Asymmetry Analysis

Rajan Sambandam, TRC

Asymmetrical relationships among variables in satisfaction research have been increasingly investigated in the last decade. However most of the work has been published in academic journals (such as Marketing Science and Journal of Marketing Research), which may not always be accessible to practical market researchers. The objective of this article is to both provide a simple introduction to this topic and add to the existing body of knowledge.

Before examining the question of asymmetry, we need to think about symmetry. Consider a regression analysis where overall satisfaction with a hotel was used as the dependent variable and the cleanliness of the room emerges as a key driver with a weight of 0.44. The implication here is that a unit improvement on the independent variable will result in a 0.44 unit improvement in overall satisfaction. Conversely, a unit decrease in the independent variable will result in a 0.44 unit decrease in overall satisfaction; this is a symmetrical relationship. If the independent variable is measured on, say, a 10-point scale, this result is true regardless of which scale point is considered. In other words, moving from nine to 10 will have the same impact as moving from one to two.

Is this a reflection of the method used or the underlying reality? First consider the method. Regression analysis as used in this example (and often in key driver analysis) is a linear method. The above symmetrical description is the only way of interpreting the results. Hence even if the underlying reality is different, the method will not allow us to see things differently. Is the underlying reality different?

One could consider this question both theoretically and empirically. The theoretical argument that the reality is different goes back several hundred years to Daniel Bernoulli. He put forward the idea that utility is inversely proportional to the quantity of goods possessed. That is, “If the satisfaction derived from each successive increase in wealth is smaller than the satisfaction derived from the previous increase in wealth, then the disutility caused by a loss will always exceed the positive utility provided by a gain of equal size” (see Bernstein 1996). This idea was further refined by Kahneman (2002 Nobel Prize winner in economics) and Tversky when they developed prospect theory to show that people weight losses more than gains of equal magnitude when changes are measured from a reference point.

Essentially, we are talking here about an asymmetric effect where the impact on the negative side happens to be larger than the impact on the positive side. Does this apply to satisfaction research and can it be demonstrated? (See Anderson and Mittal, 2000, for a review.)

The simplest way to demonstrate asymmetry is to plot the relationship between an attribute and overall satisfaction (Figure 1). For simplicity, the attribute satisfaction scale has been divided into three parts (say, Dissatisfied, Moderately Satisfied and Very Satisfied). The kink or elbow in the chart shows the existence of an asymmetric relationship. The interpretation here is that moving respondents from the bottom boxes (Dissatisfied) to the middle boxes (Moderately Satisfied) has a stronger positive impact on overall satisfaction, than does moving them from the middle to the top boxes (Very Satisfied). Similarly, moving respondents from the middle to the bottom boxes has a stronger negative impact than does moving them from the top to the middle boxes.

Such an interpretation provides multiple courses of action for the manager. If the bottom boxes are more populated than they should be, then the strategy would be to try and move some people into the middle boxes. If the bottom boxes are sparsely populated but the middle boxes are heavy, then preventing the middle box people from migrating down would help immensely in maintaining the current overall satisfaction. Attributes of this type are often called “satisfaction maintaining”, but clearly the actual distribution will have to determine the recommended action.

Given the minimal gain in moving from the middle to the top boxes, it should be pursued only if it is inexpensive to do so. On the other hand, if maintaining a large number of customers in the top boxes is very expensive, some could be allowed to slide to the middle boxes without too much of a loss in overall satisfaction ratings. Comparisons with competitors can be very useful in understanding what types of improvements are possible.

The asymmetric relationship can also manifest as shown in Figure 2. In this case, moving respondents from the middle boxes to the top boxes has a much stronger impact than moving from the bottom to the middle boxes.

As we go through these options it is clear that the number of possible action recommendations increases quite a bit when the data are analyzed this way, as opposed to doing a regular regression analysis. If this were a completely linear relationship then both slopes would be equal (the line would be straight) and the recommendations would not be quite as nuanced.

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This article was written by Rajan Sambandam of TRC, a full-service market research provider located in Fort Washington, PA.

[Nov 10, 2009]