Rankings


1 - Friedman Statistics


This test is ordering differences between samples in a general manner. In case of predetermined order, the Page statistics will be able to be implemented.
TASTEL allows the insertion of equal place ranking this leads to allocate to the statistics a minoration coefficient.

Formula calculation:

F = (12/(JP(P+1))*(R1²+R2²+...+Rp²)-3J(P+1), with:
J: assessor number
P: product number
R1, R2,...: the sum of ranks for each product with as signification test (significant if), with:
P=2 F>= 3.8
P=3 F>= 6.0
P=4 F>= 7.8
P=5 F>= 9.5
P=6 F>= 11.1


In case of equal place, the formula becomes:

F' = F/(1-(E/(JP(P²-1)))), with:
E: (n1cube-n1)+(n2cube-n2)+... n1, with as approximation
E # 6*number equal places found
Significant distance = (1,96 pour 5%)*root(JP(P+1)/6)


It has been considered as basis NF ISO-8587 - statistical interpretation. It can be taken as validation example: Norm application describes in Annex A:

Results of the ranking test with TASTEL:

Assessor number: 8
PRODUCT A: Sum of ranks: 17
PRODUCT B: Sum of ranks: 31
PRODUCT C: Sum of ranks: 32
PRODUCT D: Sum of ranks: 23
PRODUCT E: Sum of ranks: 17
SIGNIFICANT TEST: YES
PRODUCT POSITION: PREFERRED REJECTED
GLOBAL ............: .........AE...D....BC.......
SIGNIF. DISTANCE: -----------................


This test evidences samples differences in a general manner without hypothesis; In case or pre-determined order, the Page Statistics can be possible conducted.



2 - Page Statistics


Implemented calculations are the following:

Lobs.= R1+2R2+3R3+...,
with R as product sum of ranks with predetermined order (P1 < P2 < P3...).

Lthéor.(5%)= (1,645*(P(P+1)*racine(J(P-1)) + 3JP(P+1)²)/12

Lthéor.(1%)= (2,326*(P(P+1)*racine(J(P-1)) + 3JP(P+1)²)/12, avec:
P: product number, J: assessor number


Also, in the case of Lobs >= Ttheor., sample predetermined hypothesis will be verified. It has been considered also as basis the norm NF ISO-8587 - statistical interpretation. It can be taken as a validation example: Norm application described in Annex A.


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