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Calculation and statistical tools for

germination testing

ISTA Seminar on Germination

June 13, 2011

Jean-Louis Laffont

ISTA STA Committee

ISTA Statistics Committee 2

Overview

• What is an estimate?

• Sources of variation in seed testing

• Germination Tolerances

• ISTA calculators

• Practicals


Credits

• Ronald Don

• Michael Kruse

• Sylvie Ducournau

• Anny van Pijlen

• Kirk Remund


Seed Lot

True unknown

germination%: p

What is the quality of the

lot regarding germination?

p̂


Seed Lot

True unknown

germination%: p

Sample

Germination

testp̂ Estimate:

Estimate:

94%

True % in the sample: 92%


Seed Lot

True % in the lot:

90%

Germination

test87%

True % in the sample: 88%

Sample

Sources of variation


There are two main sources of variation in seed testing:

• Variation due to sampling

• Variation due to the experimental conditions:

• The testing method itself

• The seed analyst

• The Lab environment

• …

Sources of variation in seed testing


Variation due to sampling

Example: simulated seed

sampling



In the case of germination, we model random-sampling

variation using the binomial distribution

Number of

germinated

seeds

Number of

seeds

tested

A lot of computations can be performed from the binomial

distribution: probability computations, estimate of the

variation, …

0 1 2 3 4 5 6 7 8 9 10

0.0

0.1

0.2

0.3

Distribution binomiale pour un echantillon de taille 100 et p= 1 %

nombre de semences OGM dans l'échantillon

pro

b.

Number of abnormal seedlings



Binomial distribution with n=100

and 1% abnormal seedlings

There is 37% chance

of getting zero abnormal

seedlings in samples

of 100 seeds if

the true abnormal

seedlings % in the lot

is 1%



Seed Lot

True unknown

normal

seedlings%: 90%

Suppose we are taking a lot of samples

of 100 seeds from the lot and that

we are able to determine without error

the % of normal seedlings in

those samples

Samp 1

92%Samp 2

89%Samp 3

87%Samp 100

95%Samp 500

90%Samp 10,000

93%

… … …

The distribution of these %

can be visualized as follows:

80 85 90 95

0.0

0.0

20

.04

0.0

60

.08

0.1

00

.12

% normal seedlings



Samp 1

92%Samp 2

89%Samp 3

87%Samp 100

95%Samp 500

90%Samp 10,000

93%… … …

80 85 90 95

0.0

0.0

20

.04

0.0

60

.08

0.1

00

.12

% normal seedlings

The mean is: 90%

The standard-deviation is: 3

For a binomial distribution characterized by a true percentage p

and sample size n, the theoretical standard-deviation is

given by:p(100-p)

sd_binomialn

90(100-90)sd_binomial

13

00



80 85 90 95 100

0.0

0.1

00.2

0

% normal seedlings - n = 100

80 85 90 95 100

0.0

0.1

00.2

0


80 85 90 95 100

0.0

0.2

0.4


Sample size (n) =100

sd_binomial=3


sd_binomial=1.5


sd_binomial=0.95

The larger the

sample size, the

smaller the binomial

standard-deviation

(i.e. the smaller the

random-sampling

variation)



80 85 90 95

0.0

0.0

20

.04

0.0

60

.08

0.1

00

.12

% normal seedlings

For the binomial distribution,

we have formulas for

computing

Confidence Intervals,

that is intervals for which a given

% of samples will have a

percentage of normal seedlings

between two limits:

1- Confidence Interval of a percentage:

1 2

1 2 1 2

/2, ,

/2, , /2, ,

( 1);

( 1) ( 1)

ijij

ij ij ij ij ij ij

y Fy

y n y F n y y F

where:

. 1 = 2 (nij – yij +1) 2 = 2 yij

. '1 = 2 (yij +1) '2 = 2 (nij – yij)

. F /2, 1, 2 is the upper /2 point of the F-distribution with

1 and 2 d.f.

82% 95%

95% of the samples

will have % normal

seedlings between

82% and 95%


Germination Tolerances

Key concept:

Miles (1963):

Theoretically, germination tolerances should be computed

allowing for random-sampling variation only. This was done for

tests made in the same laboratory, because experience has

verified that usually the variation among replicates in one

laboratory can be accounted for by random-sampling variation.

However, experience has shown that the variation among

laboratories has been greater than that due to random variation.

Therefore, to be realistic, the tolerances for tests made in

different laboratories include true variation that existed in the

1950’s among laboratories.


Germination Tolerances – Between-laboratories variation

• Miles study: - 68 labs in 1953 and 1954, 60 labs from 1955 to 1959

- 20 ISTA and 48 AOSA referee samples used

- Number of seeds tested in each lab: 400

Note: variation is a function of the quality (p)Germination %

Sta

nd

ard

-de

via

tio

n

0 20 40 60 80 100

01

23

45

Random-sampling

variation

Total

variation

Total variation > Random-sampling variation

Observed std-dev, s, among labs >p(100-p)

= sd_binomialn

Between-labs

variation

Definition of an

overdispersion factor, f:

f = s/ = 2.38 – 0.008321p

This overdispersion will

be taken into account

for computing tolerance

tables for tests in different

laboratories


Reliability of a germination test - Intuitively

The following replicate results were obtained in a 100

seeds germination test: 93%, 81%, 94% and 92%

Are these results compatible?

% normal seedlings

75 80 85 90 95 100

Little chance to have the

value 81% coming from the

same distribution supported

by the other values

of the test!

% normal seedlings

75 80 85 90 95 100

The binomial distribution with

p equal to the mean of the 4

results (90%) is visualized

with the blue line.


Reliability of a germination test – Statistical method

• Miles (1963)* developed a statistical method for computing a

tolerated range between the replicates of a germination test.

• This method is based on:

• The standard-deviation of a binomial distribution

• The studentized range distribution

* Miles, S.R. 1963. Handbook of tolerances and measures of precision for seed testing.

Proceedings of the International Seed Testing Association, 28, 525-686

• This method has been implemented in the Germination

Tolerance Calculator freely available from the ISTA website:

Note: the rounding procedure adopted in Miles tables

is now well understood:

Quite complex:

=FLOOR(ROUND($G$18*SQRT(($B$11-0.5)*(100-$B$11+0.5)/$B$7)+0.2,2),1)

We are able to mimic exactly Miles existing tables

for germination


Reliability of a germination test – Procedure

Compute the observed range (difference

between the max and min

values of the test)

Determine the maximum

tolerated range as a function of

the mean of the values, the # of seeds

tested and the number of replicates

Observed

range

>

Max tolerated

range

OK: results are

within tolerance

Results are out

of tolerance

NOYES

13

12

13 >12

Results are out of

tolerance

93%, 81%,

94%, 92%

Using the Germination

Tolerance Calculator

Using ISTA Tolerance Tables


Determine the maximum

tolerated range as a function of

the mean of the values, the # of seeds

tested and the number of replicates

Reliability of a germination test – Procedure


Germination - Comparing test results from the same laboratoratory

For comparing test results performed in the same laboratory,

you can use the same procedure used for assessing the

reliability of a germination test.

Example: If we conduct two 400 seed germination tests on a

sample in the same lab and obtain the following results for the 2

tests: Test 1: 94

Test 2: 99Mean = 96.5

99-94 = 5 > 3 : the results are out

of tolerance


Germination - Comparing test results from the different laboratories

• Tolerances for tests conducted in different labs are not

required in the Rules, however, for statutory purposes one often

wants to compare the results from different labs.

• Miles developed the tolerance tables for tests conducted in

different labs using:

• The overdispersion factor, f

• The studentized range distribution

• This has been implemented in the Germination Tolerance

Calculator freely available from the ISTA website:


Example: If we conduct a 400 seed germination test in one lab

and repeat the analysis in another laboratory and get the

following results: Lab 1: 85

Lab 2: 78Mean = 81.5

85-78 = 7 <= 9 : the results of the two

labs are in tolerance

Germination - Comparing test results from the different laboratories


About Tetrazolium Tolerances…

• For testing reliability of the replicates in one terazolium test

Use same table for testing reliability of the replicates in

one germination test

• For comparing tetrazolium test results performed in the same

laboratory , use ISTA table 6C.TEZ committee Report 1998-2001: The tolerances take into account the

experimental error within a laboratory and are not extracted from Miles.(variation within a laboratory > random-sampling variation)

• For comparing tetrazolium test results performed in different

laboratories, use ISTA table 6D.TEZ committee Report 1998-2001: The tolerances take into account the

experimental error between the laboratories and are not extracted from

Miles.(Between labs variation for tetrazolium Between labs variation for germination )


Germination Tolerance Calculator

https://www.seedtest.org


Germination Tolerance Calculator


Germination Testing/Retesting

Test 1

Results of tests

1 & 2 & 3 within tol?

Report results

Average of 1,2 & 3YES

YES

NO

Results of reps

within tolerance?Report

results

Test 2 - Same methodRetest, different

method

Results of tests

1 & 2 within tol?

Report results

Average of 1 & 2

Test 3 – Same method

YES

NO

Retest, different

method

NO

Results of tests

(1 & 3) or (2 & 3) within tol?

Report results

Average of (1 & 3)

or (2 & 3)

(the highest one)

YES

Retest, different

method

NO


Report results

Average of highest

trioYES

NO

Results of tests

(1, 4) or (2, 4) or ( 3, 4) within tol?

Results of tests

(1, 2, 4) or (1, 3, 4) or (2, 3, 4) within tol?

Report results

Average of 1, 2, 3

and 4

YES

NO

Test 4 – Same mehod

Results of tests

1 , 2, 3 & 4 within tol?

Report results

Average of

highest pair

YES

NO

No results reported


Germination: Calculation and expression of results Calculator


Practicals


Practicals

1. The following replicate results were obtained in germination tests carried out on 10 different seed samples: Percentage Germination Replicate Sample No 1 2 3 4 1 92 97 95 95 2 99 99 98 94 3 92 88 88 96 4 84 85 80 90 5 87 98 94 97 6 66 55 50 62 7 81 86 85 90 8 91 93 99 98 9 55 45 60 55 10 91 92 96 89 Which results are out of tolerance and would be retested


Practicals

2. Compute the 95% Confidence Interval for a germination of 95% on 100 seeds.

Compute the 99% Confidence Interval for a germination of 95% on 100 seeds


Practicals

3. The results of check tests on six Maize samples are given below. The check tests were completed in the same laboratory eight weeks after the original test.

Sample No ORIGINAL

RESULT 400 Seeds

CHECK TEST RESULT 400 Seeds

1 96 98 2 93 97 3 84 92 4 77 66 5 91 82 6 95 91 Which results are out of tolerance?


Practicals

4. Wheat seed tested in two different seed testing laboratories at the same time gave the following germination results (expressed as the average of four replicates of 100 seeds): Percentage Germination Sample No

Lab 1 Lab 2

1 84 95 2 91 86 3 77 67 4 84 67 5 95 88 6 90 83 7 66 50 8 91 97 9 55 45 10 90 98 Which results are out of tolerance?


Practicals

5. The following germination test results were obtained on a sample of Cucumber Seed (four replicates of 100 seeds): Percentage Germination Replicate Test No 1 2 3 4 1 91 88 74 89 2 77 79 83 78 3 80 82 82 82 Why was the second test carried out? Why was the third test carried out? What result was reported?


Practicals

6. The following results were obtained in germination tests on a Ryegrass sample (four replicates of 50 seeds): Date of Test Replicate Normal

Seedlings Abnormal Seedlings

Fresh Seed

Dead Seed

14/11/2006 1 50 - - - 2 49 1 - - 3 34 14 - 2 4 49 - - 1 28/11/2006 1 49 - - 1 2 46 2 - 2 3 50 - - - 4 47 1 1 1 Why was the second test carried out and what percentage germination should be reported?


Practicals: answers

1. The following replicate results were obtained in germination tests carried out on 10 different seed samples: Percentage Germination Replicate Sample No 1 2 3 4 Average Difference Tolerance Comment 1 92 97 95 95 95 5 9 OK 2 99 99 98 94 98 5 6 OK 3 92 88 88 96 91 8 11 OK 4 84 85 80 90 85 10 14 OK 5 87 98 94 97 94 11 10 Retest 6 66 55 50 62 58 16 19 OK 7 81 86 85 90 86 9 14 OK 8 91 93 99 98 95 8 9 OK 9 55 45 60 55 54 15 20 OK 10 91 92 96 89 92 7 11 OK


Practicals: answers2. Compute the 95% Confidence Interval for a germination of 95% on 100 seeds.

Compute the 99% Confidence Interval for a germination of 95% on 100 seeds


Practicals: answers

3. The results of check tests on six maize samples are given below. The check tests were completed in the same laboratory eight weeks after the original test. Sample No ORIGINAL

RESULT 400 Seeds

CHECK TEST RESULT 400 Seeds

Av Dif Tol Comment

1 96 98 97 2 3 OK 2 93 97 95 4 3 Out of Tolerance 3 84 92 88 8 5 Out of Tolerance 4 77 66 72 11 7 Out of Tolerance 5 91 82 87 9 5 Out of Tolerance 6 95 91 93 4 4 OK


Practicals: answers

4. Wheat seed tested in two different seed testing laboratories gave the following germination results (expressed as the average of four replicates of 100 seeds): Percentage Germination Sample No

Lab 1 Lab 2 Av Diff Tol Comment

1 84 95 90 11 7 Out of Tolerance 2 91 86 89 5 7 OK 3 77 67 72 10 11 OK 4 84 67 76 17 10 Out of Tolerance 5 95 88 92 7 6 Out of Tolerance 6 90 83 87 7 8 OK 7 66 50 58 16 13 Out of Tolerance 8 91 97 94 6 5 Out of Tolerance 9 55 45 50 10 13 OK 10 90 98 94 8 5 Out of Tolerance


Practicals: answers

5. The following germination test results were obtained on a sample of Cucumber seed Seed (four replicates of 100 seeds): Percentage Germination Replicate Sample No 1 2 3 4 Av Diff Tol Comment 1 91 88 74 89 86 17 14 Replicates are out of tolerance 2 77 79 83 78 79 6 16 OK 3 80 82 82 82 82 2 15 OK Test 1 Test 2 Av Diff Tol Comment 86 79 83 7 6 Tests are out of tolerance

Test 1 Test 2 Test 3 Av Diff Tol Comment 86 79 80 82 7 7 OK Why was the second test carried out? Results of first are out of tolerance Why was the third test carried out? Results of Test 1 and Test 2 are out of Tolerance What result was reported? 82% (results of tests 1, 2 and 3 are in tolerance)


Practicals: answers6. The following results were obtained in germination tests on a Ryegrass sample (four replicates of 50 seeds): Date of Test Replicate Normal

Seedlings Abnormal Seedlings

Fresh Seed

Dead Seed

14/11/2006 1 50 - - - 2 49 1 - - 3 34 14 - 2 4 49 - - 1 28/11/2006 1 49 - - 1 2 46 2 - 2 3 50 - - - 4 47 1 1 1 Test Av Dif Tol Comment 14/11/2006 91 32 16 Out Test Germ Av Dif Tol Comment 14/11/2006 91 94 5 5 The two tests are in tolerance so the average of the 28/11/2006 96 two tests is reported, i.e. 94% Why was the second test carried out and what percentage germination should be reported? The second test is carried out because the replicate results of the first test are out of tolerance. The 2 tests are OK so the average of them is reported, i.e. 94%.

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