COD concentrations of samples by the mean of the COD of blanks
that seem incorrect.
Reference:
Al-‐Momani, F. (2003). Combination of photo-‐oxidation processes with biological
treatment: Universitat de Barcelona. Association, A. P. H., Association, A. W. W., Federation, W. P. C., & Federation, W.
E. (1915). Standard methods for the examination of water and wastewater (Vol. 2): American Public Health Association.
Taylor, J. (1997). Introduction to error analysis, the study of uncertainties in physical measurements (Vol. 1).