Cluster Analysis Forming Groups within the Sample of Respondents

Cluster vs. Factor Analysis Factor analysis for groups of items, identifying common traits underlying their ranges across respondents’ scores. Cluster analysis forms groups of respondents, based on the similarity of responses to “independent” items.

K-Means Cluster Procedural, judgmental approach, where you compare results of 2, 3, 4… cluster solutions. Best suited when you have a set of (6 or more) continuous, or interval coded, variables… –that have low and non-significant inter-correlation— near independence, and… –good range of responses across sample. Produces cluster scores for subsequent analysis.

Validity of Clusters Examine the relative sizes and composition of the clusters—are the sizes helpful? Do the clusters have face validity? Can you assign names to segments produced from the analysis based on the means on the individual items? Can you add new items and retain the same clusters.

Reliability of the Clusters Are the clusters “stable” across different sets of (randomly assigned) respondents? Are the clusters “stable” with the inclusion or deletion of items. Can significant differences be shown from an ANOVA across means on each of the items used in the cluster analysis? Do the clusters illustrate differences in responses to separate items?

Limitations of Cluster Is largely dependent on the composition of sample, different composition of the sample will produce different clusters. Has a well-deserved poor reputation as an a- theoretical approach toward classification and data analysis. Best suited for exploratory research designed to exaggerate differences between groups of respondents. Addicting, creative approach to forming segments.

Suggested Technique to Create an Understandable Cluster Analysis Start with a subset of the questionnaire items used to form clusters. Start with 2 clusters, and increase to 3, then 4, examining changing clusters and sizes of each. Include additional items one at a time—do the cluster definitions improve in consistency?

Discriminant Analysis Cluster analysis forms classification, or categorical variable based on responses to continuous variables. Discriminant analysis takes a pre- determined classification variable and identifies continuous variables that show significant differences.

Appropriate Analyses for Project Descriptive Statistics –Frequencies on items, particularly those showing popularity, strongest sentiments, importance. “Bivariate” Statistics –ANOVA, F-statistics for differences in means –T-tests for comparisons of means between two groups –Cross-tabulations of categorical, nominally coded items.

Multiple Regression Limited number of continuous variables that would appropriate/interesting as dependent variables for the Alltel project. Best: –Willingness to pay $xx for a certain carrier service –“Must have” vs. “Don’t need” for features items

Measurement Issues Correlations Reliability—mean inter-item correlations Factor Analysis –Data reduction to subscales and underlying traits through explained variance. –Factor loadings (pattern matrices) –Later, we’ll use factor scores for visual plots (perceptual mapping)

Classification Methods Discriminant Analysis –Categorical, nominally coded dependent variable –Wilk’s Lambda –Classification results Cluster Analysis –Creates categorical variables from sets of continuous, or interval coded items