Transcript Testing seedmixtures

Testing seed mixtures
Júlia Barabás PhD (Hungary)
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Introduction
In year 2000 two questions were addressed by the
Purity Committee to the Statistics Committee.
1. How could we compare the test result of a
sample against the labelled proportion of seed
mixture-lot?
(= does the lot has the labelled proportion?)
2. How could we compare two test results from a
seed mixture-lot?
(= we have made a test on our submitted sample
but we or another lab had to perform another test,
“are the two results compatible?” )
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Suggested methods and their mathematical
background
Subgroup to discuss the possibilities by e_mail
(leadership J. Barabás).
After about 6 circulars and different contributions,
the mathematical background was chosen and a
software was prepared to address 4 different cases
a % in number of seeds
b % in weight of seeds
1 check against label
1 a label number
1 b label weight
2 compare two tests
2 a compare numbers
2 b compare weights
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case 1 a
when we want to compare the labelled proportion with
one test result of the sample on the basis of the count of
the number of seeds of different components.
In this case we could use a well known statistical test
the Chi-squared test for goodness of fit. It measures
the difference between the expected and the experienced
frequencies.
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Ho: p i o  p i if i=1,2..k , and where, pi is the labelled
proportion of the i-th component in the whole lot.
H1 : p i o  p i exist even one component which has not the
given proportion.
The test statistic:

2

k

i1
( f i  n p io )
n p io
2
,
where fi is the observed frequency of the i.-th component.
Rejection region:
 2 :   2 . (e.g. for 5% and k=5 the critical value=9,488)
n=number of seeds tested Pi0=number of seeds of a component
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case 1 b
when we want to compare the labelled proportion with
one test result of the sample and on the basis of the
weight of the different components.
(we need to know or measure the 1000 seed-weights of
the components).
We transform the original formula and suggest to
apply in this case as follows:
Ho and H1 and rejection region are the same as in
the first case.
Ho =all frequencies are as expected
H1= at least one of the frequencies is different from expected
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The test statistic:
2 

1000 


 s

p
s
i0
 i 
 i 
pi0
mi
 mi
m



i
mi


pi0
si

pi0
mi
mi
mi
2
where s i is the measured weight of the i-th component
and m i is the 1000 seeds weight of the i-th component,
and all the  goes from 1 to k, if there are k different
components.
Pi0 = the labelled proportion % of the i-th component
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Case 2 a
when we want to compare two test results from the
same seed mixture lot on the basis of the count of the
number of seeds of different components in both tests.
The base statistic is a homogeneity Chi-squared test.
Ho: F1(x)= F2(x), that is the two distributions are the
same,
H1 : F1(x) not = F2(x) that is the two distributions are
not equal.
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The test statistic:

2
k


i 1
(
hi
li 2

)
n2
n1
hi  li
n1n2
where h i is the seed-number of the i-th
component in the first test
and l i is the
seed-number of the i-th component in the
second test,
and n 1, n 2 the total seednumbers in each test
2:
2



Rejection region:
 and degree of
freedom = the number of components -1.
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2 b case
when we want to compare two test results from
the same seed mixture lot on the basis of the
weight of different components in both tests.
The base statistic is the same but we need to transform
the original formula.
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
 v
i  wi

vi
wi

k 
mi
mi

mi ( v i  w i )
i 1
2  


2





1000 

vi

mi

wi
mi
Where vi is the weight of the i-th component in
the first test and wi is the weight of the i-th
component in the second test, and mi the 1000
seed weight.
Ho and H1 and rejection region are the same as in
case 2/a.
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Excel spreadsheet to compute
tests in seed mixtures
• In order to allow the practical use in the
many possible circumstances
• When work will be validated by Statistic
and Purity committee, it will be available
through ISTA
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Case where seed mixture composition is checked
by numbers of seeds
Chi 2 t est f or seed mi xt ur es check agai nst pr opor t i ons i n number of seeds
labelled proportion (ie
0.5 for 50%)
component
species 1
species 2
species 3
species 4
species 5
6
7
8
9
10
0.15
0.38
0.42
0.02
0.03
s ums
degrees of
freedom
1
4
observed number of
seeds
68
160
153
9
10
400
Observed Chi2
probability
0.0505
is 5.05%
observed
proportion
ex pected number of seeds
Chi2 contribution
0.1700
0.4000
0.3825
0.0225
0.0250
0.0000
0.0000
0.0000
0.0000
0.0000
60
152
168
8
12
0
0
0
0
0
1.0667
0.4211
1.3393
0.1250
0.3333
0.0000
0.0000
0.0000
0.0000
0.0000
1
400
3.2853
0. 5113 critical Chi2 at 5%
critical Chi2 at 1%
critical Chi2 at 0.1%
9.487728465
13.27669856
18.46622617
NS
NS
NS
how t o pr oceed:
step 1 click on clear data button
step 2 enter data , proportions and observed number of seeds
step 3 see results if probability is less than the critical probability chosen the test is significant < = > not conform to label
NB: you can enter the name of the components
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Case where seed mixture composition is checked
by weight of seeds
Chi 2 t est f or seed mi xt ur es check agai nst pr opor t i ons i n wei ght of seeds
labelled % of
Weight of
Weight of 1000
components (ie 50
components Si
seeds Mi
for 50%) Pi%
(grams)
(grams)
Pi/ Mi
component
20
5
20
1.0000
species xxx
30
6
24
1.2500
species yyy
10
3
12
0.8333
species zzz
20
2.5
10
2.0000
species ssss
20
5
20
1.0000
species ttttt
6
7
8
9
10
100
sums
degrees of freedom
21. 5
Observed Chi2
probability
0.0505 is 5.05%
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clear data
86
0. 0000
6. 083333333
Si/ Mi
numerator
denominator
numerator /
denominator
0.2500
0.2500
0.2500
0.2500
0.2500
1.982079189
0.046913117
6.204259711
25.90776881
1.982079189
0.205479452
0.256849315
0.171232877
0.410958904
0.205479452
9.646118721
0.182648402
36.23287671
63.04223744
9.646118721
1. 2500
36. 12310002
1. 25
118. 75
critical Chi2 at 5%
critical Chi2 at 1%
critical Chi2 at 0.1%
observed chi square
9.487728465
13.27669856
18.46622617
how t o pr oceed:
step 1 click on clear data button
step 2 enter data , in green columns for your components
step 3 see results if probability is less than the critical probability chosen the test is significant < = > not conform to label
NB: you can enter the name of the components in the column components
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Another question : Which number of seeds shall I
expect for a given labelled % and number of seeds
computation of the expected number of seeds for a given species in a seed mixture when the expected percentage is known
400 type in the number of seeds (for instance 400)
55 type in the labelled/expected percentage (for instance 55 if 55%)
confidence intervals
220 average number of seeds expected
2.48747 theoretical standard deviation
you can obtain distributions at the following web adress:
http://www.ruf.rice.edu/~lane/stat_sim/normal_approx/index.html
alpha risk
min
average
max
delta
20%
207
220
233
12.7358
10%
204
220
236
16.3178
5%
200
220
240
19.5018
1%
198
220
242
22.2877
0.10%
194
220
246
25.5712
this is a hard copy of what you can get
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