Reading a dendrogram without a statistics degree

A card sort produces a diagram that looks like an evolutionary tree, and a lot of people quietly scroll past it. That is a shame, because it is the single most useful output of the method and it takes about two minutes to learn.

What it is showing

Every item sits on the right. Lines join items into groups, groups into bigger groups, and eventually everything joins into one.

The horizontal position of a join is the whole message.

A join far to the right means those items were grouped together by nearly everybody. Strong agreement.
A join far to the left means they only ended up together because the algorithm had to put everything together eventually. Weak agreement, and often no real relationship at all.

Read it right to left and you are reading in order of confidence. The first things to join are the things your customers are most sure about.

The three things worth looking at

1. What joins first. These are your certainties. If "free returns" and "easy size exchange" join immediately at the far right, that is not a hypothesis, it is a finding. Build on it.

2. Where the big splits happen. Follow the tree from the left. The first split divides your list into the two biggest ideas in your customers' heads. That top-level division is often the most useful thing on the page, because it is usually the level your navigation or your roadmap is organised at.

3. Anything that joins late and alone. An item that refuses to join anything until the far left is a genuine finding. Either people did not understand it, or it does not belong to any theme, or it belongs to several equally. All three are worth knowing before you build anything around it.

Cutting the tree

A dendrogram does not tell you how many groups you have. You decide, by choosing where to cut it.

SortedResearch puts that on a slider, and reports the average within-group agreement as you move it. Drag to four groups and you might see 94 percent. Drag to eight and it climbs, because smaller groups are always more internally consistent. That number always rises as you add groups, so the trick is not to maximise it.

What you are looking for is the point where adding one more group stops buying you much. Go from three groups to four and agreement jumps: real. Go from seven to eight and it creeps up a point: you are splitting hairs. Take the last big jump.

Two ways to build the tree

There is a choice of clustering method, and it matters more than it sounds.

Average agreement (average linkage) builds clusters from the average level of agreement across every item in a group. It is the standard view and the one to start with. It resists a single odd pairing dragging a whole group around.

Strongest pair (single linkage) grows a cluster by joining the strongest individual pair at each step. It lets larger groups keep higher agreement scores and often holds up better with fewer participants, because it needs one strong signal rather than a consistent average.

If the two give you the same shape, trust it. If they disagree sharply, that is telling you the structure is genuinely loose, and you should be more careful about what you claim from it.

What it does not tell you

Names. The tree gives you clusters, not labels. What participants called their piles is separate data, and often better than anything your team would write. In SortedResearch, Graham will name clusters in one pass, drawing on the labels participants actually used.
Importance. A tight cluster is a cluster people agree about. It says nothing about whether they care about it. That is a different study, which is why a card sort flows into a pairwise or Best-Worst one.
Causation. People grouping two things together means they think of them together. It does not mean one causes the other, or that they should sit together in a menu. Test that with a tree test.

The honest limitation

A dendrogram makes any data look structured, including data with no structure in it. Fourteen people sorting randomly will still produce a tree, and it will still look like a tree.

Guard against it by reading the agreement figures rather than the shape. If your best cluster is sitting at 30 percent agreement, the picture is lying to you politely, and the finding is that your customers do not share a mental model for this list at all. That is a real result, and it is worth more than a pretty diagram that nobody should have believed.