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8/12/2019 Ejemplo Grubbs y Cochran
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Challenge 9.2-1
Method p erformanc e stud y acc ordin g to DIN EN ISO 10304-1 (2009)
Method Determinat ion of b romide in industr ia l water
Laboratoriesn i 8 Replicates n k 4
Data set The number of replicates of each laboratory must be equal for the test!
n k \ ni 2 3 4 5 6
1 15.10 15.20 15.50 14.80 15.20
2 15.00 15.00 15.20 14.90 15.30
3 14.90 15.10 15.40 14.80 15.00
4 15.10 15.10 15.40 14.90 15.20
4 4 4 4 4
16 16 16 16 16
Stage 1: Preliminary data
15.025 15.1 15.375 14.85 15.175
0.0957 0.0816 0.1258 0.0577 0.1258
Stage 2: Test for outliers of type 1 by Grubbs rm (P = 95%, n k)
xmax 15.1 15.2 15.5 14.9 15.3
0.783 1.225 0.993 0.866 0.993
Result no OL no OL no OL no OL no OL
xmin 14.90 15.00 15.20 14.80 15.00
1.306 1.225 1.391 0.866 1.391
Result no OL no OL no OL no OL no OL
If outliers within the laboratories are checked remove them from the data se
Type 1 OL-free data set
n k \ ni 2 3 4 5 6
1 15.1 15.2 15.5 14.8 15.2
2 15 15 15.2 14.9 15.3
3 14.9 15.1 15.4 14.8 15
4 15.1 15.1 15.4 14.9 15.2
Stage 3: Recalculation of the laboratory mean values and the standard deviations
15.025 15.100 15.375 14.850 15.175
0.0957 0.0816 0.1258 0.0577 0.1258
Stage 4: Test for outliers of type 2 by Grubbs rm (P = 95%, n k)
*i
x
.*i
s
max,mr
min,mr
*L
x*
Lxs
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15.143 sxL 0.169934482
0.6927 0.2513 1.3669 1.7225 0.1900
Result no OL no OL no OL no OL no OL
If oultliers of the mean value of the laboratories are checked remove them from the
Type 2 OL-free data
n k \ ni 2 3 4 5 61 15.10 15.20 15.50 14.80 15.20
2 15.00 15.00 15.20 14.90 15.30
3 14.90 15.10 15.40 14.80 15.00
4 15.10 15.10 15.40 14.90 15.20
15.03 15.10 15.38 14.85 15.18
Stage 7: Test for reintegration of outliers of type 1
Copy the outlier within the laboratory checked in stage 2 into G74!xmax 15.375 xmin 14.850 14.50
Result Reintegration of the outlier of type 1 is not possible!
Stage 8 : Test for outliers of type 3 by Cochran
0.009166667 0.00666667 0.015833333 0.00333333 0.01583333
0.015833333 0.0725
0.2184 C(P= 99%,n k, n i) 0.5209
Result The laboratory with the maximal variance must not be rejected!
Stage 9 : Calculation of parameters on the basis of the data set free of outliers of type
15.025 15.100 15.375 14.850 15.175
s i 0.095742711 0.08164966 0.125830574 0.05773503 0.12583057
15.143 Laboratories n L 8 n total 31
SSxx 0.027500 0.020000 0.047500 0.010000 0.047500
SSSxx 0.214167
Repeatability standard deviation, s r
sr 0.0964966
CVr% 0.64 nmean 3.870967742
Reproducibilitx standard deviation, s R
0.055421007 0.00729601 0.215837674 0.34271267 0.00417101
0.8027941 0.1146849 0.02722143
sR 0.1911361
CVR% 1.26
Stage 10 : Recovery rate
99.62
*
ikOLx
C
2
is
2i
s
2maxs
ix
x
2b
s
2xxnii
2L
s
x
iLmr ,
ix
2i
s
2xxn ii
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Stage 11 : Est imat ion of bias by an t- test
1.669 t(P= 99%, df =n - 1) 2.750
Result The result is valid!
t
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Grubbs Table
3
15.2 mg/L 4
5
7 8 9 6
15.40 15.10 15.30 7
15.40 15.00 15.20 8
15.20 15.10 15.30 9
15.30 15.10 10
11
12
rm(95%, nk)
4 3 4 rm(95%, ni)
16 9 16
31 Cochran Tabl121
15.325 15.0666667 15.225 k
0.0957 0.0577 0.0957
2
1.463 3
4
15.4 15.1 15.3 5
0.783 0.577 0.783 6
no OL no OL no OL 7
8
15.20 15.00 15.10 9
1.306 1.155 1.306 10
no OL no OL no OL
table in B10:M17!
7 8 9
15.4 15.1 15.3
15.4 15 15.2
15.2 15.1 15.3
15.3 15.1
15.325 15.067 15.225
0.0957 0.0577 0.0957
2.032
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1.0727 0.4475 0.4843
no OL no OL no OL
data set table in B10:M17!
7 8 915.40 15.10 15.30
15.40 15.00 15.20
15.20 15.10 15.30
15.30 15.10
15.33 15.07 15.23
0.00916667 0.00333333 0.00916667
1 - 3
15.325 15.067 15.225
0.09574271 0.05773503 0.09574271
0.027500 0.006667 0.027500
0.13292101 0.01734701 0.02708767
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P = 95%
P=95%
1.153
1.463
1.672
1.822
1.938
2.032
2.11
2.176
2.234
2.285
1.463
2.032
P = 99%
Degrees of freedom
1 2 3 4 5 6 7
0.9999 0.995 0.9794 0.9582 0.9373 0.9172 0.8988
0.9933 0.9423 0.8831 0.8335 0.7933 0.7606 0.7335
0.9676 0.8643 0.7814 0.7212 0.6761 0.641 0.6129
0.9279 0.7885 0.6957 0.6329 0.5875 0.5531 0.5259
0.8828 0.7218 0.6258 0.5635 0.5195 0.4866 0.4608
0.8376 0.6644 0.5685 0.508 0.4659 0.4347 0.4105
0.7945 0.6152 0.5209 0.4627 0.4226 0.3932 0.3704
0.7544 0.5727 0.481 0.4251 0.387 0.3592 0.3378
0.7175 0.5358 0.4469 0.3934 0.3572 0.3308 0.3106
0.5209
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8
0.8823
0.7105
0.5897
0.5037
0.4401
0.3911
0.3522
0.3207
0.2945
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Data set for Challenge 9.2-1
Method Determination of brom ide in indus tr ial water
Data set
n k \ i 1 2 3 4 5 6
1 13.80 15.10 15.20 15.50 14.80 15.20
2 13.90 15.00 15.00 15.20 14.90 15.30
3 14.00 14.90 15.10 15.40 14.80 15.00
4 13.70 15.10 15.10 15.40 14.90 15.20
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15.2 mg/L
7 8 9
15.40 15.10 15.30
15.40 15.00 15.20
15.20 15.10 15.30
15.30 14.50 15.10
Recommended