Consumer Learning in Awareness and Trial of New Products


Masao Nakanishi (1971) ,"Consumer Learning in Awareness and Trial of New Products", in SV - Proceedings of the Second Annual Conference of the Association for Consumer Research, eds. David M. Gardner, College Park, MD : Association for Consumer Research, Pages: 186-196.

Proceedings of the Second Annual Conference of the Association for Consumer Research, 1971     Pages 186-196


Masao Nakanishi, Graduate School of Management, University of California, Los Angeles


[Necessary computations for this study were done at the Campus Computing Network of UCLA and partly at Japan Information Service Center, Ltd., Osaka, Japan. A sincere appreciation is due to the management of the latter company for making its facilities available to the author.]

In the consumer acceptance process of new products, it is customary to identify the following five stages: awareness, interest, evaluation, trial and adoption (or acceptance). This reflects the tradition established by sociologists in their research of the adoption process of innovations. [See Everett Rogers, Diffusion of Innovations (New York, N.Y.: The Free Press, 1962), p. 78.] Much effort has been directed toward the identification of the determinants of consumer behavior in those stages, resulting in a number of studies of individual and situational ,actors which affect consumer acceptance of new products. In addition to those qualitative studies, attempts have been made to construct mathematical models of consumer response to new products. But the main thrust of past such attempts seems to have been aimed at the stages following the first (=trial) purchase. Stages preceding the trial stage have often been either ignored or simply lumped together in many of those models. It is the purpose of this study to quantitatively investigate this neglected area of transitions between the preawareness and trial stages. In so doing, a particular attention is given to consumer learning involved in the awareness and trial stages.

Models based on mathematical learning theory abound the literature of consumer behavior. But most such models appear to be derivatives of the linear operator model for subject-controlled events. [For a detailed discussion of this model, see R. Bush and F. Mosteller, Stochastic Models for Learning (New York, N.Y.: John Wiley and Sons, 1955.)] In short, this model postulates that the feedback from a purchase affects an individual's probability of purchasing the same product (or brand) next time. It is an attractive model for describing the consumer's response to new products after the first purchase, [See, for example, George Haines, "A Theory of Market Behavior after Innovation," Management Science, Vol. 10, No. 4 (July, 1964), pp. 634-657.] but is not particularly useful in dealing with consumer learning prior to the trial stage simply because there is no purchase which may give the consumer some feedback.

It is obvious that consumer learning associated with the new product acceptance process is not limited to purchase-event feedback. For example,

1. The consumer learns the existence of the new product (the awareness stage).

2. He learns the price, availability, functions and other types of information related to the new product (the interest and evaluation stages).

3. He learns what the product is like by using it (trial stage).

4. Finally, he learns how to use the product properly and even learns to like it (the acceptance stage). It is necessary, therefore, to consider other models of learning in order to describe such varied types of consumer learning.

In this study the following special question on consumer learning is examined: 30 successive exposures to advertisements have cumulative effects on the probability of a consumer's being aware and/or that of his making a trial purchase of a new product? Such cumulative effects are somehow taken for granted, but it is the purpose of this study to throw some light on this type of consumer learning through the construction and testing of mathematical models.


Two basic models which are examined in this study are the variable Markov model (strictly speaking, a first-order Markov chain model with variable transition probabilities) and the linear operator model for experimenter-controlled events. Those are chosen because they permit transition probabilities among states to vary over time, reflecting the level of marketing activities of the firm which introduced the new product. In short, the linear operator model allows for cumulative effects of successive exposures to advertising, and, therefore, one may conclude that such effects exist if the linear operator model turns out to be more descriptive than the variable Markov model. More precise specifications of those models in the awareness and trial stages follow.

Identification of States

Before turning to the model specifications, it is necessary to identify the relevant stages between which the consumer makes transitions. It is theoretically possible to identify a large number of states between the preawareness state to the post-trial state, but the availability of data severely limits the number of states which can be incorporated in the model. In this study, only those states which can be identified by the following two survey questions were considered.

1. Aided Recall Question. [It must be pointed out that an unaided recall question (e.g., "Have you noticed anything new in the line recently?") may also be used to measure awareness although it was not used in this study.] "Have you heard of (new product or brand name)?"

2. Trial Question. "Have you bought it?"

Four states corresponding to the two questions are:

No-Awareness (NA): the states in which the consumer is in if he is not aware of a new product.

Awareness (A): the state in which the consumer is if he is aware of the new product.

No-Trial (NT): the state in which the consumer is if he has not tried the new product.

Trial (T); the state in which the consumer is in if he has tried the new product.

Those who answered the aided recall question affirmatively are assumed to be in a state A; others are in state NA. Those who answered the trial question affirmatively are in state T; others are assigned to state NT. Noe that the validity of the models to be developed are to a large extent dependent on the nature of responses to those questions. For example, it is impossible to identify those consumers who have bought the product, but cannot identify it by the name with those two questions. It is important that we keep in mind that some implicit assumptions are made in order to use the responses to the aided recall and trial questions as the operational definitions of awareness and trial.

Awareness Stage Models

Let Pt be the probability that a consumer is in state A (i.e., aware of the new product) at time point t. Also let x(t) be the probability that the consumer is exposed to advertisements of the new product in period t (defined between time points t-1 and t). This x(t) plays a central role in the following development.

Variable Markov model. Consider the transition probabilities between NA and A. The variable Markov model specifies them as follows:

Prob.(NA -> A in period t) = a1x(t) 0<a1<1

Prob.(N -> NA in period t) = a2(1-a3x(t)) 0<a2,a3<1

Given those specifications, we obtain

Ept = a1X(t) (1 - pt - 1) + [1 - a2 + a2a3S(t)]pt-1

= a1x(t) + (1 - a2)pt-1 - (a1 - a2a3)x(t)pt-1

Linear Operator model. This model postulates that:

Pt = Q1Pt-1 = (1-k)Pu + kpt-1 if the consumer is exposed to advertisements in period t, and

Pt = Q2Pt-1 = (1-k)pL + kpt-1 otherwise.

The expected operator for Pt is then given by

EPt = [(1-k)pU + kpt-1]x(t) + [(1-k)pL + kPt-1](1-X(t))

+ (1-k)PL + kpt-1 + (1-k)(pU-pL)x(t).

The specification for x(t) will be deferred until the empirical test section.

Trial Stage Models

Let qt be the probability that a consumer is in state T at time point t.

Variable Markov model. Since a person has or has not tried a new product, it is reasonable to assume that qt is monotone increasing. With this assumption, the model allows only one way transition from the no trial state to the trial state. Then,

Prob.[NT->T in period t] = bx(t) Hence.

Eqt = qt-1 + bx(t)(1-qt-1).

It is convenient to redefine the above equation in terms of y(t) = (qt-qt-1)/(1-qt-1) rather than qt, i.e.,

Ey(t) = bx(t).

Linear operator model. Unlike the case of the awareness stage model, operators are applied to y(t) rather than qt.

y(t) = Q1y(t-1) = (1-h)yu + hy(t-1) if the consumer is exposed to advertisements in period t,

y(t) = Q2y(t-1) = (1-h)yL + hy(t-1) otherwise.

This results in the following expected operator.

Ey(t) = (1-h)yL + hy(t-1) + (1-h)(yu-yL)x(t)

Specified in this manner, the linear operator model for the trial stage is actually a combination of the variable Markov model and the linear model. A simple application of the linear operators to qt yields an expected operator which is essentially identical to the variable Markov model, thus making it impossible to distinguish between the two.


A test marketing of a new product was conducted in four cities for a period of ten months. Ten monthly telephone surveys of consumers (sample size = 200 each month) in those market areas constitute the data base for testing alternative formulations. [This set of data was first reported in Masao Nakanishi, "A Model of Market Reactions to New Products," unpublished Ph.D. dissertation, Graduate School of Management, University of California, Los Angeles, 1968.] A number of measures were taken in those surveys, but only the responses to the aided recall and trial questions discussed previously were necessary to compute pt, qt, and y(t). Figure 1 shows pt and qt for each area. Expenditures in newspaper advertisements, spot TV commercials, and direct mailing of coupons in each city were also recorded.



The technique for testing the alternative models used in this study is the regression analysis. In order for obtaining specific results, it is assumed that x(t) is linear in the advertising expenditures in period t. If we let A(t) be the advertising expenditures in three media mentioned above, [Actually, advertising expenditures were expressed in terms of dollar spent per 1,000 households within the effective area of each test market. For the justification of this procedure, see Nakanishi, op. cit., pp. 180-183.] then it is assumed that x(t) = do + d1A(t) for an appropriate range of A(t). Given this assumption, the expressions for Ept and Ey(t)can be rewritten as the following set of regression equations:

Awareness Stage.

A1. Variable Markov model equation

pt = c10 + c11A(t) + c12pt-1 + c13A(t).pt-1 + et


c10 = a1d0; c11 = a1d1; c12 = (1-a2) - (a1-a2a3)d0; c13 = (a1-a2a3)d1; et = the disturbance term.

A2. Linear Operator Model equation

pt = c20 + c21A(t) + c22pt-1 + et


c20 = (1-k) [PL + PU - PL)d0]; c21 = (1-k)(pU-pL)d1; c22 = k

Trial Stage.

T1. Variable Markov model equation

y(t) = c30 + c31A(t) + et


c30 = bd0; c31 = bd1

T2. Linear operator model equation

y(t) = c40 + c41A(t) + c42y(t-1)


c40 = (1-h)[yL+(yU-yL)d0]; c41(1-h)(yU-yL)d1; c42) = h

All of those equations are underidentifying in terms of the original parameters of respective models. But the differentiating factor between equations A1 and A2 is the cross product term, A(t)-pt-1. If c13 is significant one may reasonably conclude that this set of observations are better described by the variable Markov model. Similarly, if c42 (= the coefficient of the y(t-l) term in equation T1) is significantly positive, then we may conclude that cumulative exposures to advertisements increase the trial purchase probability.

The basic format of the regression analysis is the combination of time series and cross sectional analyses to take advantage of the entire data set, but equations are also run for each test area separately in order to detect any special source of variations between areas. The regression results for the combined data set are given in Table 1. Area-by-area equations are shown in the Appendix.

In equation Al, neither the coefficient of the A(t) term nor that of the A(t).pt-1 term is significant. The inspection of area-by-area equations shows that this is caused by an extremely high correlation between the A(t) and A(t).pt-1 terms. In order to cope with this multicolinearity problem, a procedure suggested by Telser is used. [See Lester G. Telser, "Least Squares Estimation of Transition Probabilities," in C. Christ and others, eds., Measurement in Economics (Stanford, Calif.: Stanford University Press, 1963), p. 287.] In equation A1', the A(t).pt-1 term is replaced by the yzt term which is less highly correlated with the A(t) term. The coefficient of the A(t) term in A1' becomes significant, but not that of the yzt term. Dropping this term, we obtain equation A2 whose coefficients are all significant. Thus it is concluded that the linear operator model is adequately descriptive of the underlying process.



Turning to the trial stage equations, we see that the coefficient of the y(t-1) term in T2 is significant but negative. Area-by-area equations show similar results. This is inconsistent not only with the linear learning model, but with the variable Markov model. Two reasons may account for the result. First, the y(t)'s are computed by dividing (qt-qt-1) by (1-qt-1). But, if qt has some upper limit, qu(<1), then the denominator should be (qu-qt-1) rather than (1-qt-1). In other words, the y(t)'s may be underestimated by using (1-qt-1) in the denominator. This underestimation becomes more serious as qt-1 approaches qu. Unfortunately, it is impossible to identify the qu value using the regression analysis. Second, because of the variability of the data, the value of y(t) was negative in some cases. This is unavoidable so long as we use telephone survey data for which a fresh sample was taken at each time point. In fact, another study which used consumer purchase diary panel data yielded a positive (and significant coefficient for the y(t-1) term), suggesting the appropriateness of the linear operator model. [See Nakanishi, op.cit., p. 146.] Since both T1 and T2 yielded a statistically significant coefficient for the A(t) term, the effect of advertising on trial purchase probability was beyond doubt. Whether successive exposures to advertisements has cumulative effects on trial purchase probabilities had to be left for more precise analyses.


To summarize the results of the previous section, it was clearly shown that exposures to advertisements affected the awareness and trial probabilities. However, the regression results were less conclusive on the existence of consumer learning related to cumulative effects of exposures to advertisements. It turned out that the linear operator model was an adequate representation in the awareness stage, but yielded an inconsistent coefficient in the trial stage. As was explained, this inconclusiveness may be due partly to the nature of data and partly to the inability of the regression analysis to identify all parameters of the model.

Perhaps, a more basic fault lies in the identification of relevant states. In the preceding formulation, all individuals who answered the aided recall question affirmatively were assumed to be in the awareness state. However, this is only one of many ways "awareness" can be operationally defined. The aided recall question in fact fails to isolate those individuals who are actually unaware of the product tin the sense of being able to identify the product by the name), but answer the question affirmatively anyway. Also, the responses to an unaided recall question are known to result in an over-time pattern totally different from that of the responses to an aided recall question. It may be more reasonable for the purpose of model construction if we treat the affirmative responses to a recall question as exactly what it is and not as a surrogate measure of "awareness."

Another serious shortcoming of model construction in the preceding sections is that very little integration was attempted between the awareness and trial stages. For example, the upper limit of qt in the trial stage was assumed to be one although it is inconceivable that qt exceeds pt at any time--particularly with the data collection procedure used here. Also, even though x(t) plays a central role in both stages, no attempt was made to estimate the parameters of x(t) from the joint data set for the awareness and trial stages.

The proposed extension of the models of this study begins with redefinition of relevant states.

No Exposure (NE): the state in which a consumer is if he has not been exposed to information concerning a new product

Exposure (E):the state in which a consumer is if he has been exposed to new product information, but has not tried it.

Trial (T);the state the consumer is in if he has tried the product.

It is assumed that a consumer answers yes to the awareness question with probability of pc (= probability of confusion), pt, and one if he is in state NE, E, and T, respectively. It is also assumed that a consumer answers affirmatively the trial question (with a probability of one) only if he is in state T. The transitions between states are summarized by the transition matrix of Table 2.



A significant characteristic of the above formulation is that awareness state is now replaced by the exposure state. What is affected by company advertising is not the probability of being aware, for which no precise definition exists, but the probability of answering the aided recall question affirmatively. This seems to be more sensible than the previous formulation. Another important point is that now x(t) is defined as the probability of being exposed to any type of new product information including advertisements for the product. There are other sources of new product information such as in-store sighting, free sampling, and word-of-mouth although advertisements are perhaps the most important to many consumer goods.

It should be noted that both y(t;t') and pt.t' have two subscripts. This is because y(t) = 0 and pt = pc prior to the first exposure to new product information in period t'. If exposures to new product information should have cumulative effects, only the x(t)'s after t' should affect y(t;t') or pt.t'. More specifically, the following linear operators are defined:

pt.t' = (1-k)pU + kp(t-1).t' if exposed to new product information in period t (t>t'),

pt.t' = (1-k)pL + kp(t-1).t' otherwise;


y(t;t') = (1-h)yU + hy(t-1;t') if exposed to new product information in period t (t>t'),

y(t;t') = (1-h)yL + hy(t-1;t') otherwise.

The expected operators for y(t;t') and pt.t' are given by

Ept.t' = (1-k)pL + kp(t-1).t, + (1-k)(pU-pL)x(t)

Ey(t;t') = (1-h)yL + hy(t-1;t') + (1-h)(yU-yL)x(t)

Also, considering the fact that the probability of a consumer's making a purchase is zero to his first exposure to new product information in period t, it seems reasonable to let y(t;t) = (1-h)yU. Similarly, pt.t may be defined as (1-k)pU.

Given the transition matrix of Table 3, we find that:

Prob.(in NE at t) = EQUATION

Prob.(in E at t) = EQUATION

Prob.(in T at t) = 1 - Prob.(in NE at t) - Prob.(in E at t)

In addition, we derive the following:


Prob.(No to awareness question) = 1 - Prob.(Yes to awareness question)

Prob.(Yes to awareness question) = Prob.(in T at t)

If we let:

nt = the sample size for a survey taken at time point t

n1t = the number of those who answered the awareness question affirmatively at t.

n2t = the number of those who answered the trial question affirmatively at t,

then the likelihood function for the observations from a series of surveys taken at time points (t1,t2,t3,...,tM) where M is the total number of surveys is given by



PAN = Prob.(No to awareness question)

PAY = Prob.(Yes to awareness question)

PTY = Prob.(Yes to trial question)

This likelihood function may be used to estimate the parameters of the model There seem to exist no closed-form estimators for the parameters of the model, and hence it will be necessary to rely on a non-linear programming routine to maximize the above likelihood function.

Tests of hypotheses on certain parameters may be performed, using the likelihood ratio test. The most interesting hypotheses are of course Ho: k = 0 and Ho: h = 0, but for practical purposes we will be interested in knowing the relative effectiveness of various vehicles of new product information. So far the relationship between x(t) and those promotional activities has not been specified because it is believed that the best functional form for the exposure probability should be empirically determined.

The proposed extension is still highly tentative, but it squarely attacks some of the more basic problems in model building in the awareness and trial stages of the new product acceptance process. The model may appear overly complex, but the complexity is a problem only in relation to the parameter estimation procedure The availability of an efficient non-linear programming routine mitigates this problem considerably. It may be added that the manner in which survey results are utilized as the data base represents a new approach. Consumer models have heavily relied on continuous consumer panels in the past. The proposed likelihood function opens up a source of data which so far has not been tapped to its maximum potential.




Masao Nakanishi, Graduate School of Management, University of California, Los Angeles


SV - Proceedings of the Second Annual Conference of the Association for Consumer Research | 1971

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