Card sorting · Analysis · Similarity matrix

The similarity matrix: reading pairwise evidence

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

The similarity matrix is the smallest unit of card sort evidence: one number for each pair of cards. The dendrogram is built from it, and it is the view to return to when a group looks wrong. This page explains what a cell counts, how to read a row, and what a cell cannot decide.

Rows, columns, cells

Rows and columns are the cards, in the same order. The cell where a row meets a column holds the number of participant sorts in which those two cards were placed in the same group. The matrix is symmetric: the cell for Returns and Order tracking is the same as the cell for Order tracking and Returns. In UXbeam the rows are ordered by the current dendrogram grouping, so cards that were often sorted together sit near each other and a group appears as a dark square along the diagonal. Hovering a cell shows the count and the total.

The count and its denominator

The count is the number of included sorts in which both cards shared a group. The total shown beside it is the number of included participant sorts, all of them. A participant who left one of the two cards unsorted is in the total and not in the count, so unsorted cards lower a pair's count without any participant having separated them. Excluded participants are in neither. The shade of a cell is the count as a share of the total.

The diagonal, each card with itself, is set to the total. It anchors the eye and carries no evidence about placement.

An example matrix

Illustrative example · six cards · twelve sorts

Each cell: the number of sorts, out of twelve, in which the two cards shared a group. Darker is more. The diagonal is the sort total.

A worked reading

Read a row, not a cell. The Order tracking row says ten of twelve sorts put it with Shipping options, six with Returns, and two or fewer with anything else. That is a card with one strong partner and one moderate one.

The Returns row is the interesting one: six with Order tracking, six with Customer support, five with Shipping options. Half the sorts put it with orders and half with support, and they are largely different halves: only two sorts put all three cards together. Returns is a two-home card. The matrix shows that; it does not say which home to choose.

Payment methods and Gift cards share seven sorts and almost nothing with anyone else. A pair with no third member is a small group, or a sign that the set is missing the cards that would make it one.

A conflicting reading

Shipping options has ten with Order tracking and three with Payment methods. Two readings: a quarter of the sample meets shipping choices at checkout and grouped it with paying, or the card name made three people think of shipping costs. The matrix cannot separate a placement instinct from a wording effect. What would: the labels those three participants wrote for the group, and a tree test task about choosing a delivery speed.

Blocks and exceptions

A block is a set of cards that are all high with each other: Order tracking and Shipping options above, or the two payment cards. Blocks are what the dendrogram turns into groups: the dendrogram page draws the tree built from exactly these twelve sorts. An exception is a cell that breaks the pattern: a high count outside a block, which marks a bridge card like Returns, or a low count inside one, which marks a card that was put in the block by the ordering rather than by participants. Reordering the rows changes what is easy to see and changes no number.

Caveats

• Unsorted cards deflate counts. If a study allowed unsorted cards, a low row may mean people could not place the card, not that they separated it from everything.
• Small samples move in big steps. With twelve sorts, one participant is a twelfth of the shade. Read differences of one or two as noise.
• The matrix pools everyone. Six of twelve can be half the people every time, or two groups of participants who never agree. The matrix and the dendrogram are both built from the pooled sorts; Mental Model Detection is a separate analysis of the individual sorts, and separates the mental models in the sample where the matrix only sums their pairs.

Not a placement table

In a closed sort, the natural table is card by category: how many participants put Returns under Orders & delivery versus Account & support. That counts placements into names you supplied. The similarity matrix is card by card and counts pairs regardless of what any group was called. A closed sort has both views; an open sort has only the matrix and the labels participants wrote.

What a cell can and cannot support