1. Quantitative Testing Plans May 8-10, 2006 Iowa State University, Ames – USA Jean-Louis Laffont Kirk Remund

2. ISTA Statistics Committee2 Overview Statistical framework Implementation in Seedcalc

3. ISTA Statistics Committee3 Testing plan design: statistical framework for quantitative methods Seed lot: true AP% = p Suppose n pools of m seeds were taken from the lot and that J flour sub-samples from each pool were measured K times. n pools of m seeds … … Grinding seeds into flour … … J flour sub-samples per pool Measurement K measures per flour sub-sample y ijk

4. ISTA Statistics Committee4 Testing plan design: statistical framework for quantitative methods Model: Measurement k made on flour sub-sample j from pool i True AP% = + + + Random effect of pool i Random effect of flour sub-sample j from pool i Random effect of measurmnt k for flour sub-sample j from pool i The parameter p is estimated by the sample mean:

5. ISTA Statistics Committee5 Testing plan design: statistical framework for quantitative methods Overall distribution of y ijk p + Flour sub-sampling Measurement Sampling n pools of m seeds : derived from the variance of and are obtained from historical experiments

6. ISTA Statistics Committee6 Homozygous reference material and hemizygous test lots Testing plan design: statistical framework for quantitative methods Remember that the true AP% p in the lot is expressed in %DNA when using quantitative methods and that is expressed on a kernel basis.  Introduction of the b-Factor (biological factor) to convert from %DNA to %Seed units: %Seed = b-Factor x %DNA or Examples: Reference material and test lots have the same zygosity/ploidy/copy number  b-Factor= 1  b-Factor= 2

7. ISTA Statistics Committee7 Testing plan design: statistical framework for quantitative methods Re-expression of in %DNA units: Re-expression of : Having observed in some experiments that  ² measurement seems to depend on p, the true AP probability, while CV measurement is fairly constant, we can rewrite as:

8. ISTA Statistics Committee8 Testing plan design: statistical framework for quantitative methods This formula serves as a basis for elaborating an OC curve that can be used to investigate properties of a testing plan We can then calculate the probability to “accept” the lot, given a true unknown AP% p: where  is the cumulative distribution function for the standard normal distribution Lets now define an Acceptance Limit (AL) such that: if  AL, “accept” the lot if > AL, “reject” the lot

9. ISTA Statistics Committee9 Testing plan design: statistical framework for quantitative methods Example: testing plan components: 2 pools of 3000 seeds, 1 flour sub-sample/pool, 3 measurements/flour sub-sample, Std-Dev of flour sub-sampling error = 0.011%, measurement CV = 15%, Acceptance Limit (AL) = 0.1% (lot « accepted » if average of the 2 x 1 x 3 readings is  AL) 95% 5%

10. ISTA Statistics Committee10 Testing plan design: statistical framework for quantitative methods Consumer risk and producer risk are given respectively by: where  is the cumulative distribution function for the standard normal distribution

11. ISTA Statistics Committee11 Testing plan design: implementation for quantitative methods All of the methods discussed have been implemented in the newest version of the Microsoft Excel ® spreadsheet Seedcalc Estimating AP% Designing testing plans Comparing testing plans

12. ISTA Statistics Committee12 Testing plan design: implementation for quantitative methods Testing plan design Enter n, m, J, K and … historical assay variation and… LQL, AQL and AL and get consumer and producer risks and OC curve b-Factor and …

13. ISTA Statistics Committee13 Testing plan design: implementation for quantitative methods The « Find Plan » tool can help the user to find testing plans satisfying certain conditions given some parameters

14. ISTA Statistics Committee14 Testing plan design: implementation for quantitative methods Parameters for the search algorithms

15. ISTA Statistics Committee15 Testing plan design: implementation for quantitative methods Find the highest AL that meets target consumer risk for the LQL. No consideration of the producer risk target. n, m, J and K are held fixed

16. ISTA Statistics Committee16 Testing plan design: implementation for quantitative methods Consumer and producer risk targets satisfied by changing AL, n, I and J

17. ISTA Statistics Committee17 Testing plan design: implementation for quantitative methods Consumer and producer risk targets satisfied by changing AL, m, I and J

18. ISTA Statistics Committee18 Testing plan design: implementation for quantitative methods Consumer and producer risk targets satisfied by changing AL, n, m, I and J

19. ISTA Statistics Committee19 Testing plan design: implementation for quantitative methods Compare plans Visual comparison of OC curves along with testing plan parameters

20. ISTA Statistics Committee20 Historical data gave 0.15% for the estimate of the flour standard-deviation. We expect that the measurement CV range is from 10% to 30% and we consider the following testing plan:. LQL = 0.7% for a consumer confidence = 95%. AQL = 0.15% for a producer confidence = 95%. 1 pool of 3000 seeds, 2 flour sub-samples, 3 measurements. AL = 0.39% 1. Does this plan meet consumer and producer requirements when the measurement CV = 10%? 2. Compare the outcomes of this testing plan when the CV is varying from 10% to 30%. Example

21. ISTA Statistics Committee21 Example 1. Does this plan meet consumer and producer requirements when the measurement CV = 10%? YES

22. ISTA Statistics Committee22 Example 2. Compare the outcomes of this testing plan when the CV is varying from 10% to 30%.