I EUROSOLAN meeting | Eurasian Soil Laboratory Network | 2 - 5 October 2019 | Chişinău, Moldova. João Coutinho

1. First Meeting of the Regional Soil
Laboratory Network for Eurasia and
Europe
Good Laboratory Practices
Internal quality control by z-score approach
J Coutinho
University of Trás-os-Montes e Alto Douro
Portugal

2. Framework
At the end of the day, we are supposed to know if we
are confident about our the daily results:
• to be used in research projects, or;
• to be published in scientific journals, or;
• to be used to take political decisions, or;
• to be sold to our clients.

3. For that decision, we need Internal Quallity Control
(IQC) for each batch of samples and for each parameter
analised.

4. Z-score
Upperadmissible limit
Lower admissible limit
Upperwarning limit
Lower warning limit
The daily Internal QC may be based on the z-score (or standard score) , which
is a measure of how many standard deviations below or above the
population mean a raw score is.
Z-score or Shewhard chart

5. The daily Internal QC may conducted by the use of:
• a reference sample
expensive, especially for laboratories with high number of samples (30
g/day x 230 working days/year ≈ 7 kg/year!);
• internal standards samples
preferably 2-3 samples with different values for most of the analyzed
parameters.

6. In order to use a z-score (which is a dimensionless quantity), we need to
know the mean (m) and the standard deviation (s) of the population:
Z-score = (x – m) / s
or
Z-score = (x – m*) / s*

7. • For reference samples, both m and s are provided;
• For internal standards samples, we need to establish those values.
How?

8. Option A
establish both values of m and s in our own laboratory,
with 10 or more replications obtained with the same
timeframe of the normal analysis. Nevertheless, we need
to remember that we only get data related with
repeatibility (precision),
but we need to be aware that we are ignoring the
accuracy of the true value, since the value of m may be
bias. The values of one specific laboratory may have an
higher precision (low s) but they can be systematically
higher or lower than the true value.

9. Option B
to provide sample(s) for PT programs (at the national,
subregional ou regional scale) and use the same
sample(s) as internal standards.
This way, and free of charge, we can obtain values of m
and s (or m* and s * ) for our internal standards.

10. In some cases circunstancies we may want:
• to evaluate the ”quality” of the s to be used
and/or
• to establish an estimated value for s
Estimation of s
For this purpose, we can use the coeficient of variation (CV), also known as the relative
standard deviation (%RSD):
%RSD (or CV) = (s / m) x 100
If we establish an expected value for %RSD, then we can estimate the (new) value of s
sestimated = (%RSDexpected * m) / 100

11. How to calculate (or establish) the expected %RSD
Option A
for soil parameters expressed in SI units, the Equation of Horwitz(1) can be used
%RSDR = 2(1-0.5logC)
where where C is the concentration expressed as powers of 10 (e.g., 1 mg kg-1 = 10-6)
and %RSDR is the CV between-laboratories
(1) William Horwitz/FDA), 1982, Analytical Chemistry, 54 (1) 67-76

12. The between-laboratory %RSDR at
• 1 mg kg-1 is 16 % (24);
• 100 mg kg-1 is 8 %;
• 10 g kg-1 is 4 %;
• 100 g kg-1 is 2.8 %
The within-laboratory RSD (%RSDr)
should ordinarily be one-half to two-
thirds the %RSDR
Then, within-laboratory %RSDr at
• 1 mg kg-1 is about 8 to 10 %;
• ....
• 100 g kg-1 is about 1.4.to 1.9 %

13. How to calculate (or establish) the expected %RSD
Option B
for soil pH values (non-expressed in SI units)
We can consider the %RSDr value of 3.17% adopted by the
Association of Official Agricultural Chemists (AOAC), which equals the
median of %RSDr obtained in the validation of pH methods for 40
mineral, saline and organic soils by 53 laboratories(2).
(2) Y.P. Kalra (1995). Journal AOAC international, 78 (2): 310-324

17. flag system

18. • 1 value out of ±3 s: the probability is < 0,3%;
• 2 values in 3 consecutive values out of ±2 s: the normal probability was exceded;
• 4 values in 5 consecutive values out of ± 1 s: the normal probability was exceded;
• 15 consecutive values inside ±1 s: the actual standard deviation is lower than the
expected;
• 9 consecutive values in the same side of m: a sistematic deviation is occurrring;
• 8 consecutive values out of ± 1 s: evidence of a bimodal distribution;
• 6 consecutive values going up or going down: evidence of a nonrandom trend;
• 14 consecutive values alternating up and down: evidence of a time series affecting
the data;
Deviation tests recommended by ISO 8258
But z-scores are also usefull of internal QC in the medium-term evaluation

19. The decisions about daily or medium-term internal QC are
more sounded if we use 2 – 3 internal references

20. Thanks for your
attention