ISO 3086:2006

INTERNATIONAL ISO
STANDARD 3086
Fourth edition
2006-04-15
Iron ores — Experimental methods
for checking the bias of sampling
Minerais de fer — Méthodes expérimentales de contrôle de l'erreur
systématique d'échantillonnage

Reference number
©
ISO 2006
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ii © ISO 2006 – All rights reserved

Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Principle. 2
5 General conditions . 2
6 Sampling and sample preparation methods. 2
6.1 Sampling. 2
6.2 Sample preparation . 2
7 Analysis of experimental data . 3
7.1 Computation of the differences. 3
7.2 Determination of the mean and the standard deviation of the differences . 3
7.3 Test for outliers – Grubbs' test. 3
7.4 Selection of data for use in statistical test for bias. 5
7.4.1 Consideration of outliers whose causes are assignable. 5
7.4.2 Consideration of outliers whose causes are not assignable. 5
7.4.3 Consideration of amount of data remaining . 5
7.5 Statistical test for bias. 5
7.5.1 Determination of the confidence interval for d . 5
7.5.2 Interpretation of confidence interval . 6
8 Test report . 7
Annex A (normative) Flowsheets of the statistical analysis. 8
Annex B (informative) Numerical examples of experiments. 11

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 3086 was prepared by Technical Committee ISO/TC 102, Iron ore and direct reduced iron, Subcommittee
SC 1, Sampling.
This fourth edition cancels and replaces the third edition (ISO 3086:1998), which has been technically revised.

iv © ISO 2006 – All rights reserved

INTERNATIONAL STANDARD ISO 3086:2006(E)

Iron ores — Experimental methods for checking the bias of
sampling
1 Scope
This International Standard specifies experimental methods for checking the bias of sampling of iron ores,
when sampling is carried out in accordance with the methods specified in ISO 3082, having as reference a
stopped-belt sampling method.
It is recommended that an inspection of the mechanical sampling system be carried out before conducting
bias testing.
Sampling systems not completely in accordance with ISO 3082 are not always expected to be biased.
Therefore, bias checking may be done when there is some disagreement about the importance of some
departure from the conditions of ISO 3082. If one party argues that the bias is likely to be substantial under
some particular set of conditions then bias testing should mostly be done when those conditions apply.
NOTE The method for analysis of experimental data described here may also be applied:
a) for checking the bias of sample preparation of iron ores, having as reference the methods for sampling preparation
according to ISO 3082;
b) for checking the bias of size distribution of iron ores by sieving, having as reference the hand sieving methods
according to ISO 4701;
c) for checking a possibly significant difference in the results obtained from the samples of one lot collected at different
places, for example, a loading point and unloading point.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3082:2000, Iron ores — Sampling and sample preparation procedures
ISO 3085:2002, Iron ores — Experimental methods for checking the precision of sampling, sample
preparation and measurement
ISO 11323:2002, Iron ore and direct reduced iron — Vocabulary
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 11323 apply.
4 Principle
The results obtained from the method to be checked (referred to as method B) are compared with the results
of a reference method (referred to as method A) which is considered to produce practically unbiased results,
from technical and empirical viewpoints.
In the event of there being no significant difference, in a statistical sense, between the results obtained by
method B and method A, method B may be adopted as a routine method. This difference is assessed by
comparing a 90 % confidence interval for the true average bias with the relevant bias, δ (see 5.2).
5 General conditions
5.1 The number of paired sets of measurement shall not be less than ten. The number of further tests
required depends on the results of the outlier test and of the statistical analysis of the confidence interval for
the true average bias, based on at least ten paired sets.
NOTE A paired set of measurement is a paired measurement data of samples, which are sampled by methods A and
B, and prepared and measured in the same way, for identical material.
5.2 The relevant bias, δ, which is considered large enough to justify the likely expense of reducing the
average bias, shall be decided beforehand. As a guide, δ is likely to be less than σ , the standard deviation
SPM
for sampling, sample preparation and measurement, determined according to ISO 3085.
NOTE If the experiment is aimed at checking sample preparation only, the value of δ is likely to be less than σ ,
PM
determined according to ISO 3085.
5.3 Quality characteristics, such as total iron content, moisture content, size distribution and physical
properties, may be used.
6 Sampling and sample preparation methods
6.1 Sampling
The reference method, method A, for checking the bias of sampling is a stopped-belt sampling method in
accordance with ISO 3082.
Method A: take each increment from the full width and thickness of the ore stream on the stopped
conveyor at a specified place, for a length of belt more than three times the nominal top size or 30 mm,
whichever is the greater.
The method to be checked, method B, carried out according to ISO 3082 as far as possible, shall be
compared with method A for the same material.
Method B: sampling methods, such as sampling from moving conveyors with a mechanical sampler and
sampling during the transfer to or from ships and wagons, are examples of method B.
Samples from Methods A and B shall be taken as close together as possible. This is particularly important for
ore streams which are known to be variable.
6.2 Sample preparation
6.2.1 Increments obtained from one lot, in accordance with methods A and B, are made up into two gross
samples, A and B.
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6.2.2 The gross samples, A and B, are subjected, in the same manner, to sample preparation as specified
in ISO 3082, and tested as specified in the relevant International Standards separately, and a pair of
measurements obtained.
6.2.3 The above procedure is performed on ten or more lots (see 5.1).
When increments for methods A and B can be taken from closely adjacent portions of the ore, it is
recommended that sample preparation and testing be carried out on individual increments or on combinations
of a small number of adjacent increments. This allows comparisons of ten or more pairs of measurements to
be made more quickly than if measurements were only made on entire lots. The above comparison of
measurements should be made on pairs of increments taken from several lots, preferably of the same type of
ore. However, it is not permitted to combine a number of paired results, originating from both increments and
gross samples. It should be either a number of pairs from increments or from gross samples.
NOTE Given the cost and inconvenience of stopped-belt sampling, it is generally economic to conduct sample
preparation and measurement in duplicate and with great care so that the number of stopped-belt samples might be
reduced.
7 Analysis of experimental data
NOTE The procedures described in 7.1 to 7.5 are also shown in the form of a flowsheet in Annex A (normative).
7.1 Computation of the differences
7.1.1 Denote measurements obtained in accordance with methods A and B, by x and x , respectively.
Ai Bi
When sampling preparation and measurement have been conducted in duplicate, these measurements will be
averaged.
7.1.2 Calculate the difference, d , between x and x using the equation:
i Ai Bi
dx=−x i= 1, 2, .k (1)
iiBAi
where k is the number of paired sets of measurements.
7.2 Determination of the mean and the standard deviation of the differences
7.2.1 Calculate the mean of the differences, d, with one decimal place more than that used in the
measurements themselves:
dd= (2)
∑ i
k
7.2.2 Calculate the sum of squares, SS , and the standard deviation of the differences, S , with one decimal
d d
place more than that used in the measurements themselves:
SS=−dd (3)
()
di i
∑∑
k
SSd
S = (4)
d
(1k−)
7.3 Test for outliers – Grubbs' test
7.3.1 Sort d into ascending order.
i
7.3.2 Calculate the Grubbs’ test statistics G and G , using the following equations:
k 1
dd−
k
G = (5)
k
S
d
dd−
G = (6)
S
d
where
d is the largest value of d ;
k i
d is the smallest value of d ;
1 i
7.3.3 Choose the larger of G and G .
k 1
7.3.4 Compare the larger of G and G with the critical value for Grubbs' test at the 5 % significance level
k 1
according to Table 1.
Table 1 — Critical values for Grubbs' outlier test
Critical value Critical value Critical value
k k k
(5 %) (5 %) (5 %)
6 1,887 12 2,412 18 2,651
7 2,020 13 2,462 19 2,681
8 2,126 14 2,507 20 2,709
9 2,215 15 2,549 21 2,733
10 2,290 16 2,585 22 2,758
11 2,355 17 2,620 23 2,781
NOTE Critical values for Grubbs’ test for a wider range of numbers of observations, and for additional significance
levels, are given in Grubbs, F. E. and Beck, G. (1972) Extension of sample sizes and percentage points for significance
tests of outlying observations, Technometrics 14, pp. 847-854.
7.3.4.1 If the larger of G and G is less than or equal to the critical value, conclude that there is no outlier.
k 1
Proceed with 7.5.
7.3.4.2 If the larger of G and G is larger than the critical value:
k 1
7.3.4.2.1 If the larger is G , conclude that the largest value of the difference, d , is an outlier.
k k
7.3.4.2.2 If the larger is G , conclude that the smallest value of the difference, d , is an outlier.
1 1
7.3.5 Exclude the outlier d , repeat the procedure described in 7.2 to 7.3.3.
i
7.3.6 Compare the larger of G and G with the critical value for Grubbs' test at 5 % significance level
k 1
according to Table 1.
7.3.6.1 If the larger of G and G is less than or equal to the critical value, conclude that there is no outlier
k 1
and proceed with 7.4.
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7.3.6.2 If the larger of G and G is larger than the critical value:
k 1
7.3.6.2.1 If the larger is G , conclude that the largest value of the difference, d , is an outlier.
k k
7.3.6.2.2 If the larger is G , conclude that the smallest value of the difference, d , is an outlier.
1 1
7.3.7 If at least 60 % of the initial set of data remain, proceed with 7.3.5.
7.3.8 If not, stop the outlier test, reinstate all outliers and proceed with 7.5.
7.4 Selection of data for use in statistical test for bias
7.4.1 Consideration of outliers whose causes are assignable
Once outliers have been detected by Grubbs' test, consideration should be given to assignable causes for
those outliers, such as change in the level of moisture, partial blockage of a cutter opening, or changes in
characteristics of the material being sampled.
For each outlier whose cause can be determined with reasonable confidence: If the cause is likely to occur in
the future then reinstate the outlier, but if the cause is not likely to occur in the future then exclude the outlier.
7.4.2 Consideration of outliers whose causes are not assignable
If the cause of an outlier could not be determined with reasonable confidence then the outlier should be
excluded.
7.4.3 Consideration of amount of data remaining
If at least 10 paired sets of measurements remain, proceed with 7.5. If not, carry out more sampling and
testing to complete at least 10 paired sets of measurements, reinstate the outliers excluded, except those
which have an assignable cause and are not likely to occur in the future, and repeat 7.1 to 7.4 since
differences previously classified as outliers may or may not be found to be outliers when Grubbs' test is
applied to the larger set of data.
7.5 Statistical test for bias
7.5.1 Determination of the confidence interval for d
7.5.1.1 Calculate the mean and standard deviation of the differences which have not been rejected as
outliers.
7.5.1.2 Calculate the lower limit of the confidence interval LL and the upper limit of the confidence interval
UL with the same number of decimal places of that used in the measurements themselves, using the
equations:
S
d
LL=−dt (7)
k
S
d
UL=+dt (8)
k
where
t is the value of Student’s t distribution for (k − 1) degrees of freedom and is given in Table 2;
k is the number of paired sets of measurements which have not been rejected as outliers.
Table 2 is prepared in such a way that when entering with a number of paired sets of measurement, k, the
corresponding t value has already (k − 1) degrees of freedom.
7.5.2 Interpretation of confidence interval
Plot on a horizontal scale, with 0 (zero) in the centre, the values of LL, UL, − δ and + δ.
Check if the interval between LL and UL is entirely contained in the interval between − δ and + δ.
If this happens, any bias is not large enough to justify the likely expe
...