41
| 4 | 2011
Klinisk Biokemi i Norden
(
Fortsætter side 42)
estimate” and a surrounding uncertainty interval.
This is the major difference and advantage compared
to the concept of “total error” which retains a known
bias. The reader is referred to ISO-JCGM “GUM” [4],
a document from EURACHEM [5] and a recommen-
dation from CLSI [6] for details on estimation and use
of uncertainty.
Precision
Precision cannot be measured but imprecision can.
Imprecision is estimated from repeated measurements.
In the clinical laboratory it is important to consider
the “within run” and the “between run” variation. The
combined within and between variations represent the
combined (total) laboratory variation.
An experimental design for verification of impre-
cision claims (EP15) [3] requires that at least five
observations are made within each at least five runs
(
group). Examples of input and output tables are
shown in Tables 1 and 2.
The identification of variations is based on analysis
of variance (ANOVA), readily available in commonly
used spread-sheet programs and virtually in all stan-
dard statistics packages.
The ANOVA is designed to reveal a difference
between a set of groups and can be understood as an
extension of Student’s independent
t
-
test. In our appli-
cation it is used for “analysis of variance components”.
The calculations can be summarized with these
assumptions:
The
MS Within Runs
(
MS
w
)
is equal to the within
run variance i.e. the mean of the variances of the indi-
vidual runs. The
MS Between Runs
(
MS
b
),
contains
a component of the within run variation and needs
correction according to (2) to yield the “pure” between
run variance (
Var
b
):
������������������������������������������������(2)
where
n
0
is the number of results in each group. In case
the groups contain different numbers of observations
then the
n
0
needs to be estimated differently
1
.
The combined variance, i.e. the within laboratory
or intra-laboratory standard deviation (
sd
L
)
is then
����������������������������������(3)
It should be recognized that the number of observa-
tions is critical for the reliability of the results. The
minimum number in EP15 will give a reliable value
of the
MS
w
whereas the
MS
b
and thus the
sd
L
would
benefit from more runs.
Under certain conditions the
MS
w
can be less than
MS
b
and thus
V
arb
negative (2). Since this is not pos-
sible the
V
arb
is then conventionally set to
MS
w
.
It is not unusual that one or several results in a
series of measurements deviate from the majority
and may be suspected as an “outlier” but still belong
to the distribution of which we only see a small part.
As a first check it is recommended to perform the
calculations with and without the suspected outlier. If
the difference is not too big it is advised to retain the
value. Although there are statistical means to identify
outliers e.g. Grubbs test, removal of unexplained out-
liers should be considered carefully.
1
where N is the total number of results,
n
i
is the number of results in each run and
k
is the number
of runs. If the number of observations is the same in all runs
this becomes equal to the arithmetic mean. In many cases
the difference between the n0 and the arithmetic mean is
negligible.
Table 1
.
Results of a precision experiment.
Run 1 Run 2 Run 3 Run 4 Run 5
Result 1
140,00 138,00 143,00 143,00 142,00
Result 2
140,00 139,00 145,00 143,00 143,00
Result 3
141,00 137,00 149,00 143,00 142,00
Result 4
140,00 139,00 141,00 142,00 143,00
Result 5
140,00 138,00 144,00 142,00 141,00
Table 2
.
Output table.
SS
is the “Sum of squares”,
df
degrees
of freedom and
MS
Mean square.
ANOVA
Source of Variation
ss
df
MS
Between Runs
113.44
4
28.36
Within Runs
42.8
20
2.14
Total
156.24
24
