# The Psychophysics of Taste: Perceptions of Bitterness and Sweetness in Iced Tea

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Joel Huber (1974) ,"The Psychophysics of Taste: Perceptions of Bitterness and Sweetness in Iced Tea", in NA - Advances in Consumer Research Volume 01, eds. Scott Ward and Peter Wright, Ann Abor, MI : Association for Consumer Research, Pages: 166-181.

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http://acrwebsite.org/volumes/5710/volumes/v01/NA-01

INTRODUCTION

A psychological space is a spatial model of a process by which subjects organize a group of stimuli. For such a perceptual map to be useful to the researcher, and indeed to the subject, the dimensions of the psychological space should bear a strong relation to the objective attributes of the stimuli. In marketing much of the work that has been done in perceptual mapping has concerned stimuli such as breakfast foods (Green and Rao, 1972) and cigarette brands (Fry, 19 B ) where the physical dimensions are numerous and generally confounded. The object of such research is to find a small number of psychological dimensions which best account for individuals' perception judgements. In psychophysics, by way of contrast, emphasis historically has been on the development of a one-to-one relationship between a perceptual scale and the underlying physical continuum. Analysis has been typically one-dimensional with the object being to determine psychophysical laws that relate physical stimuli to sensory response (see Stevens, 1957 and Moskowitz, 1971, for examples).

The present study is positioned somewhere between these two approaches in that psychophysical techniques are used in the context of a marketing problem. There are a number of ways to derive the multidimensional maps used in marketing. These, unfortunately, do not result in the same solution. Since, additionally, there are no unambiguous physical dimensions (such as occur in psychophysics), it is difficult to decide between the methods. By deriving multidimensional maps from a stimulus space for which the underlying physical dimensions are defined this study attempts to answer the following research questions:

1. What is the degree of congruence between the perceptual maps derived using different methods, and how great is the ability of each to reproduce a known physical space?

2. Can some of the results of one-dimensional psychophysical research find analogues in the relationships of the multidimensional perceptual spaces to the Physical space?

The first question can best be answered if the methods used to derive the perceptual spaces are as different as possible. If these spaces are derived from different kinds of inputs and methods of analysis, then one can be fairly certain that the results are not merely an artifact of the particular method used.

Furthermore, those aspects of the maps which agree can form the basis for hypotheses about the psychophysical relations between the perceptual maps and the known physical space. This information will be used to help answer the second research question. In particular, we shall be examining evidence for threshold and suppression effects. A threshold effect occurs where the PhYsical concentration of a stimulus is too weak to be generally perceived. It will be argued that some subthreshold changes in concentration result in perceptual changes along a different dimension than suprathreshold changes. Suppression occurs where an increase in the concentration of one variable decreases, or suppresses, the perception of a second variable. A common example of this phenomenon is where the addition of sugar to lemonade makes it less sour, the sugar acting to suppress the perception of sourness.

The following study is designed to answer the above research questions using as a stimulus set iced tea made with different levels of tea and sugar. First the experimental procedure will be presented; this includes an explanation of the physical space and a description of the tasks required of subjects. Then we will consider the derivation of three perceptual maps using different inputs and analyses. Finally we shall examine the fit of these maps to each other and to the physical space. From the relations between the maps and the physical space it will be possible to draw some tentative psychophysical conclusions.

Experimental Procedure

A convenience sample of 22 individuals was used to provide subjects for the study. Most of these were students recruited from 1973 summer courses at the University of Pennsylvania. Each was paid five dollars upon completion of the experimental tasks.

The stimuli consist of different levels of Lipton tea concentrate and sugar with constant amounts of beverage base (1.9 grams) in one pint of Philadelphia tap water. The beverage base contains lemon, food coloring and stabilizers so that the stimuli with low levels of tea are essentially colored lemonade. The physical space is illustrated in Figure 1. The convention of indicating a stimulus by its level of sugar and then its level of tea will be continued throughout this paper.

Each subject was required to make similarity and preference judgments on the 120 pairs of the 16 stimuli shown in Figure 1. The similarity judgments were made on a five point scale anchored at "slight" and "great" difference between stimuli. For the preference judgments,subjects were asked which of each pair is preferred, and, on a five point scale, the degree of that preference.

Following their judgments of stimulus pairs, subjects provided judgments on each stimulus taken individually. TheY provided:

1. The degree to which the subject's ideal iced tea is preferred to the given stimulus and

2. An estimate of whether the levels of sweetness and tea are too high or too low relative to that ideal. This was done on a seven point scale anchored at "-3" for "too little," "O" for "just right, and "+3" for "too much".

The task was divided into sets which subjects completed over a period of six days. They were permitted to make up their own schedules. Most subjects came in once in the morning and once in the afternoon and sampled a limited number of stimuli at each session. Stimuli were contained in plastic bottles imprinted with identification numbers. Sampling was done from these common vessels through straws. Very little difficulty was encountered using these procedures.

To summarize, then, for each subject the following data was collected:

1. Similarity (sij) and preference (Pij) judgments on each pair of the 16 stimuli

2. A categorical judgment (Ci) for each stimulus i indicating how much more preferred the ideal is than it.

3. The degree to which each stimulus has too much, or not enough, sugar or tea. Symbolized by dik for stimulus i by perceptual dimension k.

This data is then analyzed by the following methods to derive group perceptual spaces:

S1. A two dimensional space derived from the diks averaged across all subjects. The average perceived values for sugar make up one dimension while those for tea make up the second.

S2. A space derived from an INDSCAL analysis of the similarity (sij) judgments.

S3. A space derived from an MDPREF analysis of individual preference scales obtained from the pijs.

The next section will present an explanation of these methods and a qualitative evaluation of the spaces they derive.

DERIVATION OF THE PSYCHOLOGICAL SPACES

S1. Space derived from perceptions of tea and sweetness.

The diks are not direct evaluations of sweetness and tea in the stimuli. They are rather the degree to which each stimulus has not enough, or too much, sugar or tea relative to the subject's ideal. On the assumption, however, that the preference values are single peaked with respect to charges in a given dimension, the diks should be monotonically related to the underlying subjective dimension. This effect, illustrated for a hypothetical subject, is given in Figure 2.

RELATIONSHIP OF diks AND UNDERLYING DIMENSIONS, ASSUMING A SINGLE-PEAKED PREFERENCE FUNCTION

In the above hypothetical case of a single-peaked preference function, asking for dik produces little distortion of the underlying subjective dimension and, additionally, gives information on the position of the subject's ideal point.

Thus a strong monotone relationship between the diks and the physical dimensions provides evidence for a single-peaked utility function and for the assertion that the diks can be considered a reasonable surrogate for a direct perceptual scale.

There is reason to believe from the work by Moskowitz (1971) and Kamen et al. (1962) that sugar and tea will mutually suppress the effects of one another. That is, if the level of sugar increases given a set level of tea, then the perceived tea level should decrease.

Both of the above hypotheses can be tested by attempting to predict the diks as functions of the physical dimensions. The index of fit provides evidence of reasonable subjective scales while the parameter values provide evidence of suppression.

Since the diks are at best ordinally scaled any monotone transform of their values is permissible. Phase IV of PREFMAP (Carroll, 1972) finds the best monotone transform, Fm, of the diks so that they are predicted by a linear combination of the physical dimensions. For perceptual dimension k we have:

(1) F

_{m}(d_{ik}) = a_{1}x_{is}+ a_{2}x_{it}

Here, = represents the best least-squares fit of the monotone transform of the diks to a linear combination of the physical levels of sugar (xis) and tea (xit). This monotone regression was done for both sweetness and tea for each of the 22 subjects.

The indices of fit indicate the degree to which the assumption of a single-peaked preference function is justified. For sweetness the root-mean-square correlation between the left and right hand sides of Equation (1) is o.969, while for tea it is o.884. Both are fairly good fits especially considering the fact that the regressions were made at the individual level using an independent variable having only seven possible values.

The degree to which the levels of sugar and tea mutually suppress one another can be assessed by the positions of the perceptual vectors in physical space. These projections are shown in Figure 3.

The vector's from the origin indicate for each subject the direction in which that subject's perception of sugar or tea has the greatest increase. Notice that most of the subjects give evidence of mutual suppression for both sugar and tea. For example, a subject whose vector of perceived tea is in the third quadrant (as most of them are) assesses the level of tea to be higher as the level of sugar decreases. Conversely, a higher sugar level suppresses the perception of tea for that subject. In the same way, additional tea suppresses perceived sweetness for those subjects whose vectors lie in the fourth quadrant. It is impossible to tell whether the lack of suppression indicated by those subjects whose vectors lie in the first quadrant is due to different perceptual mechanisms or merely to response errors.

In any case, the data do provide solid evidence for both hypotheses:

1. using the diks to represent the psychological dimensions and

2. for the mutual suppression of sugar and tea.

Given that the diks can be considered to produce reasonable psychological dimensions then it should not be invalid to form a group space of perceived sweetness and tea by averaging across subjects. The space, which we can call S1, is given in Figure 4. For ease of interpretation equivalent sugar levels have been linked together.

AVERAGE PERCEIVED SWEETNESS AGAINST AVERAGE PERCEIVED TEA

There are several aspects to note about this space. First, subjects appear more sensitive to changes in sugar than to changes in tea. This is especially true considering the fact that the ratio of adjacent levels of tea is 1:2 while for sugar it is 1:1.6. Second, there appears to be little ability to discriminate between the two lowest levels of tea -- probably due to a threshold effect. Finally) the degree of mutual suppression appears to depend on the levels of the stimuli. For example, an increase in tea from level three to level four reduces the perception of sweetness at middle levels of sugar but not at the highest or lowest levels.

In conclusion, the foregoing has attempted to justify the use of the desired degree of change in a stimulus as a surrogate for direct perceptual scales. The scales that are formed exhibit expected mutual suppression of tea and sugar for most of the subjects. Finally the two dimensional space that is formed from the two perceptual scales is found to reasonably reproduce the underlying physical space. Some of the particular idiosyncracies of this space may be due to an artifact of the method or may really represent psychophysical phenomena. A comparison of this map with the other perceptual maps that will be derived should help resolve this issue.

S2. Psychological space derived from proximity measures, sij

The proximity measures of each subject were used as input to Carroll and Chang's (1970) INDSCAL. It was hoped that INDSCAL would be of particular promise in revealing the physical structure because its unique orientation produces dimensions along which individuals differ in their perception of stimuli.

Carroll (1972) used INDSCAL to analyze responses to tea that differed over temperature and amount of sugar and was able to reproduce quite well the original dimensions. Unfortunately, in this case subjects were not tasting tea but only asked to imagine a comparison between, say, stirring hot tea with three teaspoons of sugar against luke warm tea with one sugar. It could be argued that in these kinds of thought experiments the subjects devise decision rules that enable them to get through the experiment. It is not too surprising under such conditions that a fairly well defined physical space should emerge.

A three dimensional INDSCAL solution was required to produce reason dimensions of tea and sugar. The space, made up of the first and third dimensions, is shown in Figure 5. The second dimension, representing average preference, is left out. Psychological sweetness and tea appear to be at about a 30 degree clockwise rotation from the given orientation. The two given dimensions seem to best represent strength (sweetness x tea) and balance (sweetness/tea). Furthermore, the two lowest levels of sugar are highly confounded. One plausible interpretation of the structure is that an increase of sugar from its lowest level to its next level is perceived not as an increase in sweetness but as a decrease in tea. Thus, the higher level of sugar is not perceived directly but acts instead to mask the level of tea. As appealing as this hypothesis might be, it is not supported by the space of perceived sweetness and tea in Figure h. In that case an increase in sugar from level one to level two is seen as an increase in sweetness.

In conclusion, the INDSCAL model failed to reproduce the physical dimensions as well as was hoped. Specifically, tea is once more indistinguishable at its lowest levels while the perception of sugar at its lowest levels appears to be confounded with the perception of tea. The third perceptual space should give some indication as to whether these conclusions are spurious or not.

S3. Psychological space derived from Preference judgements

If one has preference vectors for a group of subjects it is possible to derive a group space of subjects and stimuli such that the closeness of a subject point to a stimulus reflects his preference for that stimulus. Ross and Cliff (1964) and Schonemann (1970) developed a solution to the linear analogue of Coombs' (1964) unfolding model. The stimulus space derived here is a modification of their solution suggested by Carroll (1972) which he claims has superior least-squares properties and is less susceptible to degeneracy. The process, in the present case, has the following steps:

1. Preference scales are derived from preference judgements on pairs of stimuli via MONANOVA. As this procedure is quite novel, an explanation is given in an appendix to this paper.

2. The 22 subject by 16 stimuli matrix is column centered. This has the effect of removing the average Preference vector.

3. This matrix is entered into MDPREF (Carroll and Chang, 1964) which used Eckart-Young decomposition to produce the stimulus space shown in Figure 6.

S3. PSYCHOLOGICAL SPACE DERIVED FROM MDPREF ANALYSIS OF PREFERENCE DATA.

What is most striking about this space is its resemblance to the INDSCAL solution in Figure 5. A forty degree clock-wise rotation of Figure 6 lines-up the two solutions very closely. Furthermore. the same suppressive effect is found at low levels of sugar so that an increase in sugar in the first two levels is interpreted as an decrease in tea.

The correspondence between these two solutions is all the more gratifying given their methodologies. Recall that the INDSCAL solution is derived from a three dimensional space where the dimension representing average preference is left out. Similarly, the data for the MDPREF solution were first column centered which has the effect of removing the average preference vector. Of course, this result could be an artifact of the data collection procedures due to the fact that the preference judgements on each stimulus pair were given right after the similarity judgements. However, a one dimensional proximity solution of the similarity data does not reveal preference while a two-dimensional solution of the preference judgements (treated as distances) does not reveal physical attributes. So-if experimental artifact is driving the similarity between these two spaces, it is not because the data are identical.

The slopes of the lines connecting equivalent sugar levels indicate the degree to which increases in tea suppress perceived sweetness. Thus, a negative slope indicates that more tea masks perceived sugar. Given the arbitrary orientation of the MDPREF solution it is impossible to tell which slopes are negative. By comparing, however, the relative slopes, it is clear that the degree of suppression is a function of the level of sugar. Thus, in Figure 6, the degree of suppression is much higher at the highest levels of sugar than at the lowest levels. If, then, this pattern of slopes is compared with the patterns of the other perceptual maps, no consistent pattern of suppression emerges. For example, the two highest levels of sugar have approximately the same slope in the MDPREF solution while they diverge sharply in the other perceptual maps.

To summarize, then, the MDPREF space fails to reproduce the physical space in much the same way as the INDSCAL solution. The first two levels of sugar appear to be perceptually confounded with lower levels of tea, and, once again the two lowest levels of tea form no clear pattern. Looking, however, at the patterns of suppression, all three solutions appear to be somewhat different from each other.

Relationship between the spaces

In order to ascertain the degree of congruence between the three psychological spaces, S1, S2, and S3 and the physical space, which we may call S0, the spaces are rotated and expanded to maximal congruence. The procedure, developed by Cliff (1966) and programmed by Pennell and Young (1967) allows a similarity transform to best match the corresponding points in the two spaces. The program produces two measures of goodness of fit: (1) the average cosine of the angle between corresponding stimuli, and (2) the product moment correlation of the interpoint distances. The first criterion is somewhat less restrictive in that it allows for differential expansion and contraction of the axes. Both are given in Table 1 below:

The correspondences between the perceptual maps and the physical space are about the same -- there is no clear dominance of one method in terms of being able to reproduce the physical space. The general agreement of the maps is remarkable considering that they were derived by different methods on different kinds of data. On the other hand, no one map was able to do a really good job of reproducing the physical dimensions. We can, however, be fairly confident that those features that the three derived maps have in common relative to the physical space, represent perceptual phenomena and not methodological artifact.

These features are summarized below:

1. The two lowest levels of tea seem to be indistinguishable. This is probably a threshold effect.

2. The two lowest levels of sugar separate only in S1. In the MDPREF and INDSCAL solutions a higher level of sugar appears to bring a decrease in the tea dimension rather than being directly perceived as an increase in sweetness.

3. In general the degree of mutual suppression appears to be a function of the levels of the stimuli, but the function is not clearly consistent across solutions.

Summary and conclusions

Three methods were used in an attempt to reproduce the physical space of the stimuli. None of these worked very well, and they all seem approximately equivalent in their ability to reproduce the physical structure. By comparing, however, those aspects that are similar across solutions some psychophysical generalizations could be made.

The results of this study are not encouraging from the perspective of forming perceptual maps. If subjects are not able to reproduce the physical structure in this simple case, it is probable that they would do even worse in more complex situations where the physical dimensions are confounded or not even known.

APPENDIX

THE DERIVATION OF A PREFERENCE SCALE

We shall consider four ways to produce an individual preference scale from data in this study. The results of these various scales will be intercorrelated to see if any scale seems to be 'central' with respect to the others.

P1. Categorical judgement scale

This scale consists simply of the categorical judgement values Ci (i=1,16), where Ci is the degree to which the ideal iced tea is preferred to stimulus i. For analysis the values are subtracted from six so that a high score will reflect preference for the stimulus.

This scale is expected to be relatively inaccurate for the individual subject because each value reflects just one judgement forced onto a five point scale.

P2. The linear scale

This scale, similar to one developed by Scheffe (1952), assumes that there exist scale values n1, n2, .., nn such that the given preference judgments take the following form:

(1) Pij = ni - nj + eij

where eij are identically distributed normal variates. It can be shown that an unbiased estimator of ni is

An F-test exists to perform a (descriptive) test of the null hypothesis that all of the nis are identical.

P3. The nonmetric absolute-value scale

This scale assumes that there exist scale values n1, n2, ..., nn such

that the absolute-value of the preference judgments is monotonically related to the absolute-value of the differences between affective values. Mathematically this is

(3) Fm|Pij| = |ni-nj|

where Fm is the best monotone transformation of the data and = indicates a least squares approximation.

This scale is being tested because it is readily available in nonmetric scaling packages. The problem is formally equivalent to determining the positions of points in one-dimensional space given the distances between points. Of course, some information is lost by taking the absolute-value which may or may not distort the final preference scale.

TORSCA 8 (Young and Torgerson, 1967) is used with its nonmetric option to derive P3.

P4. Nonmetric signed-value scale

This scale assumes that there exist scale values n1, x2, .., nn such that

(4) Fm(Pij) = ni =nj

where, once again, Fm is the monotone transformation that produces the best least-squares fit to the model.

MONANOVA, a conjoint measurement program by Kruskal (1965) is used to solve for such scale values. If a skew-symmetric matrix of preferences is inputted into MONANOVA as a two-way design it will determine values of ai and bj such that

(5) Fm(pij) = ai + bj.

here Fm, ai and bj are chosen such that the sum of squared errors is at a minimum. Since, however, the input is skew-symmetric, so that Pij equals -Pji, the solution for ai will be approximately equal to -bi. If we allow our scale values to be

(6) Pi = (ai-bi)/2

then MONANOVA does essentially what is done in Equation (4).

The last two methods for deriving a preference scale, P3 and P4, only assume that the input data is of ordinal quality. As such, they are theoretically stronger in that they assume less. They may, however, suffer from problems of degeneracy and local minima. Klemmer and Shrimpton (1963) found this to be the case in attempting to derive a nonmetric absolute value scale using a modification of Shepard's (1+ 1) model. Similarly, Sibson (1972) reports difficulty applying the same model to produce a temporal sequence of grave sites where the proximity measure is the degree of overlap in the contents of the graves. To my knowledge MONANOVA has not been used in an attempt to solve these kinds of problems.

Interrelations between the preference scales

The four preference scales were compared for each subject using the product moment correlation and the Spearman rank correlation. The root-mean-square across all individuals is shown in Table 2.

P2 and P4 appear to be the most central in that their correlations dominate the rows and columns. The high correlation between these two scales can be interpreted in two ways. On the one hand, the linear scale is shown to produce as good results as a model that allows free monotone transformation of the input data; an indication that the more complex model is not necessary. On the other hand, the high correlation of the MONANOVA result with the stable linear model, indicates that it has not been plagued with problems of degeneracy or local minima. A better test of the two methods would be on data that is highly nonlinear. In such a situation the MONANOVA solution should Produce better results.

MONANOVA, with a skew-symmetric matrix serving as input, could be used for more than just the production of reliable preference scales with strong metric properties. Indeed, the procedure could be used any time it is reasonable to ask respondents how much more of an attribute one stimulus has than another. By this method, for example, scales could be developed of power, risk or sweetness.

BIBLIOGRAPHY

Carroll, J. D. (1972) "Individual Differences in multidimensional scaling" in R. N Shepard, A. K. Romney & S. Nerlove, eds. Multidimensional Scaling: Theory and Application in the Behavioral Sciences, Academic Press, N. Y.

Carroll, J. D. and J. J. Chang (1970) "Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckhart-Young decomposition" Psychometrica, Vol. 35, pp. 283-319.

Caroll, J. D. (1964) "Nonmetric Analysis of Paired Comparison data" Paper presented at the joint meeting of the Psychometric and Psychonomic Societies, Niagra Falls, October 1964.

Cliff, Norman, (1966) "Orthogonal Rotation to congruence," Psychometrica, Vol. 31, pp. 31-42.

Coombs, Clyde H., (1950) "Psychological scaling without a unit of measurement" Vol. 57, p. 148-158.

Fry, Joseph N. (1971) "Personality variables and Cigarette brand choice" Journal of Marketing Research, Vol. VIII, (August, 1971) pp. 298-304.

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Shepard, R. N. (19625 "The analysis of proximities: Multidimensional scaling with an unknown distance function" Psychometrica, Vol. 27, Part One, p. 125-139, Part Two, p. 219-246.

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