comparison of the efficiency of pair, duo-trio and triangle tests

COMPARISON OF THE EFFICIENCY OF PAIR, DUO-TRIO AND TRIANGLE TESTS

PIERRE FRANCOIS

Laboratoire d 'Eveljdaun Sensurielle Suprad, I719 Quai du President P Doumer, 92414 COURBEVOIE, Cedex, FRANCE

and FRANCOIS SAUVAGEOT

Laboratoire de Biologie Physico-Chimique, ENS. BANA, Campus Universitaire Montmuzard, 21 100 DIJON, FRANCE

Received for Publication October 30, 1987

ABSTRACT

f i e pair, duo-trio and triangle tests were compared, using three levels of instructions with orange drink as medium and sucrose as stimulus. I f the subjects know only the nature of the test, the pair test cannot be pe$ormed and the f ie- quencies of correct responses above chance of the two other tests do not differ significantly, in this case the triangle test is the more eficient. I f the subjects know the Bature of the test and the nature of the stimulus, the frequency of correct responses above chance obtained for the pair test is significantly higher than those of the two other tests, in this case the pair test is more eficient. Finally, if the subjects know the nature of the test, the nature of the stimulus and whether or not the sample to be selected contains the stimulus, the conclusions are more d$- ficult to achieve but the triangle test seems to be the more eficient.

INTRODUCTION

In the food industry, pair, duo-trio and triangle tests are used to investigate whether or not there are differences between two products. The experimenter must choose the most efficient test, i.e. that statistically optimal for the detection of differences. In order to determine the most efficient test, an experimental method consists of comparing the frequencies of correct responses observed from different test performed with the same difference of stimulus between samples. O'Mahony et al. (1986) used such a method with the duo-trio and dual standard tests. However, the most satisfactory method is to study and compare the power functions of the different tests, which give the probabilities of rejec- ting the null hypothesis when it is false. The test whose function dominates is statistically optimal.

Two models exist and they lead to contrasting results. The first model (Ura 1960; David and Trivedi 1962) is based on the existence of an internal sensory continuum and leads to the efficiency scale: Pair > Triangle > Duo-trio. Ura

Jourhal of Sensory Studies 3(1988) 81-94. All Rights Reserved. @Copyright 1988 by Food & Nutrition Press, Inc., Trumbull, Connecticut. 81

82 PIERRE FRANCOIS AND FRANCOIS SAUVAGEOT

verified experimentally the pair test’s superiority by asking eight judges to compare plates of different thicknesses using the three tests. The second model (Hopkins and Gridgeman 1955) defines the power functions of the three tests for the detection of flavor intensity in relation to the probability of sensory detection (Px) or frequency of correct responses above chance and leads to the efficiency scale: Triangle > Duo-trio > Pair (Fig. 1).

A P x mar

/ / /

I ,

B e 0 2 0 4 8 6 8.8 1 8

PX

FIG. 1. POWER FUNCTIONS OF THE DUO-TRIO (*), PAIR (+), AND TRIANGLE (0) TESTS AT a = 0.05 IN RELATION TO THE

FREQUENCY OF CORRECT RESPONSES ABOVE CHANCE Px FOR EQUAL NUMBERS OF REPLICATIONS (n = 21) ACCORDING TO

HOPKINS AND GRIDGEMAN (1955). Taken from Gacula and Singh (1984)

N.B. Hopkins and Gridgeman model suppose that pair and duo-trio tests are two tailed and one tailed, respectively, which is not always true for pair test.

According to Hopkins and Gridgeman, for a test x, the frequency P* of observed correct responses is the sum of Px plus the conditional probability of chance guessing after failing discrimination:

Pair test Duo-trio test

P* = P1.2 + (1 - P,J2; P* = P2.3 + (1 - P2.3)/2;

P,.2 = 2P* - 1 P2.3 = 2P* - 1

Triangle test P* = PI + (1 - P1.3)/3; PIJ = (3P* - 1)/2

EFFICIENCY O F PAIR, DUO-TRIO AND TRIANGLE TESTS 83

Note that = Px for Pair, Duo-trio and Triangle test respectively. Px is unspecifiable a priori, but the Hopkins and Gridgeman model (1955) in- volved that = P2.3 = If this implicit assumption is not true, the position on the abcissa of the power curves of Fig. 1 in relation to each other might be modified.

The results obtained by Byer and Abrams (1952), Filipello (1956), Gridgeman (1955) and Sauvageot (1976, 1984a) suggested that the probability Px of sensory recognition may, in fact, be greater in the pair test when the three tests are performed under the same conditions. However, the analysis of their experimental designs revealed that the instructions given to the subjects prior to the tests were not of the same nature for all three tests (Table l), except in the experiment performed by Byer and Abrams.

In order to obtain comparable results, three main levels of instructions should be defined: LEVEL 1 : The subject is only told the nature of the test. This level corresponds to the classic presentation of the duo-trio and triangle tests. The pair test cannot be performed because the subject knows the nature of the sensory characteristic differentiating the two samples. LEVEL 2: The subject knows the nature of the test and the nature of the stimulus (e.g., sucrose) or the nature of the sensory characteristic differentiating the two samples (e.g., sweet flavor). LEVEL 3: The subject knows the nature of the test, the nature of the stimulus or the sensory characteristic involving differences, and knows whether or not the sample to be selected contains the stimulus. This instruction level corresponds, for the triangle test, to the mAFC procedure defined by Green and Swets (1966).

The purpose of this paper is to investigate, for the three levels of instructions previously defined, if the Hopkins and Gridgeman’s model implicit assumption of the equality of Px in all three types of tests for an identical contrast of stimulus is correct.

P2.3,

MATERIALS AND METHODS

Medium Stimulus

The medium consisted of a powdered orange drink (TANG donated by General Foods - FRANCE) added to nongaseous mineral water (EVIAN). The stimulus was trading sucrose (BEGHIN SAY). The tests were performed between the medium and the medium with sucrose added.

TAB

LE 1

. T

HE

INST

RU

CTI

ON

S G

IVEN

TO

TH

E S

UB

JEC

TS IN

DIF

FER

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EXPE

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ENTS

OF

TEST

CO

MPA

RIS

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S A

ND

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ND

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L IN

TH

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RES

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EXPE

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ENTA

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o"O-tr10

Test

I

Grid

gema

n N.

T.

1195

51

Aqueoun

~Olvtion : -Uhlch 1s the s

tron

ger

?-

(P2)

Toma

to j

uic

e : "W

hich

in

the

norm

al.

untr

eate

d sa

mple

?"

01

Grou

nd b

eef

: -Which has

the

str

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r flavor?" l

P2)

Not

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cate

d

Triangle

No

t in

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ted

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pell

o 119561

Judg

ment

of the

sam

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the

high

er intensity.

lP2)

Not

stud

ied

Indicate the od

d sa

mple

(PI)

Hopkins and Gr

idge

man

11.9541

Rank

rn

order of st

rent

gh of

flav

or.

(P2)

Sa

uv

ag

eo

t. 1976. bitterness

and

acidity of coffee. pair

and

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tests

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question

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the

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Th

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diluted

orange j

uice sample

Determine

the od

d sa

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P

EFFICIENCY OF PAIR, DUO-TRIO AND TRIANGLE TESTS 85

Determination of the Amount of Sucrose Added

The aim was to get, for each subject individually, the difference in sucrose between samples leading to frequencies of correct responses observed superior to random and inferior to 1 during the session for the three tests. Indeed, if the difference in sucrose between samples was too small, the frequencies of correct responses above chance for the three tests would be equal to 0 and comparisons would be impossible. The situation would be the same if the difference in sucrose was too high, but in this case the frequencies of correct responses above chance would be equal to 1.0.

The test used for the determination had no large importance because the determination is only an approximation (about 50% of correct responses above chance). The duo-trio test had been chosen arbitrarily. The pair test was not used because it could not be performed in the case of the Level 1 instructions.

A sequential approach carried out with the duo-trio test was used. The scale of sucrose amounts followed a geometric progression of the ratio 2* and was limited by the two concentrations 2.5 and 28.3 g/L. The following procedure was adopted: 4 duo-trio tests were prepared with the same difference in sucrose (Sn) between samples and presented simultaneously to the subject in a box (Fig. 2) :

If the number of correct responses obtained was inferior or equal to 2, duo-trio tests of the following box were prepared with the same difference in sucrose between samples just over the previous amount of sucrose of the scale (Sn + 1); If the number of correct responses obtained was equal to 3, duo-trio tests of the following box were prepared with the same difference in sucrose between samples than the previous (Sn); If the number of correct responses obtained was equal to 4, duo-trio tests of the following box were prepared with the difference in sucrose just under the previous of the scale (Sn - 1).

The chosen criterion was the following one: the subject had to obtain two times in succession 3 correct responses on 4 tests performed with the same amount of sucrose. The number of tests performed during the determination varied between 12 and 40, depending on the subject and on the repetition.

Instructions

The three protocols presented to the subjects corresponding to the 3 levels of instructions described in the introduction are listed in Table 2 . Subjects

Six students (3 women, 3 men, 22-27 years old) participated in the experiment. All subjects were trained in sensory analysis. They were paid and were unaware of the aim of the experiment. The subjects accepted to be filmed on video during the sessions.


Organization of a Basic Cycle

Each cycle was composed of 12 tests: Protocols 2 and 3: the 12 tests were divided as follows: 4 duo-trio, 4 triangle,

4 pair tests. In order that the number of tests (duo-trio, triangle) in which the stimulus was not repeated be equal to the number of tests in which the stimulus was repeated, the samples were presented in two boxes as shown in Fig. 2.

Protocol 1: as the nature of this protocol implies that the subjects do not suspect the sensory characteristic involving differences between the two samples, the two pair tests of each box were replaced by two "trap" tests: one duo-trio and one triangle test with phenol (35 mg/L) as stimulus (Fig. 2).

Protoool1 Protocol 2 and 3

0 0 i o 0 0

0 0 0 0 0 0 Boxes n'?

0 . 0 0 1 0 T- TJ

( 0 ) : Pair test (0) : Duo-trio test ( 0 ) : Triangle test Characters ( o ) , (0) and ( 0 ) filled : samples containing stimulus.

( 1 ) : Samples taste order ( - ) : Tests realization order (T) : Example of the position of the "trap" tests. (s) : Position of the subject. The position of the sample to select was randcxnized in each test. After tasting, the subjects only had to leave the selected sample outside the box in order to note their judgement. ~~

FIG. 2. REPARTITION OF THE TESTS IN THE BOXES IN RELATION TO THE PROTOCOL

EFFICIENCY O F PAIR, DUO-TRIO AND TRIANGLE TESTS 87

TABLE 2. THE THREE PROTOCOLS OF INSTRUCTIONS USED

Protocol 1 (P1)

During this evaluation two different tests will be presented to you : each contains two samples.

Duo-trio test : You have at your disposal a standard. Between the two samples of the pair presented simultaneously, determine the sample identical to the standard.

Triangle test : Two samples are presented to you : one of them is repeated twice : determine the odd sample.

During this evaluation, three different tests will be presented to you ; each contains two samples which differ in the sweet taste. Pair test : Two samples are presented to you : determine the

sweeter sample. Duo-trio test : Idem protocol 1. Triangle test : Idem protocol 1.

Protocol 3 (P3)

During this evaluation, three different tests will be presented to you : each contains two samples which differ in the - taste. For each test, you will be told whether you have to select the less sweet or the sweeter of the two samples. Pair tests : Idem protocol 2 ;

Duo trio test : Idem protocol 1 + the standard is the ... sweet : Triangle test : Idem protocol 2 f the odd sample is the .__ sweet

Organization of a Session

Each session consisted of two parts: (1) Determination by the duo-trio test of the amount of sucrose to be given to

specific subject in order to obtain a frequency of correct responses observed near 75%. The instructions the subject received depended on the protocol to be performed.

(2) Realization of 5 cycles; each subject then repeated each type of test 20 times.


Experimental Design

Four repetitions of each protocol were made by each subject. During a given session all tests were carried out in accordance with the same protocol. The experiment was spread over 12 sessions (one per day). The randomized order of the realization of the repetitions was: P1, P2, P3, P1, P2, P2, P1, P3, P3, P2, PI, P3.

Statistical Analysis

For each protocol and each couple of tests, a graph was constructed with which point determinated the two frequencies of correct responses above chance (Px) obtained by the same subject in a session. Each frequency was calculated on twenty judgments at the same difference in sucrose between samples using the same protocol.

The Hopkins and Gridgeman implicit assumption (PI*z = PZe3 = P,.3) is verified if both the slope of the regression does not significantly differ from 1 .O (bisecting line) and the means of the two frequencies (Px) are not significantly different at P = 0.05, i.e. if the experimental points cluster around the bisecting line (X = Y and Y(0) = 0). When one of the statistical tests is significant the equality assumption is rejected. To test the experimental “clouds” of points in comparison with the bisecting line, the classic regression cannot be used, because the two variables are subject to error. Therefore, we used a method pro- posed by Sokal and Rolf (1969), the reduced major axis regression or rec- tangleness regression.

RESULTS

The results of the 7 comparisons are shown in Fig. 3 and Table 3. Protocol 1 : The means of the frequencies of correct responses above chance

(Px) obtained with the duo-trio and triangle tests did not differ significantly, nor did the slope of the regression differ from 1 .O. Therefore, for this comparison the Hopkins and Gridgeman implicit assumption can be accepted.

Protocol 2: The regression slopes of the three comparisons were not significantly different from 1 .O. However, in the two comparisons that included the pair test, the means of the frequencies of correct responses above chance were significantly different; consequently for the two comparisons pair/duo trio and pairhiangle the Hopkins and Gridgeman implicit assumption can be rejected.

Protocol 3: No significant differences were found between the frequencies of correct responses above chance of the pair and duo-trio tests, but the Hopkins and Gridgeman equality assumption was rejected in the case of the duo- triohiangle and pairhriangle comparisons. For the comparisons duo-trio/pair

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and duo-triohiangle, the results were calculated only with 5 subjects because the analysis of the video recording obtained during the sessions showed that one subject (digit 3 on the graph) performed the duo-trio test once as if it was a pair test (knowing whether the standard was the more or the less sweet of the two samples, the subject doesn’t need to taste it to give his judgement). The other subjects followed the instructions, except perhaps subject 5 showed a behavior similar to subject 3 but only once out of the ten tests.

DISCUSSION

The implicit assumption of Hopkins and Gridgeman model seems to be valid for protocol 1 where the subjects do not know the nature of difference between products. Then triangle test is more powerful than duo trio-test. But, as the three protocols were performed by the same subjects, and the nature of the difference between the samples was indicated for Protocols 2 and 3, the authors have tried to specify for Protocol 1, whether or not the subjects used preferentially the sweet taste to investigate the difference between the samples in spite of the phenol “trap” tests inserted. Therefore, at the end of the fourth repetition of Protocol 1, the following question was posed to each subject: “For the realization of the Protocols 2 and 3 we have told you that the difference is based on the sweet taste; in your opinion, what was the nature of the difference(s) in the tests performed in accordance with the Protocol 1 (4 answers maximum); indicate in each case your degree of confidence on the scale from 0 to 10”. Of the 6 subjects, 4 indicated the sweet taste was used as a criterion but only one with a degree of confidence higher than for the other criteria mentioned.

For the Protocols 2 and 3, the Hopkins and Gridgeman’s implicit assumption was verified once for each protocol (Table 3). So it seems that it is not valid, especially for pairhiangle comparison where the assumption is not verified and the mean values of sensory correct responses of pair test are significantly higher than triangle test. But this conclusion does not involve that the pair test is always more powerful than the triangle test. Indeed examination of Fig. 1 shows the maximum increment APx (P,.3 - P,e2) in the probability Px of correct responses above chance required to equalize the power of pair and triangle tests in relation to PI is equal to 0.18. In the present experiment, the difference of mean frequencies of correct responses above chance between pair and triangle tests (PI . 2

- PI .J is equal to 0.29. Under this condition, for Protocol 2 the pair test is more efficient than the triangle test and this result agrees with Ura’s model of efficiency. The pair test seems also to be more powerful than the duo-trio test in the case of Protocol 2 .

Concerning Protocol 3, the difference is too low and the pair test is not always more efficient. However this protocol where the eventual differences between


samples can be exactly known a priori by the experimenter corresponds to a very particular situation, rarely encountered in the food industry.

The results of the present experiment concerning triangle test are open to discussion. Indeed, the correction of frequency of the observed correct responses with the triangle test (in accordance with Hopkins and Gridgeman) was contested by Morrison (1982). According to Morrison, “The triangle method (corresponding to Protocols 1 and 2) uses 6 types of trial with equal frequency-the AAB, ABA and BAA, where B is the sample containing the stimulus, plus ABB, BAB, BBA. The subject task is to identify the sample that is different. For the first three trial types this means selecting the sample containing the stimulus (. . .) and P* = PI . 3 + (1 -PI .3/3. For the other three types it is quite different. With two stimuli and a blank the subject may either detect both

detect exactly one of them (2P1.3 (l--Pl.3)), or detect neither (1 -Pl.3)2. If both are detected a correct response will be made with probability 1 .O. If neither are detected the probability of a correct response is 1/3, but if only one is detected the probability of an incorrect response will be 1 .O since this will appear to be 2 blanks, 1 stimulus type trial and the subject will select the interval in which he had detected the stimulus. For the trials the probability of a correct response becomes P* = PI .32 + (1 -PI .3)2/3 and for the entire session, assum- ing an equal number of all six trial types it is P* = 1/2(P1.3 (1 -P1.J3 + P1.32 + (1 -P,.3)2/3. Note that P1.3 = ((3P* - 1)/2). If we apply this equation to the calculation of PI .3 from the experimentally observed proportion P* with the triangle test, the conclusion obtained for the paidtriangle comparison performed in accordance with the Protocol 2 changes is that there is no longer a significant difference between the frequencies of correct responses above chance Px. However, two points of criticism can be mentioned concerning Morrison’s correction; the postulate claiming that a blank is not sensorially perceived like a stimulus by the subject when it is presented with 2 real stimuli is not verified. At the same time, the validity of the equation has been contested by Frijters (1981) who takes into account a steady excitatory detection state in the determination of the equation. This excitatory state appears during the realization of the tests containing both stimuli. The effect of a variable excitatory state on the decision rule that the subject uses for overt response selection cannot be evaluated if an internal sensory continuum has not been taken into account.

Some particular working conditions have been used to carry out this experiment. During a session of about 90 min., each subject performed 60 tests, i.e., about one test per minute and half. Did those conditions lead to sensory fatigue and may diminish the significance of the results? The response is negative. On one hand in the present experiment the proportions of obtained correct responses for each test in relation to the basic cycle number, all subjects and protocols combined, remain steady with time (see Table 4). On the other hand, according to previous studies, when a subject is motivated no sensory fatigue is detectable (Pfaffmann 1955; Sauvageot 1984b; Sauvageot and De Gaulmyn 1985; Moskowitz 1985 and Ha Duyen et al. 1987).


TABLE 4. PERCENTAGE OF OBTAINED CORRECT RESPONSES FOR THE THREE TESTS IN RELATION TO THE BASIC CYCLE NUMBER,

ALL SUBJECTS AND PROTOCOLS COMBINED

Duo-trio test 70 Trianqle test 56 58 51

202 207 212 208 204

CONCLUSION

If the experimenter does not know the nature of the difference between the two samples (situation corresponding to the classic presentation of the tests, Protocol l), it seems preferable to choose the triangle test rather than the duo-trio test. If the experimenter does know the nature of the difference between the two samples (Protocol 2) and that this criterion is relevant, the pair test is to be preferred.

ACKNOWLEDGMENTS

We wish to express our thanks to T. Ha Duyen for the use of his study using video films and S. Orsoni for editing the text.

REFERENCES

BYER, A.J. and ABRAMS, D.A. 1953. A comparison of the triangular and two-sample taste-test methods. Food Technol. 7, 185- 187.

DAVID, H.A. and TRIVEDI, M.C. 1962. Pair, triangle and duo-trio test. Technical report 55 , Department of statistics, Virginia Polytechnic Institue, Blacksburg, Virginia.

FILIPELLO, F. 1956. A critical comparison of the two-sample and triangular binomial designs. Food Research 21, 235-241.

FRIJTERS, J.E.R. 1979. Variations of the triangular method and the relation- ship of its unidimensinal probabilistic model to three alternative forced choice signal detection theory models. Brit. J. Math. Stat. Psych. 32, 229-241.

FRIJTERS, J.E.R. 1981. The excitatory state in the triangular constant method. Psychometrica 46, 2 19-222.


GACULA, M.C. and KUBALA, J.J. 1978. Weighting coefficient for the estimation of sensory threshold. Chem. Senses and Flavour 3, (l) , 105-121.

GACULA, JR. M.C. and SINGH, J. 1984. Statistical Methods in Foods and Consumer Research. pp. 378-383. Academic Press, Orlando.

GREEN, D.M. and SWEETS, J.A. 1966. Signal Detection Theory and Psychophysics, pp. 1456 . J. Wiley & Sons, New York.

GRIDGEMAN, N.T. 1955. Taste comparisons-two or three? Food Technol. 9,

HA DUYEN, T. 1988. Contribution a l’etude du comportement de sujets au cours de seances d’evaluation sensorielle, Sc. D. Thesis, Dijon University FRANCE, In preparation.

HA DUYEN, T., MAISON, M.A. and SAUVAGEOT, F. 1987. Quelques don- nees comportementales observees sur 6 sujets hurnains au cours de seances d’evaluation sensorielle de longue duree, Sciences des Aliments, n o hors serie

HOPKINS, J.W. and GRIDGEMAN, N.T. 1955. Comparative sensitivity of pair and triad flavour intensity difference tests. Biometrics, 11, 63-68.

O’MAHONY, M., WONG, S.Y. and ODBERT, N. 1986. Sensory difference tests: some rethinking concerning the general rule that more sensitive tests use fewer stimuli. Lebensm. -Wiss. u. -Technol. 19, 93-94.

MORRISON, G.R., 1982. Measurement of flavour thresholds. J. Inst. Brew.,

MOSKOWITZ, H., 1985. New Directions for Product Testing and Sensory Analysis ofFoods. pp. 103-1 15. Food and Nutrition Press, Trumbull, Conn.

PFAFFMANN, C. 1954. Variables affecting difference tests. IN Food Accep- tance Testing Methodology. Advisory Board on Quatermaster Research and Development, Committee on Foods and Natl. Acad. Sci., Natl. Research Council, pp. 4-20. Chicago, Illinois.

SAUVAGEOT, F. 1976. Un exemple d’etude d’arnelioration des methodes d’evaluation sensorielle . In ‘ ‘L’evaluation Sensorielle de Denrees Alimen- taires”, APRIA, 35 Rue du General Foy, 75008 PARIS, 95-114.

SAUVAGEOT, F. 1984a. Contribution a la caracterisation d’un groupe en evaluation sensorielle de denrees alimentaires. 342 p. Sc. D. thesis, Dijon University, FRANCE.

SAUVAGEOT, F. 1984b. Evolution des reponses de sujets humains en fonction de la duree de l’evaluation. Science des aliments, 4, n o hors-serie 111,

SAUVAGEOT, F. and DE GAULMYN, CH. 1985. Evolution des estimations d’intensite de saveur et d’aromes au cows de seances d’evaluation sensorielle. Science des Aliments, 5, n o hors-serie V, 73-78.

SOKAL, R.R. and ROHLF, F.J. 1981. Biometry, 2nd ed., pp. 454-557. W.M. Freeman and Co. San Francisco.

URA, S. 1960. Pair, triangle and duo-trio test. Report of Statistical Application Research, JUSE, 7, 107-1 19.

148-150.

VIII, 83-88.

88, 170-174.

129-135.

comparison of the efficiency of pair, duo-trio and triangle tests

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