Upload
ngodang
View
225
Download
5
Embed Size (px)
Citation preview
GNIS - GEVES
Germination inter-laboratory test variability
and accuracy
D. Demilly(1) – B. de Goyon (2)
(1) SNES(2) GNIS-SOC
GNIS - GEVES
• Statistical analysis use in France for germination ring tests or referee tests
• Statistical analysis developed by Mrs J.J. Daudin and Ph. TrécourtFrom the department of Mathematics of the INA-PG
• Computer program developed by Mr de Goyon (SOC GNIS).
GNIS - GEVES
SUMMARY
I) Analysis of the Variability
II) Analysis of the Accuracy
Principles of the Barycentric Presentation
Examples of the using of the Barycentric Presentation
GNIS - GEVES
VARIABILITY ANALYSIS WITHIN
A LABORATORY
GNIS - GEVES
The objective of the variability analysis is to measure the fidelity
of the used methods, bystudying the variability of the results obtained within a given
laboratory.
To make this analysis about one or more types of germs, and in order to make the calculation easier, we
use an angular transformation
GNIS - GEVES
2 N ARCSINUS P× ×N = seeds Numbers by replication
P = Value ( % )
We know that, if the variability observed is only the variability of seeds sampling,
the expected value of the varianceof the random variable obtained with the above
transformation must be equal to 1( Angular Transformation )
GNIS - GEVES
( )1 2CHI
k r 1−
× −α ( )
α 2CHIk r 1× −
k = Samples Numbersr = Replications numbers
Degrees of Freedom for Chi Squarred Distribution = k x ( r -1 )
REJECTION REGION ACCEPTANCE REGION REJECTION REGION
0,072 1 3,116
LowerLimit
UpperLimit
EXPECTED
GNIS - GEVES
Seeds Number by replication : Rep1 Rep2 Rep3 Rep4 MEAN Upper Lower
Total Seeds : 400 Replications ( r) : 4 Samples (k) : 1
81% 87% 88% 89% 86% 89% 81%
22,4 24,04 24,34 24,65
Variance 1,013Standart deviation 1,007
TEST CONCLUSION 1 %Lower Limit
Upper Limit
0,024 1,013 4,279NS
TEST CONCLUSION 5 %Lower Limit
Upper Limit
0,072 1,013 3,116NS
EXPECTED
VALUE = 1
1,0130,0721
3,116Angular transformation
GNIS - GEVES
Seeds Number by replication : Rep1 Rep2 Rep3 Rep4 MEAN Upper Lower
Total Seeds : 400 Replications ( r) : 4 Samples (k) : 1
85% 79% 95% 90% 87% 95% 79%
23,49 21,90 26,91 24,88
Variance 4,521Standart deviation 2,126
TEST CONCLUSION 5 %Lower Limit
Upper Limit
0,072 3,116 4,521heterogeneous
TEST CONCLUSION 1 %Lower Limit
Upper Limit
0,024 4,279 4,521heterogeneous
EXPECTED
VALUE = 1
4,5210,0721
3,116
GNIS - GEVES
Seeds Number by replication : Rep1 Rep2 Rep3 Rep4 MEAN Upper Lower
Total Seeds : 400 Replications ( r) : 4 Samples (k) : 1
89% 87% 88% 88% 88% 89% 87%
24,55 24,04 24,34 24,34
Variance 0,045Standart deviation 0,212
TEST CONCLUSION 5 %Lower Limit
Upper Limit
0,045 0,072 3,116too Homogeneous
TEST CONCLUSION 1 %Lower Limit
Upper Limit
0,024 0,045 4,279NS
EXPECTED
VALUE = 1
0,045 0,0721
3,116
GNIS - GEVES
The variability analysis can be computed for several types of germs,
on the different replications ( r ) of only one sample
or on the different replications of all the samples ( k ).
GNIS - GEVES
ConclusionResults are generally within the accepted limits– Heterogeneous results are exceptional as laboratories check there results against ISTA compatibility table
– Too homogeneous results could happen when analysts harmonize their results between replicates
GNIS - GEVES
ANALYSIS OF THE ACCURACY
GNIS - GEVES
The analysis of the Accuracy must show if the results given by a laboratory are “as close as possible” to the reference
results.
The reference results are - the mean of the all laboratories,- the results of one laboratory, - the mean result from several laboratories chosen as reference.
GNIS - GEVES
PRINCIPLES OF THE BARYCENTRIC PRESENTATION
GNIS - GEVES
This analysis is carried out in two steps.
First
Analyse sample by sample the results of each laboratory to find specific deviations.
Second
Analysis of all the samples to find the general tendency of each laboratory,
and thus to appreciate accuracy.
GNIS - GEVES
THE BARYCENTRIC PRESENTATION
by SAMPLE
GNIS - GEVES
0 100NORMAL
0
100
ABNORMAL
0
100
UNGERMINATED SEEDS
GNIS - GEVES
0 100NORMAL
0
100
UNGERMINATED SEEDS
0
100
ABNORMAL
Lab 2
Lab 1 40 %
40 %
20 %
25 %
25 %
50 %
GNIS - GEVES
0
100
UNGERMINATED SEEDS
0 100NORMAL
0
100
ABNORMAL
Lab 2
Lab 1 40 %
40 %
20 %
25 %
25 %
50 %
MEAN
GNIS - GEVES
( )0 1 2 0 0P U P P1 10N
11N± × × − × +
−α
P0 : MEAN OF THE REFERENCE
N0 : TOTAL SEEDS NUMBER FOR THE REFERENCEN1 : TOTAL SEEDS NUMBER FOR EACH LABORATORY
P0 : MEAN OF THE REFERENCE
N0 : TOTAL SEEDS NUMBER FOR THE REFERENCEN1 : TOTAL SEEDS NUMBER FOR EACH LABORATORYU
21 α− : NORMAL LAW VALUE
Computation of a confidence interval
GNIS - GEVES
M
Band of Confidence for Normal
Band of Confidence for Abnormal
Band of Confidence for Ungerminated Seeds
A
B CNormal
Abnormal
UngerminatedSeeds
AREA OF CONFIDENCE FOR
NORMAL
ABNORMAL
UNGERMINATED SEEDS
GNIS - GEVES
0% 100%
100% 0%
0% 100%
Ungerminated Seeds
Abnormal
Anormal 76 %
24 %
GNIS - GEVES
ABNORMAL
A
B CNORMAL
UNGERMINATED SEEDS
0 %
24 %
24 %
0 %
100 %76 %
GNIS - GEVES
THE BARYCENTRIC PRESENTATION FOR SEVERAL SAMPLES
A global accuracy of the laboratories
GNIS - GEVES
Normal + Abnormal + Ungerminated = 100
For a laboratory and a given sample
E1 E2 E3
Normal + Abnormal + Ungerminated = Normal ref + Abnormal ref + Ungerminated ref
(Normal - Normal ref )+ ( Abnormal- Abnormal ref ) +(Ungerminated - Ungerminated ref ) = 0
+ + =0For a laboratory and all samples
Sum (E1)+sum (E2)+Sum(E3)=0
GNIS - GEVES
-1,33% 4,61%
5,13%
-3,28% 3,18%
UNGERMINATED SEEDS
ABNORMAL
NORMAL
-1,33% 4,61%
5,13%
-3,28% 3,18% 0 %
0 %
0 %
UNGERMINATED SEEDS
ABNORMAL
NORMAL
-1,33% 4,61%
* 9 - 22
* 8 - 17* 7 - 34
* 11* 32
5,13%
-3,28% 3,18% 0 %
0 %
0 %
UNGERMINATED SEEDS
ABNORMAL
NORMAL
-1,33% 4,61%
* 1
* 41
* 9 - 22
* 8 - 17* 7 - 34
* 11* 0 * 32
5,13% * 5* 73
-3,28% 3,18% 0 %
0 %
0 %
UNGERMINATED SEEDS
ABNORMAL
NORMAL
GNIS - GEVES
Examples of use of this
Statistical analysis in France
GNIS - GEVES
Example on Pea
GNIS - GEVES
Analyse sample by sample
GNIS - GEVES
0% 40%
40% 0%60% 100%68,71%
27,86%
3,43%
UNGERMINATED SEEDS
NORMAL
ABNORMAL
0% 40%
40% 0%60% 100%68,71%
27,86%
3,43%
UNGERMINATED SEEDS
NORMAL
ABNORMAL
0% 40%
* 67* 51
* 1* 120* 58* 124* 40* 114* 41* 2* 27* 34* 46* 0* 35* 29* 33* 79* 4* 13* 12* 7* 22
40% 0%60% 100%68,71%
27,86%
3,43%
UNGERMINATED SEEDS
NORMAL
ABNORMAL
0% 40%
* 72* 67* 51
* 14 * 1* 120
* 130 * 58* 124* 40* 114* 41* 2* 27* 34
* 61 * 46* 0* 123 * 35* 29
* 33* 79* 4* 13* 12* 7* 22
* 81
40% 0%60% 100%68,71%
27,86%
3,43%
UNGERMINATED SEEDS
NORMAL
ABNORMAL
Pisum ring test
29 licensed laboratories
Comparison with general mean
Sample P2 –confidence level 1/1000 – 6 outliers
GNIS - GEVES
0% 44%
* 58* 22* 3* 0* 61* 120* 114* 1* 35* 47* 76* 67* 62* 86* 115* 4* 13* 2* 40* 34* 46* 27* 121* 14* 123* 78* 119* 28* 126* 81* 95* 72* 55* 124* 106* 79* 10* 60* 64* 125* 29* 7
* 80
0%
100%66,50%
31,50%
2,00%
INATED SEEDS
NORMAL
ABNORMAL
Sample N° P1
Pisum ring test
43 laboratories
Comparison with general mean
Confidence level 1/1000
1 outlier
GNIS - GEVES
0% 39%
* 125* 120* 47* 115* 34* 55* 78* 40* 86* 7* 76* 124* 3* 58* 1* 35* 106* 0* 61* 27* 2* 72* 67* 14* 114* 46* 4* 22* 62* 79
* 80 * 13* 126* 123* 121* 60* 81* 119* 64* 10
* 28* 95
* 29
39% 0%
61% 100%71,75%
26,50%
1,75%
UNGERMINATED SEEDS
NORMAL
ABNORMAL
Sample N° P2
Pisum ring test
43 laboratories
Comparison with general mean
Confidence level 1/1000
2 outliers
GNIS - GEVES
0% 33%
* 78* 14* 114* 13* 0* 3* 61* 76* 4* 95
* 86 * 1* 119* 60* 126* 106* 72* 46* 62* 7* 58* 40* 115* 34
* 80 * 67* 35* 124* 29* 28* 10* 47* 2
* 121 * 125* 27* 64* 22* 120* 81* 55
* 79* 123
33% 0%
67% 100%77,00%
21,75%
1,25%
UNGERMINATED SEEDS
NORMAL
ABNORMAL
Sample N° P3
Pisum ring test
43 laboratories
Comparison with general mean
Confidence level 1/1000
5 outliers
GNIS - GEVES
Analyse of all samples
GNIS - GEVES
-1,33% 3,33%
* 3* 78* 58* 76* 86* 0* 61* 115* 1* 47* 114* 120* 40* 34* 14* 4* 35* 13* 62* 67* 46
* 22* 106 * 72* 2* 125* 126* 7* 124* 119
* 27 * 55
* 60* 121* 95
* 81* 28* 80* 123* 10* 79* 64
9,25% -7,25%* 29
-2,00% 8,58% 0 %
0 %
0 %
UNGERMINATED SEEDS
ABNORMAL
NORMAL
GNIS - GEVES
Example on Tomato :results according different
references
GNIS - GEVES
Tomato-Sample T5 – 5% level –reference global mean: 7 outliers
GNIS - GEVES
Sample T5 – 1/1000 level –reference global mean: 3 outliers
GNIS - GEVES
Sample T5 – 1/1000 level –ref. global mean except 95 : 2 outlier
GNIS - GEVES
Sample T5 – 1/1000 level –reference global lab « 0» : 7 outliers
GNIS - GEVES
-2,32% 9,14%
* 95
* 1
* 93
* 7* 9
* 3* 4* 8* 11
9,38% -2,56%* 0
-6,82% 4,88% 0 %
0 %
0 %
UNGERMINATED SEEDS
ABNORMAL
NORMAL
Tomato – global mean
1% - 7 outliers
GNIS - GEVES
-3,25% 11,70%
* 95
* 1
* 93
* 7* 9
* 3* 4* 8* 11
8,45% 0,00%* 0
-8,45% 3,25%0 % 0 %
0 %
UNGERMINATED SEEDS
ABNORMAL
Tomato – reference « lab 0 »
1% - 9 outliers !!!
GNIS - GEVES
-1,34% 9,69%
* 95
* 1
* 93
* 7* 9
* 3* 4
* 8* 11
10,36% -2,01%* 0
-8,36% 3,34% 0 %
0 %
0 %
UNGERMINATED SEEDS
ABNORMAL
NORMAL
Tomato – global mean except
93 & 95 – 1% - 6 outliers
GNIS - GEVES
Conclusion 1
• Representation : Usefulness of the barycentric representation for the technician to visualise the 3 values on one graph
GNIS - GEVES
Conclusion 2
• Computer program : Usefulness of a program that allow both – To edit standard tables and
representations, to print reports of the referee or ring tests.
– To make choice of reference and confidence level.
GNIS - GEVES
Conclusion 3
• Statistical evaluation based on the binomial distribution and not the variability of the data.