Product Familiarity and the Strength of Brand-Attribute Associations: a Signal Detection Theory Approach

J. Wesley Hutchinson, University of Florida
Mike Zenor, University of Florida
ABSTRACT - The theory of signal detectability (TSD) is applied to pick-any data for brand/attribute associations. It is argued that the pick-any methodology introduces a desirable form of item selection bias and the TSD method of analysis removes undesirable response biases. The assumptions of the methodology are presented and tested with exploratory data from the domain of non-prescription cold remedies.
[ to cite ]:
J. Wesley Hutchinson and Mike Zenor (1986) ,"Product Familiarity and the Strength of Brand-Attribute Associations: a Signal Detection Theory Approach", in NA - Advances in Consumer Research Volume 13, eds. Richard J. Lutz, Provo, UT : Association for Consumer Research, Pages: 550-453.

Advances in Consumer Research Volume 13, 1986      Pages 550-453


J. Wesley Hutchinson, University of Florida

Mike Zenor, University of Florida


The theory of signal detectability (TSD) is applied to pick-any data for brand/attribute associations. It is argued that the pick-any methodology introduces a desirable form of item selection bias and the TSD method of analysis removes undesirable response biases. The assumptions of the methodology are presented and tested with exploratory data from the domain of non-prescription cold remedies.


It is commonly assumed that there is a strong relationship between product familiarity and consumer knowledge (e.g., Bettman and Park 1980; Brucks 1585; Johnson and Russo 1984; Kanwar, Olson and Sims 1981; PunJ and Staelin 1983). That is, one result of numerous encounters with product information (including purchase, usage and advertising) should be that consumers will learn more facts about the various competing brands. These facts are presumably represented in memory by corresponding associations between brands and attributes (Anderson 1983; McClelland and Rumelhart 1985). Under perfect conditions valid facts would be represented by strong associations and invalid facts would be represented by weak (or nonexistent) associations.

In actuality, however, there is good reason to suspect that validity and strength of association will sometimes be at odds with each other. That is, through lack of involvement, lack of education, and/or misleading advertising, consumers may become confused about which brands have which attributes. Since associative strength is likely to be a major determinant of which facts will be accessed during decision making, it is important to know the extent to which validity and strength are correlated.

Measurement Issues

In cases which are designed to test general properties about consumer information processing, the specific brands and attributes investigated are typically either hypothetical or some small convenience sample of all possible brand/attribute associations in an existing market. The problem of whether such a sample will generalize to the total population of brands and attributes is often not given serious attention. One reason for this is that this population is extraordinarily large. For instance, consider non-prescription drug products (which will be discussed in greater detail later). The FDA has estimated that there are approximately 500 active ingredients distributed among approximately 300,000 brands. Thus, there are 150 million possible brand/attribute associations that may exist in consumer memory. Of course, only a small fraction of these are valid associations and an even smaller fraction are likely to be represented in memory for most consumers. In this sense, measuring consumer knowledge is rather like searching for the proverbial needle in a haystack. Therefore, it is of considerable theoretical and pragmatic value to be able to estimate, at an aggregate level, the amount and validity of consumer knowledge about various product domains. The remainder of this paper presents one methodological approach to this problem and illustrates its use in an exploratory study of the relationship between product familiarity and the strengths of brand/attribute associations for cold remedy products.

Using Pick-Any Data

The most straightforward approach to estimating consumer knowledge might be a test instrument such as a simple true/false test covering brand/attribute associations. This approach would require preselecting a subset of items that was somehow representative of the product domain. Great care would be needed in order to ensure that experimenter bias was not introduced by the selection procedure. An alternative approach that has been suggested for situations such as this is the use of pick-any data (Holbrook, Moore and Winer 1982). In particular, respondents might be allowed to choose the brands that they are most familiar with and then indicate the attributes they believe are possessed by those brands. This approach is especially appropriate for descriptive studies, such as the one reported later, because the respondents choices focus the data on the brands that are most likely to be in the realm of consideration during purchase. Thus, the use of pick-any data converts item selection bias from a liability to an asset.

Signal Detection Theory Analysis

In addition to the problem of item selection bias, there is great potential for response biases of various sorts to affect the measurement of brand/attribute associations. It seems likely that some attributes may be more frequently chosen or avoided in general, regardless of the strength of the association between that attribute and any particular brand. One methodology that has proven extremely useful in eliminating such biases is the theory of signal detectability (TSD; Baird and Noma 1978; Combs, Dawes and Tversky 1970; Green and Swets 1966; McNicol 1972). This approach assumes that respondents are trying to discriminate two types of events. The most developed domain for this method is psychophysics where the events are typically trials in which a stimulus was presented and trials in which no stimulus was presented. The goal of the methodology is to measure the sensitivity of the respondent to the presence of the stimulus unbiased by the respondents beliefs about the likelihood of such events or their predispositions to respond one way or another. This methodology is not limited to psychophysics, however, and has been recommended as a preferred method for measuring recognition memory as well (Murdock 1982; Srull 1984).

In the present context, the goal of the analysis is to measure consumer sensitivity to true vs. false brand/ attribute associations. This application of TSD is illustrated in Figure 1.



The associative strength of a given brand, a, and a given attribute, b, is assumed to be normally distributed random variable, Sab. Figure 1 depicts the probability distribution functions for a true association (SabT) and a false one (SabF). The TSD model assumes that people use associative strength to judge the validity of a brand/ attribute association. There is considerable psychological evidence for the plausibility of this assumption in memory-based decision making (Atkinson and Juola 1974; Murdock 1982; Smith, Shoben and Rips 1974).

For pick-any data, it is natural to assume that an attribute is chosen for a given brand whenever its strength exceeds some criterion, or threshold (c in Figure 1). The probability that a given valid attribute will be chosen (referred to as a "hit") is given by the area to the right of the criterion under the p.d.f. for SabT. The area under the curve to the left of the criterion corresponds to the probability that a valid attribute will not be chosen (referred to as a "miss"). Similarly, the probability that a given invalid attribute will be chosen (referred to as a "false alarm") is given by the area to the right of the criterion under the p.d.f. for SabF, and the area under that curve to the left of the criterion corresponds to the probability that an invalid attribute will not be chosen (referred to as a "correct rejection").

The TSD model assumes that response bias results in raising or lowering the criterion, but does not alter the strength distributions for the two types of associations. Therefore, the difference between the means of the two distributions (referred to as d') is an unbiased estimate of sensitivity. If the two distributions are assumed to have equal variances, then d' can be estimated as follows:

d' = ZH - ZF = SabT - SabF (1)

where ZH and ZF are the z-score transforms of percent hits and percent false alarms, respectively. Moreover, correct choices will be maximized when the likelihood ratio, b = HT/HF, of the two distributions at the criterion is such that

b = p(F)/p(T) (2)

where p(F) and p(T) are the base rate probabilities associated with false and true associations, respectively. The subjective value of hits (VH) and correct rejections (VCR) and the subjective costs of false alarms (CFA) and misses (CM) may vary depending on the situation, however. Under such circumstances, optimal B is given by

b = p(F) x (VCR + CFA)

      p(T) x (VH + CM) (3)

In summary, TSD makes three basic assumptions.

A1 Associative strength is normally distributed.

A2 The distributions of strength for different brand/attribute pairs may have different means but variances are equal.

A3 Respondents set their criteria at optimal levels.

Given assumptions A1 and A2, response rates for hits and false alarms are sufficient for estimating an unbiased sensitivity measure, d', and a measure of response bias, B. If A3 is also holds, then the base rates may be divided out of B to yield the ratio of subject "importances" which we will denote by v.

v= VCR + CFA        b x          p(T)

       VH + CM                         p(F)          (4)

Level of Aggregation

TSD seems most appropriate as an individual level model of association strength for particular brands and attributes. As such the estimation of d' and B would require numerous within subject observations for each brand attribute pair. This is clearly not feasible given our earlier discussion. Therefore, a major issue becomes whether or not there is a reasonable way to aggregate data such that the assumptions of TSD are at least approximately preserved. That is, various groups of individuals, brands and/or ingredients must be identified that are plausibly homogeneous with respect to associative strength. Since the present goal is to develop a viable, descriptive measure of consumer knowledge, a relatively liberal criterion for the satisfaction of TSD assumptions may be adopted. If the goal were to develop a theoretical model of information processing based on TSD, the criterion would need to be much more strict. That is, we are more concerned with removing response bias and estimating sensitivity than with modeling the decision process in a pick-any task, per se.


In order to illustrate the application of TSD to pick-any data, we have analyzed a subset of a larger data base comprised of several measures of consumer knowledge about non-prescription cold remedies. We will not describe the full study since its details are not relevant for the present analysis.


Subjects. One hundred and fifty-four undergraduate Marketing majors at the University of Florida participated in the study for course credit during the Fall semester of 1982

Stimuli. All brands listed in the Handbook of Non- Prescription Drugs (1979) as either Internal Analgesic Products or Cold and Allergy Products as well as a few new brands not listed (total = 154) were displayed in alphabetical order down the left hand side of three consecutive response sheets. A list of several types of descriptors (ingredients, symptoms relieved, side effects, dosage forms, etc.) was given on a cover page. In this analysis we focus on the four major types of ingredients found in cold remedies: analgesics, antihistamines, decongestants, and cough suppressants. The exact response alternatives are given in Table 1. On the cover sheet, they were listed along with 16 other ingredients in alphabetical order.



Procedure. Respondents were given a four-page booklet. The first page contained instructions, a reference list of brand descriptors, and a response form for indicating for each of five cold symptom categories (1) the number of times in the past year that they experienced each symptom type, (2) the brands they used last in treating those symptoms, and (3) the brands they would consider purchasing for those symptoms if they needed them today. The five cold symptom categories were Allergy, Cough/Sore Throat, Flu, Headache, and Head Cold. The subsequent three pages listed the 154 brand names and provided spaces for reporting brand descriptors. Respondents were given three tasks. First, they were to examine the brand names and identify approximately twenty brands with which they felt "very familiar." Second, they reported their frequencies of illness, brands used last and brands they would currently consider. Finally, next to each brand they had previously identified as "very familiar," they recorded the number associated with each descriptor they felt applied to the brand (up to a maximum of 14 descriptors). Sex and age information was also recorded.


The average number of brands chosen as familiar was 19.1. The Handbook of Non-Prescription Drugs (1979) was used to identify the correct ingredients for each brand. Then, for each brand chosen as familiar, each ingredient was classified as either a hit, a miss, a false alarm, or a correct rejection depending on its validity and whether it was chosen, or not. Thus, there were over 41,000 observations in the initial data base (i.e., 154 respondents x 19.1 brands per respondent x 14 ingredients per brand).

Respondents were classified on the basis of whether, or not, their self-reported symptom frequency was above the group average. (Flu was excluded because of its generally low frequency and because computer capacity constraints required a reduced analysis; therefore, there were four Symptom Frequency variables: Allergy, Cough/ more Throat, Headache, and Head Cold.) Brands were classified on the basis of whether, or not, they were recorded as used last (referred to as Brand Usage) and/or currently considered (referred to as Brand Consideration). These two variables are jointly referred to as Brand Familiarity. Finally, Ingredients was also used as a classification variable. Hits, misses, false alarms, and correct rejections were aggregated within each class formed by crossing these variables (i.e., 896 possible classes). Any class with less than four valid brand/ ingredient associations (i.e., hits plus misses), less than four invalid brand/ingredient associations (i.e., false alarms plus correct rejections), or less than four positive responses (i.e., hits plus false alarms) was dropped from the data base in order to ensure a minimal level of stability. (Only 8 of the 14 ingredients given in Table 1 met this criterion.) An estimate of d', B, and the importance ratio, v, was computed for each of the 220 remaining classes.

Specific Assumptions. In order for the TSD measures to be meaningful the three assumptions discussed earlier must be modified as follows.

SA1 The associative strengths of all valid respondent/brand/ ingredient triples within each aggregation class are indePendent, identically distributed normal random variables.

SA2 The associative strengths of all invalid respondent/brand/ ingredient triples within each aggregation class are independents identically distributed normal random variables.

SA3 All associative strengths within each aggregation class have equal variance (although their means may differ).

SA4 All respondents have knowledge of the base rates, have the same importance ratio and set their criteria so as to maximize subjective utility.

Strictly speaking, it is highly unlikely that these assumptions will hold. However, as an approximation they are fairly reasonable. Since the classification scheme uses those variables that seem a priori most related to associative strength (i.e., Symptom Frequencies, Brand Familiarity and Ingredients), SA1 and SA2 are plausible. SA3 is also plausible since the sources of error variance in memory are probably fairly general and large relative to error variance due to specific aspects or valid versus invalid information. Moreover, there are several ways that SA3 can be tested (McNicol 1972). The standard tests require manipulations that are designed to affect B and v but not d'. These include changing the base rates for the stimuli and changing an explicit payoff scheme for the four types of responses. In the present analysis, certain factors are hypothesized to affect d', but not B or v, or d' and 3, but not v. Specifically,

H1 Frequency of illness and the brand usage/ consideration variables should affect d', but not b or v,

H2 Different ingredients are likely to be associated with different base rates and therefore both dt and b, but not v, may be affected by which ingredient is involved.


H3 None of the factors should affect v and, therefore, b should be linearly related to the objective base rates across aggregation classes (see Equation 3).

SA4 is stated in rather strong terms so that v can be computed empirically. Even if people have imperfect knowledge of the base rates and are unable to be completely optimal in setting their criteria, v should be related only to Ingredients and the relationship should be weaker than for d' or B. If SA3 does not hold, however, and true and false associations have substantially different variances, then differences in their means will affect the computed values of B and v as well as d'.

Data Analysis. As a check on the validity of assumptions SA3 and SA4, hypotheses H1 and H2 were tested by simple dummy variable regressions of d', B and v on Ingredients, Symptom Frequencies, and Brand Familiarity. The results of these regressions (given in Table 2) were generally consistent with the hypotheses. The three classes of knowledge related variables had significant effects on d', but not on B or v. Thus, H1 was supported and H2 was partially supported. The absence of an effect of Ingredients on B most likely resulted from consumers having a poor knowledge of base rates. Interestingly, the effects of Ingredients and Brand Familiarity were larger than the effects of need related factors (i.e., Symptom Frequencies). If consumers who needed the drugs were learning about product alternatives prior to purchase (in order to make an informed choice) rather than after purchase, a stronger effect of Symptom Frequency would have been expected. Alternatively perhaps people who have frequent symptoms use prescription drugs and, therefore, do not know much more than others about nonprescription drugs.



H3 was tested by regressing B on the ratio of the objectively determined) base rates, p(F)/p(T). Overall, this regression was not statistically significant. However, inspection of the scatter plot of these data revealed a linear trend for high values of B. Separate analyses revealed that there was a significant positive relationship for B > 10 (r=.57. o<.001, df=30), but not for B < 10.


The application of TSD to pick-any data appears to provide a potentially fruitful method of measuring associative strength at an aggregate level. A preliminary test of the assumptions required for such analyses was positive and the estimated values of d', in general, conformed to a priori expectations. However, these results must be qualified by the facts that (1) the pick-any methodology lead to many specific ingredients be largely ignored, and (2) the assumption that respondents use knowledge about base rates to make subjectively optimal choices in the pick-any task (i.e., A4) received only weak support. This suggests that this approach will be most useful for revealing relatively large differences in consumer knowledge or for establishing a reasonable unit of measurement (d') for comparisons between different product classes. Fine grained Analyses of consumer knowledge are likely to require other methods.


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