Discrimination tests


1 - Code design


Code design is suggested (automatic preparation in discrimination test in TASTEL) in order to avoid bias in the sample presentation. This code design is implemented for the following tests: paired/duo - trio, triangle, and 1 on 4 tests.

For instance, suggested code design for triangle tests represents the six random presentations, taking into account the two products "A/1", and "B/2":

ABB BAA AAB BBA ABA BAB

It has been considered as basis the norm NF V09-013 - Operative mode, for the triangle test example.


2 - General calculation


Discrimination test statistics are based on gaps as compared to a B(n, p) binomial distribution, with the following parameters:

  • n: the answer total number
  • p: the random good answer probability: 1/2 for paired, 1/3 for triangle , and 1/4 for 1 on 4 tests.

It has been considered as basis norm NF V09-012, and NF V09-013 - Test Report. It can be taken as validation example in the next applications:

Test value in paired test with TASTEL:
Assessors number: 14
Correct answer number: 11
5% TEST SIGNIFICANCE: YES
Test level(%): 2.86


Test value in triangle test with TASTEL:
Assessor number: 10
Correct answer number: 8
5% TEST SIGNIFICANCE: YES
Test level(%): 0.33


It is noticeable preference significance during demand of this information comes from similar statistical calculations in B(n, 1/2) distribution. It has been added also information about risk levels as:

  • Alpha risk (1st hand): Test level (risk to declare products as different, even if they are not it)
  • Beta risk (2nd hand): Risk of finding no difference, even if this one exists (usual situation)
  • Test power: Probability to find a difference, if this one exists (opposite of beta risk: 1 - br).

Hypothesis used for the beta risks calculations are based on % of recognition in the real population which are the following:

  • Small difference: 25 %
  • Medium difference: 37.5 %
  • Great difference: 50 %

It will be possible to refer to the article « Risk tables for discrimination tests - Food Quality and Preference » 4 (1993) 141-151 - P. SCHLICH.


3 - A no-A Test


Test A no-A statistics are depending on the answer total number taken into account in the calculation.

If answer total number <21: CALCULATION FOR SMALL STAFFS (FISHER)
AB = 1: de I = 2 à NBRPA% + NBRPB%: AB = AB * I
CD = 1: de I = 2 à NBRPC% + NBRPD%: CD = CD * I
AC = 1: de I = 2 à NBRPA% + NBRPC%: AC = AC * I
BD = 1: de I = 2 à NBRPB% + NBRPD%: BD = BD * I: Next I
NN = 1: de I = 2 à NBRPTO%: NN = NN * I
AA = 1: de I = 2 à NBRPA%: AA = AA * I
BB = 1: de I = 2 à NBRPB%: BB = BB * I
CC = 1: de I = 2 à NBRPC%: CC = CC * I
DD = 1: de I = 2 à NBRPD%: DD = DD * I: Next I
PROBANI = AB * CD / NN * AC * BD / AA / BB / CC / DD
Significant if PROBANI < 5%, to the threshold 5%


If answer total number >=21 et <41: CALCULATION FOR MEDIUM STAFFS (YATES)
I = (NBRPA% + NBRPB%) * (NBRPA% + NBRPC%) / NBRPTO%
J = (NBRPA% + NBRPB%) * (NBRPB% + NBRPD%) / NBRPTO%
K = (NBRPC% + NBRPD%) * (NBRPA% + NBRPC%) / NBRPTO%
L = (NBRPC% + NBRPD%) * (NBRPB% + NBRPD%) / NBRPTO%
If I,J,K,or L lower to 5, then use of Fisher statistics
AB = NBRPA% + NBRPB%
CD = NBRPC% + NBRPD%
AC = NBRPA% + NBRPC%
BD = NBRPB% + NBRPD%
X2 = (NBRPTO% * (NBRPA% * NBRPD% - NBRPB% * NBRPC% - NBRPTO% / 2) ^ 2) / AB / CD / AC / BD
Significant for 1% threshold X2 > 6.635, 2% for 5.412, 5% for 3.841 respectively


If answer total number >= 41: CALCULATION FOR GREAT STAFFS
AB = NBRPA% + NBRPB%
CD = NBRPC% + NBRPD%
AC = NBRPA% + NBRPC%
BD = NBRPB% + NBRPD%
NBRPA = NBRPA%
NBRPB = NBRPB%
NBRPC = NBRPC%
NBRPD = NBRPD%
NBRPTO = NBRPTO%
X2 = (NBRPTO * (NBRPA * NBRPD - NBRPB * NBRPC) ^ 2) / AB / CD / AC / BD
Significant for 1% threshold if X2 > 6.635, 2% for 5.412, 5% for 3.841 respectively.


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