Cluster Analysis 9

Differentiation of the Data

To examine whether the final partition differentiates the data well, we need to examine the cluster centroids. This step is highly important, as the analysis sheds light on whether the clusters are truly distinct. Only if objects across two (or more) clusters exhibit significantly different means in the clustering variables (or any other relevant variable) can they be distinguished from each other. This can be

easily ascertained by comparing the means of the clustering variables across the clusters with independent t-tests or ANOVA (see Chap. 6).

Furthermore, we need to assess the solution’s criterion validity. We do this by focusing on the criterion variables that have a theoretical relationship with the clustering variables, but were not included in the analysis. In market research, criterion variables are usually managerial outcomes, such as the sales per person, or willingness-to-pay. If these criterion variables differ significantly, we can conclude that the clusters are distinct groups with criterion validity.

3. Profiling

As indicated at the beginning of the chapter, cluster analysis usually builds on unobservable clustering variables. This creates an important problem when work- ing with the final solution: How can we decide to which cluster a new object should be assigned if its unobservable characteristics, such as personality traits, personal values, or lifestyles, are unknown? We could survey these attributes and make a decision based on the clustering variables. However, this is costly and researchers therefore usually try to identify observable variables (e.g., demographics) that best mirror the partition of the objects. More precisely, these observable variables should partition the data into similar groups as the clustering variables do. Using these observable variables, it is then easy to assign a new object (whose cluster membership is unknown) to a certain cluster. For example, assume that we used a set of questions to assess the respondents’ values and learned that a certain cluster comprises respondents who appreciate self-fulfillment, enjoyment of life, and a sense of accomplishment, whereas this is not the case in another cluster. If we were able to identify explanatory variables, such as gender or age, which distinguish these clusters adequately, then we could assign a new person to a specific cluster on the basis of these observable variables whose value traits may still be unknown.

4.