Germination inter- laboratory test variability and accuracy · Germination inter-laboratory test...

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).

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SUMMARY

I) Analysis of the Variability

II) Analysis of the Accuracy

Principles of the Barycentric Presentation

Examples of the using of the Barycentric Presentation

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VARIABILITY ANALYSIS WITHIN

A LABORATORY

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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

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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 )

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( )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

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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


Upper Limit

0,072 1,013 3,116NS

EXPECTED

VALUE = 1

1,0130,0721

3,116Angular transformation

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85% 79% 95% 90% 87% 95% 79%

23,49 21,90 26,91 24,88



Upper Limit

0,072 3,116 4,521heterogeneous


Upper Limit

0,024 4,279 4,521heterogeneous

EXPECTED

VALUE = 1

4,5210,0721

3,116

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89% 87% 88% 88% 88% 89% 87%

24,55 24,04 24,34 24,34



Upper Limit

0,045 0,072 3,116too Homogeneous


Upper Limit

0,024 0,045 4,279NS

EXPECTED

VALUE = 1

0,045 0,0721

3,116

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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 ).

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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

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ANALYSIS OF THE ACCURACY

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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.

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PRINCIPLES OF THE BARYCENTRIC PRESENTATION

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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.

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THE BARYCENTRIC PRESENTATION

by SAMPLE

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0 100NORMAL

0

100

ABNORMAL

0

100

UNGERMINATED SEEDS

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0 100NORMAL

0

100

UNGERMINATED SEEDS

0

100

ABNORMAL

Lab 2

Lab 1 40 %

40 %

20 %

25 %

25 %

50 %

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0

100

UNGERMINATED SEEDS

0 100NORMAL

0

100

ABNORMAL

Lab 2

Lab 1 40 %

40 %

20 %

25 %

25 %

50 %

MEAN

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( )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

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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

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0% 100%

100% 0%

0% 100%

Ungerminated Seeds

Abnormal

Anormal 76 %

24 %

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ABNORMAL

A

B CNORMAL

UNGERMINATED SEEDS

0 %

24 %

24 %

0 %

100 %76 %

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THE BARYCENTRIC PRESENTATION FOR SEVERAL SAMPLES

A global accuracy of the laboratories

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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

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-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

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Examples of use of this

Statistical analysis in France

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Example on Pea

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Analyse sample by sample

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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

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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


Confidence level 1/1000

1 outlier

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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



2 outliers

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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



5 outliers

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Analyse of all samples

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-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

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Example on Tomato :results according different

references

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Tomato-Sample T5 – 5% level –reference global mean: 7 outliers

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Sample T5 – 1/1000 level –reference global mean: 3 outliers

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Sample T5 – 1/1000 level –ref. global mean except 95 : 2 outlier

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Sample T5 – 1/1000 level –reference global lab « 0» : 7 outliers

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-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

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-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 !!!

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-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

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Conclusion 1

• Representation : Usefulness of the barycentric representation for the technician to visualise the 3 values on one graph

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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.

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Conclusion 3

• Statistical evaluation based on the binomial distribution and not the variability of the data.

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