Estimation of the Effect of Attributes on Overall Liking
Introduction
One of the fundamental issues in brand related marketing research concerns the ability to estimate the importance of an attribute, such that manipulation of that attribute causes a change in the overall acceptability of a brand. It may be fairly simple to define the characteristics of an important attribute. For example, an attribute which in some statistical sense has an association with responses given to overall liking of a brand is one of the more highly respected criteria. However, estimation of that association from which importance is derived is quite another issue. Traditionally, measures of importance have been expressed as functions of statistical relationships such as regression coefficients, correlations, the amount of variance explained and so forth. This paper describes a statistic which, while based on a function of the statistical relationship, expresses the association between an attribute and overall liking in terms of the proportion of those respondents whose overall liking is attributable to or influenced by positive perceptions of the attribute. Conversely, the statistic can be interpreted as the change in the proportion of respondents liking the brand if it no longer provided adequate performance on the attribute being studied.
An Example
First, consider the data table below as an example. As background, frequent users of a specific type of shampoo were asked to evaluate a number of shampoo brands on a set of attributes relating to performance. Overall liking was obtained for each brand as well. This was a small set of rating tasks imbedded in a fairly typical segmentation- type questionnaire. Interest centers on the relationship between overall liking and fragrance performance for one specific brand. While all evaluations were obtained using 5-point rating scales, the data have been dichotomized into top two box vs. bottom three box responses to facilitate the analysis. For simplicity, responses will be considered as liked or not liked for overall liking and good or bad for fragrance.
Attributable Effect
A useful simple statistic, called the attributable effect, will be estimated to help summarize the information in the table. This statistic is oriented towards treating fragrance perceptions as causal, influencing ratings of overall liking, with the goal of assessing the effect of fragrance on liking. The statistic is interpreted as the proportion of respondents liking the brand overall that is attributable to a positive (i.e., good) fragrance perception. Conversely, the statistic is an estimate of the extent to which the proportion of respondents liking the brand overall could decline if fragrance perceptions changed from good to bad. As such, this statistic estimates the proportion of the sample with positive overall liking who are vulnerable to change if perceptions of the fragrance changed (i.e., if the positive effect or impact of fragrance on overall liking was removed).
Strictly speaking, while fragrance may be viewed as a causal factor influencing overall liking, its effect cannot be clear1y measured from the data considered here or, in general, from designs such as that depicted here to obtain these data. The most effective approach to assessing causality would be an experiment through which fragrance was actually changed, with the corresponding change in overall liking noted. For the purpose of this paper, quantifying the relationship between fragrance and overall liking will suffice.
The attributable effect has two components. The first is an estimate of the positive perception of the fragrance among those disliking the brand overall. This estimate is then coupled with a second statistic reflecting the effect of fragrance on overall liking in the total sample.
The group of respondents for whom fragrance was acceptable yet disliked the brand overall provides an estimate of the extent to which fragrance acceptance has no effect on, or nothing to do with, overall brand liking. This is the first component referenced above. Those disliking the brand overall serve as a control group of sorts, providing upon extrapolation an image of the marketplace in which the brand was unacceptable despite fragrance performance. The proportion of fragrance acceptors in this group is estimated as .6041, from the 148 of 245 respondents disliking the brand overall.
The second statistic necessary to estimate the attributable effect requires that two proportions be estimated. The first is the proportion of respondents liking the brand within the subset of those stating the fragrance was good: .35 from a base of 228 respondents. Conversely, 25 of the 122 respondents, .20, rating the fragrance as bad felt the brand was good overall. This is the second proportion. Separately, these proportions aren't particularly enlightening, but they can be combined in the form of a ratio: .35/.20 or 1.75. The ratio is a measure of the relative effect of fragrance on overall liking, suggesting that there is a 75% greater chance of liking the brand overall among those who felt the fragrance was good as compared to those who thought the fragrance was bad.
The relative effect is coupled with the estimate of fragrance liking among those disliking the brand overall to yield the attributable effect:
(p x r - p) / (p x r - p) + 1)
where p is the proportion of respondents saying the fragrance was good among those not liking the brand overall, .6041, and r is the relative effect, 1.75. The attributable effect is then .31: a proportion of .31 of those liking the brand overall is attributable to positive perceptions toward fragrance. Further, the proportion of those liking the brand overall in the total sample would decline .31 if fragrance perceptions were to change for the worst.
Interpreting the Attributable Effect
In a very rough, figurative sense, the numerator of this statistic is an estimate of the proportion of the sample liking the brand and potentially influenced by fragrance, and hence at risk if fragrance perceptions were to change. If .6041 is an estimate of the proportion disliking the brand overall despite good fragrance performance, and there is a 75% greater chance (based on the relative effect of 1.75) of overall liking among fragrance acceptors, then p x r represents the proportion liking the brand overall and liking the fragrance. p x r is 1.057. This proportion is then adjusted to remove those fragrance acceptors disliking the brand: .6041 is subtracted from 1.057 to yield .4529. The denominator serves simply to standardize or rescale this proportion (to correct for the fact that p x r may be greater than 1). As such, the .4529 is rescaled to yield .31. (Note for comparison that the correlation between fragrance and overall liking is .15. The square of this figure, around .02, is typically taken in a causal sense as the proportion of variance explained. This number suggests an effect far smaller than that obtained above.)
To provide some insight, first note what happens to the attributable effect for various levels of the relative effect. A relative effect can range in value from 0 to infinity. At 0 and, in general, values less than 1, the attributable effect is negative. This would suggest a bad fragrance perception increasing overall liking, an unlikely event. A relative effect of 1 indicates equal chances of fragrance acceptance or rejection regardless of overall liking and hence, no relationship between them. Then the attributable effect is 0; there is no effect and overall liking will not change if fragrance performance turned bad. However, as r increases in value, as the statistical relationship between overall liking and fragrance strengthens, the effect on overall liking increases. If the relative effect were, say, 100 then the attributable effect becomes essentially 1. Referring back to the example, overall liking would be completely determined by fragrance acceptance. Conversely, poor fragrance performance would lead to complete loss of those liking the brand.
An Alternative Approach to Estimation
A second approach to estimating the attributable effect is available, algebraically equivalent to that given above, which supplies a different perspective on the estimation. Consider the group of respondents who liked the brand overall as the base representing the current franchise and from which the attributable effect is calculated. There are 105 of these people in the example. This base can be split into two segments, those at risk of leaving the franchise due to poor fragrance performance and those unaffected by such a change i.e., those feeling fragrance was bad but liking the brand anyway). The size of the segment unaffected by fragrance can be estimated from the proportion liking the brand overall among those considering the fragrance as bad. From the example, that is 25 / 122 or .205. This proportion is then multipled by the total sample, 350, to supply a figure compatible with the base of 105 drawn from the same total sample. An estimate of 72 people is obtained which is subtracted from the base of 105. The remainder, roughly 35 people, represents those potentially affected and lost to the brand if fragrance was considered bad. Dividing this number by the base of 105 yields an estimate of the attributable effect. In numbers:
(105 - 72) / 105 = .31.
From this perspective, the attributable effect reflects the reduction, as a proportion, in the user base due to a change in the status of the effect, i.e., bad fragrance.
Estimating a Standard Error
A standard error for the attributable effect can be estimated and used to create confidence bounds within which the population effect lies. To simplify calculations, consider the following table layout.
For example, the standard error is .1152. A 95% confidence bound can be constructed around the attributable effect estimate of .31 to yield an interval from .084 to .536. (Note the significance of the effect, with 95% confidence, since the interval did not include O. In general, the significance of the effect can be tested by dividing the estimate of the effect by its standard error. The result can be compared to the z-distribution.)
Considering Several Attributes
Fragrance was one of several attributes evaluated for each brand. Given that the general purpose for estimating measures of derived importance is to identify some few attributes of greatest interest, the attributable effect may be obtained for each attribute and used as a basis for selection. Attributes can be ranked in terms of effect size with the top few attributes being retained as important. Considering, though, the correlated nature of the attributes evaluated, the top few chosen may contain an unreasonable amount of redundant information and may not represent well all facets of brand performance.
One solution typically encountered to resolve this problem with correlated attribute ratings is to parcel attributes into clusters (using some form of cluster or principal components analysis) such that attributes merged together have some aspect of brand performance in common. Each cluster then represents a different facet. From each cluster, an attribute may be selected which best characterizes the features measured by all attributes in that cluster. For example, that attribute which correlates most highly with all other attributes in the cluster may be chosen. Or, with the assumption that all attributes in a cluster are equally correlated, that attribute with the greatest statistical association (using the attributable effect or perhaps correlations) with overall liking may be taken. The effect of each cluster of brand performance characteristics, through the use of the attribute chosen to represent each, can then be estimated using the attributable effect. However, rather than estimate the attributable effect separately, the effects of each attribute on overall liking can be estimated with the influence of the other attributes held constant.
Consider evaluations of a shampoo brand on ten attributes, taken from the same study which provided the example above. When analyzed, three clusters of attributes seemed to provide a reasonable summary of the data. The three clusters represented aspects of fragrance, cleansing ability and value. One item was chosen from each cluster for further analysis. (The fragrance item used in the above example was the one retained from the fragrance cluster.) As was done above, the responses to the three attributes were dichotomized to simplify the analysis. For presentation purposes below, top two box responses were recorded as "+" signs and bottom three box responses received a "-". The attributes were then cross-tabulated to form the eight cells representing all possible response combinations. The eight cells were further cross-tabulated by overall liking responses to yield the 8 x 2 table displayed on back page.
Recall that the attributable effect for fragrance above was .31. Considering that fragrance perceptions would be positively correlated with other brand features, like cleansing ability and value, this .31 is undoubtedly inflated, reflecting at least partially the influences of the other attributes. A cleaner assessment of the effect of fragrance can be obtained by estimating the attributable effect separately for all possible combinations of responses to the other two attributes considered here. Data required to calculate these estimates are provided in the above cross-tabulation. The first four rows are combined to provide a control group, those who felt the fragrance was bad, to which information in the remaining cells, the fifth through eighth rows, are compared, one row or cell at a time. The formula given above for estimating the attributable effect is used here as well. The table below summarizes the results of the analyses.
Perhaps the most useful result of this analysis is the reduced size of the attributable effect for fragrance, obtained when the 29 respondents in the "positive fragrance, negative cleansing, negative value" cell are compared with the control group. The attributable effect, with cleansing and value held constant at negative levels, is .12, that portion of overall liking attributable solely to a positive perception of fragrance. Note also that the attributable effect for fragrance does not change appreciably when one of the two other attributes is held constant at the positive (top two box) level of response. Fragrance does achieve a larger effect only when positive fragrance responses are coupled simultaneously with positive responses to cleansing and value. The data suggest the presence of an interaction among the three attributes such that the three must be perceived positively in concert to exert an influence on overall liking, and that influence accounts for a proportion of .26 of the overall liking responses. (Although the four attributable effects are drawn from tour mutually exclusive and exhaustive sets of the sample of respondents considering the product as having good fragrance, the associated effects are not additive. Each is estimated separately, not using common marginal distributions as a basis for calculation. While an approximate approach is available for providing an additive break-up of the total sample attributable effect, .31 for fragrance as estimated above, the numbers obtained here are closely related, yielding essentially the same interpretation.)
Summary
In summary, the attributable effect of a brand characteristic is relatively easily calculated with a straight forward, readily actionable interpretation. When used in analyses such as shown above, it can be an effective research tool for estimating derived importance.
