TECHNICAL WORKING PARTY ON AUTOMATION AND COMPUTER PROGRAMS. Twenty-Sixth Session Jeju, Republic of Korea, September 2 to 5, 2008

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1 ORIGINAL: Englsh DATE: September 24, 2008 INTERNATIONAL UNION FOR THE PROTECTION OF NEW VARIETIES OF PLANTS GENEVA E TECHNICAL WORKING PARTY ON AUTOMATION AND COMPUTER PROGRAMS Twent-Sth Sesson Jeju, Republc of Korea, September 2 to 5, 2008 ADDENDUM CORRELATION BETWEEN DIFFERENT TYPES DISTANCES/SIMILARITY ON A SET OF WINTER OILSEED RAPE CHARACTERISTICS OF DIFFERENT TYPES (NOMINAL TO RATIO) Document prepared b eperts from German n:\orgupo\shared\document\twc\twc26\twc_26_20_add.doc

2 page 2 CORRELATION BETWEEN DIFFERENT TYPES OF DISTANCE/SIMILARITY MEASURES ON A SET OF WINTER OILSEED RAPE CHARACTERISTICS OF DIFFERENT TYPES (NOMINAL TO RATIO SCALE) Uwe Meer Bundessortenamt Hannoer German TWC/26/20 Jeju Introducton Ams of the CPVO-project: European Communt Plant Varet Offce Stud of management of WOSR reference collectons (see also TWC/26/18) Identfcaton of approprate statstcal procedures to analze morphologcal data Jeju

3 page 3 Datasets Dataset 1: Dataset 2: Notes and measurements UK, FR, DK and DE n 2003, 2004 and 2005 Consoldated Notes and measurements UK, FR, DK and DE n 2003, 2004 and 2005 Consoldaton = Harmonzaton between countres Januar Februar March Eample: Harmonzaton of dates (Add =60 das) (char: tme of flowerng has dfferent startng ponts n the countres: 1 th Januar, 1 th Aprl, ) Jeju Defntons Smlart measures Cosnus, Dce, Jaccard, M, RR, Kulcznsk, Dssmlart measures Mnkowsk metrc, Ctblock, Eucldan dstance, mamum dstance Correlaton measures Pearson Jeju

4 page 4 Notaton j j w j W number of arables (here characterstcs) or the dmensonalt data for obseraton on the th arable (characterstc), where =1 to (here obseraton = aret per ear) data for obseraton on the th arable (characterstc), where =1 to weght for the th arable. w =0 when ether or s mssng the sum of total weghts mean for obseraton mean for obseraton Jeju Weghted means = 1 = ( w * ) = 1 w W = 1/ =1,, Jeju

5 page 5 Standardzaton - Z-Score standardzaton: z = σ -Range standardzaton: z = ma mn mn Jeju Mnkowsk metrc d(, ) = p = 1 p For p = 2 p = 1 Eucldan dstance Ctblock dstance Jeju

6 page 6 Ctblock dstance (p=1) d(, ) = = 1 Jeju Scale leels TGP/8 - Nomnal scale - Ordnal scale - Interal scale - Rato scale Influence - Smlart measures - Dssmlart measures - Correlaton measures - Standardzaton Jeju

7 page 7 s nde (1) -S(,) = δ = 1;, w * δ *, d = 1wδ, = 1, for nomnal, ordnal, nteral and rato chars -Specal case: - for asmmetrc nomnal arable - f ether or s present δ = 1;, δ = 0;, - f both and are absent Jeju s nde (2) - S(,) = w * δ *, d = 1wδ, = 1, - for nomnal chars d = 0, f, d = 1, f =, - for ordnal, nteral and rato chars - for ordnal chars ranks has to be used d, = 1 Jeju

8 page 8 Pearson correlaton coeffcent r(s,t) = n ( s) *( t) s j= 1 j j 2 2 n ( s s) * j ( t t) n j t j= 1 = 1 j for assessng lnear relaton between two arables s and t Varables s and t are here dfferent dstance measures. Jeju Selecton of approprate methods Two Categores (notes) Nomnal >two Categores (notes) Ordnal Interal Rato Combnaton nomnal/ ordnal/ nteral/rato Ctblock Eucldan Chebche Cosnus Dce Jaccard M coeffcent RR coeffcent Kulcznsk coeffcent 's nde Jeju

9 page 9 Influence of the ear Data: Dataset 1 (german part) Smlart measure: s nde Results: Sample 1 Sample 2 Smlart Measure Correlaton coeffcent DE2003 DE2004 s nde (P<0.0001) DE2003 DE2005 s nde (P<0.0001) DE2004 DE2005 s nde (P<0.0001) Influence of the ears n German Dataset was er low. Jeju Modfcaton of dataset 1 Am: Comparson of dfferent dstance/smlart measures b1 (Seed: erucc acd; 1=absent, 9=present) b6 (Leaf: lobes; 1=absent, 9=present) b13 ( Producton of pollen; 1=absent, 9=present) =! ordnal =! ordnal =! Ordnal Nomnal wth 2 categores (notes) = ordnal wth 2 categores (notes) b10 (Flower: Colour of petals; 1=whte, 2=cream, 3=ellow, 4=orange-ellow) dropped It s forbdden to handle char b10 whch s nomnal scaled wth more than two categores (notes) as ordnal, nteral or rato scaled characterstc. Jeju

10 page 10 Correlaton coeffcents Sample Measure 1 Measure 2 Correlaton Coeffcent DE2003 Ctblock Eucld (P<0.001) Chebche (P<0.001) (P<0.001) Eucld Chebche (P<0.001) (P<0.001) Chebche (P<0.001) Jeju Correlaton coeffcents Sample Measure 1 Measure 2 Correlaton Coeffcent Consoldated dataset 2 Ctblock Eucld (P<0.001) Chebche (P<0.001) (P<0.001) Eucld Chebche (P<0.001) (P<0.001) Chebche (P<0.001) Jeju

11 page 11 Conclusons (1) Man efforts are to be made on harmonzaton of protocols, and harmonzaton of notatons between eperts that regster the measures Statstcal computatons, as shown aboe, need to be selected accordng to the tpe of scale of the characterstcs When some characterstcs hae a great nfluence on the snthetc (calculated) alue (e.g. s nde) obtaned oer all characterstcs, or when there are dfferent tpes of scales n a dataset, one has to consder usng ether the whole dataset, or to drop some characterstcs, or to compute subsets per tpe of characterstc The s nde s the most approprate procedure for the structure of dataset 1 and 2 because t s the onl one whch allows a combnaton of the present data tpes It s not allowed to use nomnal scaled characterstcs lke characterstc b10 (Flower: color of petals; 1=whte, 2=cream, 3=ellow, 4=orange-ellow) wth more than two categores (notes) for ealuaton of the Ctblock dstance Jeju Conclusons (2) For comparson of dfferent dstance measurements dchotomous characterstcs (b1, b6, b13) can be handled as ordnal characterstcs. Nomnal characterstcs wth more than two categores (b10) hae to be dropped for that comparson. The best correlated measure to s nde on the bass of dataset 1 and 2 s the Ctblock dstance Jeju [End of document]