validation of the performance of process stream analyzer systems
TRANSCRIPT
PRACTITIONER’S REPORT
Validation of the performance of process stream analyzer systemswith nonparametric behavior
Aerenton Ferreira Bueno • Deborah Aparecida Flores Ozaki • Eduardo Barbosa •
Evandro Evangelista dos Santos • Maura Moreira Gomes • Patrıcia Hiromi Iida •
Soraia Cristina Almeida dos Santos • Fagner Geovani de Sa • Elcio Cruz de Oliveira
Received: 3 January 2014 / Accepted: 8 April 2014
� Springer-Verlag Berlin Heidelberg 2014
Abstract Literature describes several procedures based
on statistical principles to validate whether the degree of
agreement between the results produced by a stream ana-
lyzer system—systems for determining chemical and
physical characteristics by continual sampling, automatic
analysis, and recording or otherwise signaling of output
data—and those produced by an independent test mea-
surement procedure, which purports to measure the same
property, meets user-specified requirements. However,
these documents always consider that the data gathered
during validation procedure are normally distributed, and
this supposition it is not always true. The aim of this
manuscript is to develop four different procedures applied
to data with nonparametric behavior. The most represen-
tative validation procedure compares measures of position
and dispersion, using typical process samples, while the
less representative one compares only measures of posi-
tion, using a reference sample. These nonparametric data
are also treated using parametric statistics for comparison.
The results show that different conclusions can be reached
when the nonparametric data are treated as parametric. A
new Brazilian standard is being carried out based on this
subject, in order to complement the international standards.
Keywords Validation � Performance �Stream analyzer systems � Nonparametric data
Introduction
With the increasing industrial automation, off-line ana-
lyzers (bench or laboratory analyzers) have been replaced
by online analyzers or stream analyzer systems for the
following advantages: high speed, continuous monitoring
suitable for closed-loop control; better accuracy due to
absence of sample manipulation and human error, and less
exposition to risk and hazardous samples.
In this work, a total analyzer system design addresses the
chemical and physical properties of the process or product
stream to be measured, provides a representative sample, and
handles it without adversely affecting the value of the spe-
cific property of interest. Moreover, it includes a sample
loop, piping, hardware, a sampling port, sample conditioning
devices, analyzer unit instrumentation, any data analysis
computer hardware and software, and a readout display [1].
However, when a new stream analyzer is initially
installed, or after major maintenance has been performed, a
set of tests must be performed to demonstrate that the
analyzer meets the manufacturer’s specifications, the his-
torical performance standards, and the specification limits
set by the process being analyzed. These diagnostic tests
may require that the analyzer be adjusted so as to provide
predetermined output levels for certain certified reference
materials (CRMs) or compared with other reliable ana-
lyzers [1]. This practice is considered in this manuscript as
‘‘validation.’’
A. F. Bueno � D. A. F. Ozaki � E. Barbosa �E. E. dos Santos � M. M. Gomes � P. H. Iida �S. C. A. dos Santos � F. G. de Sa
Petroleo Brasileiro S.A., Rio de Janeiro, Brazil
F. G. de Sa � E. C. de Oliveira
Post-Graduation Metrology Programme, Metrology for Quality
and Innovation, Pontifical Catholic University of Rio de Janeiro,
Rio de Janeiro, RJ 22453-900, Brazil
E. C. de Oliveira (&)
Petrobras Transporte S.A., Av. Presidente Vargas,
328, Rio de Janeiro, RJ 20091-060, Brazil
e-mail: [email protected]
123
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DOI 10.1007/s00769-014-1053-8
Validation can be defined as a statistically quantified
judgment, so that the analyzer system or subsystem being
assessed can produce predicted primary test method results
with acceptable precision and bias performance when
compared with actual results from a primary test method
measurement system for common materials [2].
The literature quotes several international standards to
validate the performance stream analyzer systems [1, 3–5].
ASTM D6708 [6] and ASTM D7235 [7] are also cited for
data treating. However, all of them deal specifically with
Gaussian data.
In 2004, a nonparametric statistics study, focused to
sampling in atmospheric chemistry, has been carried out
[8].
The aim of this manuscript is to develop procedures to
validate the performance of the stream analyzer systems
with nonparametric behavior, because this is a common
situation in real-life data, for example, more than 60 % in
oil and gas online analyzers in Brazil.
Procedures
Some definitions are required:
• Reference Test (RT): Measurement procedure used in
the laboratory or portable analyzer to produce reliable
results under control, which can be compared with
those obtained by the process analyzer (PA);
• Process Typical Sample (PTS): Sample obtained from
the process stream so as to represent the typical
characteristics of the product;
• Reference Sample (RS): primary standard, mixing/
dilution of standards, CRMs or sample from interlab-
oratory comparisons;
• Validation Sample (VS): Sample used in the validation
procedure. It may be a PTS or RS whose parameter of
interest does not change significantly during the
validation procedure.
Validation is divided into two steps: initial validation
and continual validation. Continual validation is necessary
in order to guarantee that, after initial validation, the stream
analyzer systems continue in conformance to CRMs or
other reliable analyzers. Statistical process control (SPC)
chart monitoring is carried out with new production sam-
ples. However, continual validation is not treated in this
manuscript.
Initial validation
Initial validation is defined as a relationship between the
analyzer results and RT, RS, or PTS. Depending on the
approach, the initial validation can be carried out by the
combination of the RT, RS, and PTS.
The validation procedure should be selected according
to Fig. 1.
Revision of the nonparametric statistical analysis
Median absolute deviation (MAD)
This test applies to data set with behavior that departs from
normality and is an important robust univariate spread
measure [9]. In these situations, Grubbs’ test is not
recommended.
The median absolute deviation is considered as a mea-
sure of statistical dispersion. Moreover, the MAD is a
robust statistic, being more resilient to outliers in a data set
Fig. 2 Flow diagram for each procedure: Procedure A (a), Procedure
B (b), Procedure C (c), and Procedure D (d). a This procedure can be
considered as the best situation, because the validation is most
representative. The results from the analyzer for a set of typical
process samples are obtained, and these same samples are mandato-
rily tested by a reference test. Results are evaluated by specific
statistical tests, in order to compare measures of position (paired data)
and dispersion. b This procedure uses synthesized samples in the
laboratory or reference samples, when it is not possible to obtain
typical process samples. The validation process uses comparison of
position (unpaired data) and dispersion measures necessarily using a
reference test. c In this procedure, it is not possible to introduce a
validation sample into the analyzer, so dispersion measures cannot be
taken. Comparison of position measures (paired data) necessarily
using a reference test or typical process samples is carried out.
d When there is no reference test available, this procedure is
recommended. The confidence interval from a reference sample is
compared to the confidence interval derived from the process analyzer
only for position measures
c
Fig. 1 Selection of the validation procedure
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(a) (b)
(c) (d)
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than the standard deviation, mostly used in parametric
statistic. In the standard deviation calculations, the dis-
tances from the mean are squared, so large deviations are
weighted more heavily, and thus, outliers can strictly
influence it. In the MAD, the deviations of a small number
of outliers are irrelevant (Fig. 2).
The median value separates an equal number of higher
values from lower values of a set of data, a population, or a
probability distribution, from the lower half. It is recom-
mended when the data are not parametric.
A more logical approach to a robust analysis, focused
set of data with non-normal behavior, can be based on the
concept of a distance function. A robust estimate of the
variance [10] of xi values can be obtained from MAD,
Eq. (1):
MAD ¼ median xi �median ðxiÞj j ð1Þ
For the suspect result (lowest or higher value of a set of
data), x0, if x0 �median ðxiÞj j=MAD provides results
greater than 5, is rejected being considered as an outlier.
For instance, considering the data set (0.380, 0.400,
0.401, 0.403, 0.410, 0.411, 0.413), the median of these
numbers is 0.403, given in bold font. The absolute ordered
deviations calculated from the median are 0.000, 0.002,
0.003, 0.007, 0.008, 0.010, and 0.023. The MAD is the
median of these seven numbers, that is, 0.007, Eq. (1). For
the lowest value of the set one finds, |0.380–0.403|/
0.007 = 3.3, what is lower than the limit 5, and therefore,
this value is not considered an outlier [10].
Wilcoxon signed-rank test
The Wilcoxon signed-rank test is a nonparametric statisti-
cal hypothesis test used as an alternative to the paired
Student’s t test, t test for matched pairs, or the t test for
dependent sets of data when the population cannot be
assumed to be normally distributed [11].
For each pair set, the value of the first set of data is
clearly associated with the respective value of the second
set of data. These differences are sorted in ascending
order, and orders are given to them if they are different
from zero. If two or more differences are identical, the
average order used is that which would have been used if
the observations had differed. Considering a set of sam-
ples of which the same property is measured using two
different procedures, the difference between the mea-
surement results for each sample is evaluated and sorted
with increasing absolute value thus attributing order
numbers (excluding zero differences). These numbers
denote the rank Ri unless the absolute differences for two
or more samples are equal, when the average rank is
attributed to each of them. This is exemplified in Tables
1 and 2 with mass concentration values of zinc, deter-
mined by two different measurement procedures, for each
of eight samples of health food [10].
The ranking of these results presents an additional
worry, that of tied ranks, as 0.2, 0.4, and 0.7. In such cases,
it is worth verifying that the ranking has been done cor-
rectly by calculating the sum of all the ranks without regard
to sign, so each gets the average of those ranks, 1.5.
The sum of ranks of positive differences (in bold) is 7.5,
whereas the sum related to negative ranks amounts to 28.5.
A systematic difference between the data sets x2,i and
Table 3 Example of Wilcoxon rank-sum test
Measurementprocedure
Silverconcentration(lg mL-1)
Rank Measurementprocedure
Silverconcentration(lg mL-1)
Rank
2 7.7 1 1 9.8 6
2 8.0 2 2 9.9 7
2 9.0 3 1 10.2 8
1 9.5 4 1 10.5 9
2 9.7 5 1 10.7 10
Table 1 Measurement results of zinc mass concentration in eight
samples of health food (x2,i using EDTA titration, x1,i using atomic
spectroscopy) and their difference di
i x2,i (mg L-1) x1,i (mg L-1) sgndi |di| (mg L-1)
1 7.2 7.6 –1 0.4
2 6.1 6.8 –1 0.7
3 5.2 4.6 1 0.6
4 5.9 5.7 1 0.2
5 9.0 9.7 –1 0.7
6 8.5 8.7 –1 0.2
7 6.6 7.0 –1 0.4
8 4.4 4.7 –1 0.3
Sgn is the sign function
Table 2 Example of Wilcoxon signed-rank test applied to the data
presented in Table 1: ordering by absolute difference |di|
i x2,i (mg L-1) x1,i(mg L-1) sgndi |di| (mg L-1) Ri Risgndi
4 8.5 8.9 –1 0.2 1.5 –1.5
6 5.9 5.7 1 0.2 1.5 1.5
8 4.4 4.7 –1 0.3 3 –3
1 7.2 7.6 –1 0.4 4.5 –4.5
7 6.6 7.0 –1 0.4 4.5 –4.5
3 5.2 4.6 1 0.6 6 6
2 6.1 6.8 –1 0.7 7.5 –7.5
5 9.0 9.7 –1 0.7 7.5 –7.5
Bold fonts indicate positive differences di
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x1,i must be assumed if the smaller sum is below a critical
value, which for 8 pairs and a probability of 0.05 is 3 [10].
Obviously, the data of the example do not provide evidence
for a systematic difference between the two measurement
procedures.
Wilcoxon rank-sum test
The Wilcoxon rank-sum test is a nonparametric alternative
to the two set of data t test which is based solely on the
order in which the observations from the two sets of data
fall [12].
This statistical test proposes to compare mean values for
two groups (sizes n1 and n2) that are not correlated. The
variances of the groups should be evaluated if they are
statistically identical or different.
Let X11, X12,…, and X21, X22,…, be two independent
random sets of data of sizes n1 B n2 from the contin-
uous populations X1 and X2, that is, populations in
which a random variable is measuring a continuous
characteristic.
The test procedure is as follows. Arrange all n1 ? n2
observations in ascending order of magnitude and assign
ranks to them. If two or more observations are tied (iden-
tical), use the mean of the ranks that would have been
assigned if the observations differed.
Considering W1 as the sum of the ranks in the smaller set
of data, and W2 as the sum of the ranks in the other set of
data [13], then
W2 ¼ ððn1 þ n2Þ � ðn1 þ n2 þ 1Þ=2Þ �W1 ð2Þ
As an example [11], a sample photographic waste was
analyzed for silver by atomic absorption spectrometry, five
successive measurements giving values of 9.8, 10.2, 10.7,
9.5, and 10.5 lg mL-1, measurement Procedure 1, without
chemical treatment. After chemical treatment, the waste
was analyzed again by the same analytical technique, five
successive measurements giving values of 7.7, 9.7, 8.0, 9.9,
and 9.0 lg mL-1, measurement Procedure 2.
These data are analyzed in ascending order and ranked
as shown in Table 3.
The sum of the ranks for measurement Procedure 1 is
W1 = 4 ? 6 ? 8 ? 9 ? 10 = 37, and for the measure-
ment Procedure 2 is W2 = ((5 ? 5) � (5 ? 5 ? 1)/2) -
37 = 18.
Since neither W1 nor W2 is less than or equal to
W0.05 = 17 [13], there is not a statistically significant dif-
ference between both measurement procedures for a
confidence level of 95 %.
Test of Moses
This statistical test attempts to compare the variability
(dispersion) from two independent populations, when at
least one of them presents non-normal distribution [14].
The observations of each group are randomly distributed
to their respective subgroups m1 and m2.
The sum of the squares of the differences is calculatedP
D2ji ¼
PXi � X� �2
and sorted increasingly (progres-
sively, gradually), and orders are given. If two or more
observations are identical, the average of the orders due to
different observations is used, where �X is the average of all
Xi values. Note that the notationP
Dji2 represents the sum
of the squared difference scores of the ith subsample in
each Group j. Here, a subsample is a set of scores derived
from a sample.
The ranks of each group, R1 and R2, are separated into
their respective groups with their respective sums equal toP
R1 andP
R2, subsamples m1 and m2, scores k and
n = m�k.
Here, we use an example, Table 4, based on a result of
the small set of data, with each subsample comprised of
k = 2 scores, m1 = 3 subsamples for Group 1, and m2 = 3
subsamples for Group 2. Since n1 = n2 = 3�2 = 6, 12
Table 4 Numerical example of Test of Moses, 2 groups with 3 subsamples each
Subsample �X X � �Xð Þ X � �Xð Þ2P
X � �Xð Þ2¼P
D21i Rank
Group 1
1, 10 5.5 -4.5, 4.5 20.25, 20.25 40.5 4.5
10, 0 5.0 5.0, -5.0 25.00, 25.00 50.0 6
9, 0 4.5 4.5, -4.5 20.25, 20.25 40.5 4.5
Subsample �X X � �Xð Þ X � �Xð Þ2P
X � �Xð Þ2¼P
D22i Rank
Group 2
4, 4 4.0 0.0, 0.0 0.0, 0.0 0.0 1
5, 6 5.5 -0.5, 0.5 0.25, 0.25 0.5 2.5
5, 6 5.5 -0.5, 0.5 0.25, 0.25 0.5 2.5
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subjects are employed in the analysis. In this instance, it is
used a table of random numbers to select the scores for
each of the subsamples.X
R1 ¼ 4:5þ 6þ 4:5 ¼ 15 andX
R2 ¼ 1þ 2:5þ 2:5 ¼ 6:
U1, U2, and U are calculated as:
U1 ¼ m1 � m2 þm1 � ðm1 þ 1Þ
2�X
R1
¼ 3 � 3þ 3 � ð3þ 1Þ2
� 15 ¼ 0 ð3Þ
U2 ¼ m1 � m2 þm2 � ðn2 þ 1Þ
2�X
R2
¼ 3 � 3þ 3 � ð3þ 1Þ2
� 6 ¼ 9 ð4Þ
Ucalculated is the minimum value between U1 and U2:
Ucalculated ¼ min U1; U2ð Þ ¼ 0
As Ucalculated ¼ 0�Ucritical ¼ 0, there is not a statisti-
cally significant difference between the variances of
Groups 1 and 2.
Test of Bonett-Price [15]
This test is applied to data sets with nonparametric distri-
butions. In this situation, the confidence interval is based
on a linear function of medians of the population.
The median (Md) of the data set and estimation the
variance, varMd, are calculated by
varMd ¼ Y n�aþ1ð Þ � Y að Þ� ��
2z� �2
Y(i) represents the quantitative score of the response vari-
able in the position i (ordered).
a and z are tabulated, in function of the data number and
level of significance [15].
The confidence interval, CI, can be calculated by:
CI ¼ Md � za=2 varMdð Þ�A simple example is related to the salt concentration in
waste water, expressed in lg mL-1: 13.53, 28.42, 48.11,
48.64, 51.40, 59.91, 67.98, 79.13, and 103.5. The median,
Md, is 51.4. Referring to values of parameters for the Price–
Bonett variance estimate [15]: n ¼ 9; a ¼ 2 and z ¼ 2:064:
Y(9-2?1) = Y(8) = 79.13; Y(2) = 28.42.
Table 6 Comparing mean and median of ammoniacal nitrogen resultsfrom ten different samples by parametric and nonparametric tests
Process analyzer (PA) [mg L-1] Reference test (RT) [mg L-1]
8.6 10.4
3.7 4.2
2.1 2.5
2.3 2.1
0.9 1.1
1.3 1.4
0.8 1.2
0.8 1.0
0.9 1.2
0.8 0.9
Parametric statistics Nonparametric statistics
Paired t test Wilcoxon signed-rank test
tcalculated = 2.237\ tcritical = 2.262
Wcalculated = 4.00\ Wcritical = 8.00
There is not a statisticallysignificant differencebetween the means
There is a statistically significantdifference between the medians
Table 7 Precision evaluation of results from ten replicate measurements
of ammoniacal nitrogen concentration in the same sample by parametric
and nonparametric tests
Process analyzer (PA) [mg L-1] Reference test (RT) [mg L-1]
8.6 8.2
8.6 8.6
8.5 8.5
8.6 8.6
8.5 8.5
8.6 8.6
8.5 8.5
8.5 8.5
8.6 8.6
8.7 8.4
SWcalculated = 0.8021
\ SWcritical = 0.8420
SWcalculated = 0.7733
\ SWcritical = 0.8420
Non-normal distribution Non-normal distribution
Parametric statistics Nonparametric statistics
F-Fischer–Snedecor Moses
Fcalculated = 3.417
\ Fcritical = 3.179
Ucalculated = 11.00
[ Ucritical = 2.00
There is a statistically
significant difference
between the variances
There is not a statistically
significant difference
between the variances
Table 5 Comparing parametric and nonparametric tests
Aim/statistical test Normal
distribution
Non-normal
distribution
Outliers Grubbs’ test Median absolute
deviation (MAD)
Comparing means/medians Paired t test Wilcoxon signed-
rank test
Comparing means/medians
(unpaired samples)
Unpaired
t test
Wilcoxon rank-sum
test
Comparing dispersion
measures
F-Fischer–
Snedecor
Moses
Confidence interval t test Bonett-Price
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The variance estimator, varMd,
varMd ¼ Y n�aþ1ð Þ � Y að Þ� ��
2z� �2
¼ ð79:13� 28:42Þ=ð2� 2:064Þ½ �2¼ 150:91:
A 95 % confidence interval, CI ¼ Md � za=2 varMdð Þ� ¼51:4� 1:96ð150:91Þ� ¼ ð27:33; 75:47Þ.
Experimental
Four case studies, one for each procedure, are discussed in
this work.
Data were collected from Alberto Pasqualini Refinery,
Canoas, Brazil.
In the first study, ammoniacal nitrogen concentration in
effluent samples is determined by RT and PA. Validation is
performed using Procedure A. The process analyzer is GLI
International (IL, USA), model 750-500 ion selective
electrode whose work range is 0–20 mg L-1. The mea-
surement procedure is based on Standard Methods 4500.
In the second study, ethane amount of substance fraction
in the same sample hydrogen recycle is determined by RT
and PA. Validation follows Procedure B. The process
analyzer is a Yokogawa (Tokyo, Japan) chromatograph,
model GC 1000 Mark II, work range 0–1 mmol/mol. The
measurement procedure is correlated to UOP 539.
The next study involves flash point in diesel oil. The
process analyzer is an integrated flash point, Precision
Scientific Petroleum Instruments (IL, USA), model 45624,
work range 10–121 �C. The measurement procedure is
correlated with ASTM D93.
For the last study, propane amount of substance fraction
in a reference sample of hydrogen recycle is determined by
PA, validated by Procedure D and compared with the
certified result. The process analyzer is a Yokogawa
chromatograph model GC 1000 Mark II, work range
0–1 mmol/mol. The measurement procedure is correlated
with UOP 539.
Results and discussion
Nonparametric data from case studies are calculated by
both parametric and nonparametric tests, Table 5. Before
choosing one of these tests, it is necessary to assess whe-
ther or not the data follow a normal distribution. In this
work, the Shapiro–Wilk test, named as SW, is used to check
deviation from normality/normal distribution [16].
All calculations are conducted by Microsoft Excel, and
critical values are based on a confidence level of 95 %. No
value is considered as an outlier by Grubbs and MAD tests.
Case study: Procedure A
Comparison of mean and median is evaluated by ten dif-
ferent samples that are analyzed by PA and RT. The mass
Table 8 Precision and comparing mean and median evaluations of results from the same sample for ethane determination by parametric and
nonparametric tests
Process analyzer (PA) [mmol/mol] Reference test (RT) [mmol/mol]
0.102 0.102 0.103 0.102
0.102 0.102 0.102 0.102
0.103 0.102 0.102 0.102
0.103 0.102 0.102 0.102
0.103 0.102 0.102 0.102
0.103 0.102 0.102
0.103 0.102 0.102
0.102 0.102 0.102
SWcalculated = 0.591 \ SWcritical = 0.887 SWcalculated = 0.311 \ SWcritical = 0.866
Non-normal distribution Non-normal distribution
Parametric statistics Nonparametric statistics
F-Fischer–Snedecor Moses
Fcalculated = 2.98 [ Fcritical = 2.62 Ucalculated = 4.00 [ Ucritical = 1.00
There is a statistically significant difference between the
variances
There is not a statistically significant difference between the
variances
Unpaired t test Wilcoxon rank-sum test
tcalculated = 1.656 \ tcritical = 2.056 Wcalculated = 3.05 [ Wcritical = 1.96
There is not a statistically significant difference between the
means
There is a statistically significant difference between the
medians
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concentrations are shown in Table 6. Shapiro–Wilk test
for the differences of each pair, between PA and RT:
SWcalculated = 0.7253 \ SWcritical = 0.8420. The distribu-
tion is non-normal.
Precision is evaluated by comparing ten results of the
same sample that is analyzed either by PA or RT. The mass
concentrations and the results treated by parametric and
nonparametric tests are shown in Table 7.
Case study: Procedure B
Precision and mean/median are evaluated by the same
sample. PA and RT use sixteen and thirteen replicates,
respectively. The amount of substance, comparing preci-
sion (variance) and mean/median evaluations by
parametric and nonparametric tests, is shown in Table 8.
Case study: Procedure C
Only, comparison of mean and median is evaluated in this
procedure. Ten different samples analyzed by PA and RT are
compared. The flash points and comparison of mean and
median by parametric and nonparametric tests are shown in
Table 9. Shapiro–Wilk test for the differences of each pair,
between PA and RT: SWcalculated = 0.8294 \ SWcritical =
0.8420. The distribution is non-normal.
Case study: Procedure D
Only, comparison of mean and median by parametric and
nonparametric tests is evaluated in this procedure. A con-
fidence interval derived from twenty-three replicates of a
reference sample analyzed by PA is compared with the
certified value. The amount-of-substance fraction is shown
in Table 10.
Conclusions
New procedures for performance validation of process
stream analyzer systems have been developed to deal with
nonparametric data. The procedures can be applied to all
common situations faced in that activity, such as non-
availability of a reference test, impossibility of introduction
of the validation sample in the analyzer, and non-avail-
ability of a typical process sample. From the studied
Table 9 Comparison of mean and median of flash point results from ten different
samples by parametric and nonparametric tests
Process analyzer (PA) [�C] Reference test (RT) [�C]
40.0 39.0
40.0 41.0
41.0 41.0
41.0 41.0
40.5 40.0
39.5 39.5
43.0 43.0
43.0 43.0
41.5 41.5
42.0 41.0
Parametric statistics Nonparametric statistics
Paired t test Wilcoxon signed-rank test
tcalculated = 0.818 \ tcritical = 2.262 Wcalculated = 4.00 \ Wcritical = 8.00
There is not a statistically
significant difference between the means
There is a statistically significant
difference between the medians
Table 10 Comparison of mean and median of replicates of a reference sample for propane determination by parametric and nonparametric tests
Process analyzer (PA) [mmol/mol]
0.3011 0.3030 0.3041
0.3020 0.3030 0.3040
0.3020 0.3030 0.3052
0.3030 0.3030 0.3050
0.3029 0.3030 0.3050
0.3030 0.3030 0.3060
0.3030 0.3030 0.3061
0.3030 0.3030
SWcalculated = 0.8531 \ SWcritical = 0.9140
Non-normal distribution
Parametric statistics Nonparametric statisticst test Bonett-Price
Process Analyzer (PA) 0.3029–0.3040 0.3025–0.3035
Reference Sample (RS) 0.3037–0.3043 0.3037–0.3043
There is not a statistically significantdifference between the means
There is a statistically significantdifference between the medians
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examples, it is possible to observe that when parametric
statistics are applied to nonparametric data, different
results can be obtained, leading to wrong conclusions,
which highlight the importance of the use of the right
statistics in each case. This manuscript can be very useful
for readers to understand better this subject given that
international standards do not foresee and deal with it. In
2014, this study will be part of a new Brazilian standard in
order to cover this deficiency.
Acknowledgments This work was supported by Petrobras, and the
original idea and the meetings to elaborate it were sponsored by
Marcia Beatriz Ruiz Del Frari, manager from Products Engineering
and Oil Stockpiling of the Downstream-Refinery.
References
1. ASTM D 3764 (2009). Standard practice for validation of the
performance of process stream analyzer systems. American
Society for Testing and Materials, West Conshohocken
2. ASTM D4175 (2009) Standard terminology relating to petro-
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