Exact pair evidence
How a card-sort similarity matrix is calculated.
similarity(A, B) = together(A, B) / comparable(A, B)
Worked example
Suppose seven included responses contain both “Opening hours” and “Getting here.” Six put them in the same group. The pair similarity is 6 / 7 = 85.71%. The matrix should show both 6/7 and 85.71%, not only a colored square.
If only five responses sorted both cards, the denominator is five. A card left in the unsorted tray is not a decision about that card, so it is excluded from every pair it belongs to: two cards a participant never touched are not evidence that the participant grouped them together. When a partial sort leaves a pair with no comparable response, that pair is reported as unknown with a zero denominator rather than as agreement. The explicit denominator is what makes a partial sort readable.
What counts as together?
Two cards count as together when their final group IDs match within one response. The label text does not need to match labels from another participant. In an open sort, “Visit planning” and “Before you come” may be different raw labels but can both contribute card-pair evidence for the cards inside them.
What a zero means
- 0/n: observed apart across n included responses.
- 0/0: unknown because there is no included comparable evidence.
- n/n: observed together in every included comparable response, not proof of universal grouping.
Why exact denominators matter
A percentage can hide the evidence base. 100% from 2/2 and 100% from 40/40 are numerically equal but not equally informative. The field lab keeps counts visible in the strongest-pairs table, full matrix, CSV, and analysis report.
How clustering uses the matrix
The supported agglomerative methods convert similarity to distance with distance = 1 - similarity. Single, complete, and average linkage define cluster-to-cluster distance differently. The matrix does not choose the linkage or the threshold, and a dendrogram does not add evidence beyond the underlying pairs.