Card sorting · Analysis · Dendrogram

The dendrogram: reading the tree at more than one cut

By UXbeam · Information architecture tools since 2021 · Published September 21, 2026

The dendrogram is the hierarchical summary of the similarity matrix: every pair count folded into one tree. It is the view that makes groups visible, and an easy one to mistake for an answer. This page explains what the tree shows, what moving the threshold does, and how to read the same tree at two cuts so the groups you keep are the ones that persist.

Leaves and branches

The leaves are the cards. A branch joins two cards, or two branches, that were often sorted together; the closer to the leaves the join sits, the more sorts agreed. The root joins everything. The tree is built from all included sorts pooled.

The similarity threshold

UXbeam shows a similarity threshold under the tree. The groups at any setting are the branches that still hold together at that similarity: raise the requirement and groups split, lower it and they merge. The panel headed At this similarity threshold lists the groups the current setting produces, with the number of groups.

Two things the threshold does not mean. It is not a promise that every pair inside a group meets it; a group is defined by where its branch joins, and a card at the edge of a branch can be weakly tied to some of its members. And there is no optimal value. UXbeam opens on a default cut; the right cut is the one that answers your question, and a question about top-level sections is answered lower down than a question about sub-groups. Closed sorts show the tree as agreement evidence without a threshold control, because the categories were decided at setup.

The same evidence at two cuts

Illustrative example · the six cards and twelve sorts from the matrix page

One fixed tree, two cuts. Leaves join where their branches meet the similarity axis; in this illustration a join sits at the average pair similarity between the two sides, computed from the twelve sorts on the matrix page. The bracket columns show the groups each cut produces.

The same two cuts as group lists. The payment pair and the orders pair survive both; Returns stands alone at cut A and is inside the four-card group at cut B.

Read the two cuts against each other. What is together at both is a candidate section. What changes between them is where the decisions are. Here, Returns is the decision. Between the two cuts it joins Customer support first, at 0.50, ahead of the orders pair at 0.46: a margin of one sort in twelve. The tree has to pick a side; the matrix row for Returns, six with Order tracking and six with Customer support, shows that it barely did. That is the reading to take back to the matrix, and then to a tree test task.

Persistent groups

A group that holds across nearby cuts is one whose members were sorted together far more often than with anyone outside; UXbeam labels the strength of each group at the current cut. Persistence across cuts tells you the group is not an artefact of where you set the threshold. Whether the sample contains one mental model or more is a different question: the dendrogram pools everyone, and Mental Model Detection separates those mental models.

Boundary cards

A card whose join sits near the threshold moves between groups with a small change in the setting. UXbeam lists these as cards between groups. Treat each as a question rather than a placement: go to its matrix row, see which partners it has in each direction, and write a tree test task about it. Boundary cards are candidates for cross-links or duplicate destinations in the finished navigation.

Singletons

A card that stays alone across cuts has no strong partner in this set. Three explanations: the card is genuinely standalone and needs a top-level home of its own; the card was unclear and people placed it at random; or the set is missing the cards it would have joined. The individual sorts and any description-reveal counts usually tell you which.

One tree for everyone

The dendrogram pools every included sort into one structure. When participants broadly agree, the tree is a fair summary. When two groups of participants organize the cards on different rules, the tree blends them and can describe a structure that no participant proposed. Nothing in the tree signals that this has happened. The matrix and the dendrogram are both built from the pooled sorts; Mental Model Detection is a separate analysis of the individual sorts, and shows whether the sample contains one mental model or more, keeping each one separate.

Not a navigation

The groups at a cut are not a menu. They have no labels: the names come from what participants wrote, read on the labels view. Their nesting is similarity, not the levels of a navigation; a group's sub-branches are not sub-sections unless you decide they are. The path from tree to navigation is Sitemap +, which opens the current cut as an editable draft, and then a tree test with tasks for every boundary card.