How to Strengthen Your Quantitative Research Outcomes with Attributable Effects Analysis
Article originally posted in Quirk's by David A. Bryant, MA
While it may be simple to define the characteristics of an important attribute, estimating its derived importance is another matter unless you have attributable effects analysis in your toolbox. With this probability-based analytical tool, you can identify which attribute(s) offer the most opportunity and/or the most risk while also providing a clear view of how the relationships between these attributes can help improve purchase intent.
What is Attributable Effects Analysis?
Traditionally, measures of importance have been expressed as functions of statistical relationships such as regression coefficients, correlations and/or the amount of variance explained. Attributable effects analysis takes it further in that, while based on a function of the statistical relationship, it expresses the association between an attribute and overall liking. It does so 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.
How Attributable Effects Works
Attributable effects partitions the impact of each possible attribute into two components: potential and loss. The goal is to identify areas of greatest opportunity (expressed as Potential), and areas of greatest risk (expressed as Loss).
“Potential” is the percentage of those dissatisfied who would become satisfied if perceptions on that attribute were improved. Potential is largest when current performance of that attribute is low and it is closely related to satisfaction.
“Loss” is the percentage of those satisfied who would become dissatisfied if perceptions on that attribute declined. Loss is largest when current performance is strong and it is closely tied to satisfaction.
Attributable Effects in Action
In this example, frequent users of a specific type of body spray were asked to evaluate a number of body spray brands on a set of attributes relating to performance. Overall liking was obtained for each brand as well. We’re looking at 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 separated into top two box vs. bottom three box responses. Those responses will be considered as liked or not liked for overall liking and good or bad for fragrance to simplify.
Attributable effects is used with the goal of assessing the effect of fragrance on liking. 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).
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 overall brand liking. This is the first component referenced above. 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: .3509 from a base of 228 respondents. Conversely, 25 of the 122 respondents, .2049, rating the fragrance as bad felt the brand was good overall. This is the second proportion. These proportions can be combined in the form of a ratio: .3509/.2049 or 1.7123. The ratio is a measure of the relative effect of fragrance on overall liking. As such it suggests that there is a 71% 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 * r – p) / ((p * 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, 1.7123.
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 worse.
Interpreting the Attributable Effect
Essentially, the numerator of this statistic is an estimate of the proportion of the sample liking the brand and potentially influenced by fragrance (and 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 71% greater chance (based on the relative effect of 1.7123) of overall liking among fragrance acceptors, then p * r represents the proportion liking the brand overall and liking the fragrance. p * 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 * r may be greater than 1). As such, the .4529 is rescaled to yield .31.
Knowing that estimating derived importance isn’t as elusive as you may have once thought is a win for any researcher. But being able to do so with a tool like attributable effects analysis that’s relatively easily calculated and offers a straightforward, actionable interpretation can be a game changer for your research.
Another Way to Estimate Attributable Effects
There is another way to estimate attributable effects. It’s algebraically equivalent to the approach above, yet supplies a different perspective on the estimation. Consider the group of respondents who liked the brand overall as the base 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 due to poor fragrance performance
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 who like the brand overall among those considering the fragrance as bad. From the example, that is 25/122 or .205. This proportion is then multiplied by the total sample, 350, to supply a figure compatible with the base of 105 drawn from the same total sample. This gives us an estimate of 72 people 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.