Cluster method sensitivity

Single, complete, and average linkage answer different questions.

Short answer: single linkage merges clusters when any cross-cluster card pair is close, complete linkage uses the farthest pair, and average linkage uses the mean of all cross-cluster pair distances. The same similarity matrix can therefore produce different trees and cuts.

Method	Cluster distance	Useful lens	Watch for
Single	Minimum cross-pair distance	Whether any strong bridge connects two sets	Long chains held by a small number of strong pair relationships
Complete	Maximum cross-pair distance	Whether all cross-pairs remain close	Splitting a broader concept because one pair is weak
Unweighted average	Mean cross-pair distance	Overall cross-cluster pair closeness	Averages hiding a mix of strong and weak relationships

A four-card thought experiment

Imagine A and B are grouped together by nearly everyone, C and D are grouped together by nearly everyone, and only B and C share a moderate relationship. Single linkage can join the two pairs through B-C. Complete linkage waits for the weakest cross-pair to improve, which may never happen at the same threshold. Average linkage considers all four cross-pairs and may merge between those outcomes.

The threshold is another assumption

A threshold cut asks: which merges occurred at or above this similarity? Raising it usually yields more groups; lowering it usually yields fewer. The field lab stores the threshold in basis points and displays exact group membership. It does not infer the number of menu categories your product should have.

How to make the analysis auditable

Record the edition fingerprint and included-response count.
Export the pair matrix with exact counts.
Name the linkage definition, not just “cluster analysis.”
Record the cut threshold and merge ledger.
Compare card-pair membership across all supported linkages.
Describe which conclusions survive method changes.
Carry one cut into an editable draft, then validate that draft separately.

Clustering is exploratory. Hierarchical clustering is one way to summarize pair evidence. Other analysis families can expose overlapping or different structures. Method stability is evidence about robustness, not proof of correctness.

For broader methodological context, see Capra's comparison with factor analysis and published comparison of multiple card-sort analysis methods.