Card Sort Analysis: How to Read a Similarity Matrix and Dendrogram

What a Card Sort Gives You

After participants have finished sorting, you have three main outputs:

• Category names and groupings: Each participant created categories (open sort) or placed cards into your categories (closed sort).
• A similarity matrix: Shows how often pairs of cards were grouped together across all participants.
• A dendrogram: A tree diagram that visualises hierarchical clustering based on the similarity data.

Your job now is to turn these outputs into navigation structure that makes sense for your users.

Step 1: Standardise Category Names

In an open sort, participants create their own category names. You'll see variations like "About Us", "Company Info", "Who We Are" for the same grouping. Before analysing clusters, merge these synonyms into a single label.

Look for:

• Plurals vs singulars ("Product" vs "Products")
• Synonyms ("Help" vs "Support" vs "Customer Service")
• Abbreviations ("FAQ" vs "Frequently Asked Questions")
• Spelling variants ("Colour" vs "Color")

Most card sort tools standardise names manually or with simple text matching. Do this step before generating the similarity matrix, or patterns will be split artificially.

Step 2: Read the Similarity Matrix

The similarity matrix shows how often pairs of cards were grouped together. Each cell displays a percentage: 100% means every participant put those two cards in the same category, 0% means none did.

What to look for:

• High percentages (70%+): Strong agreement. These cards belong in the same navigation category.
• Moderate percentages (50-69%): Reasonable agreement, but check whether subcategories make sense.
• Low percentages (below 30%): Cards are seen as separate. Don't force them into the same category.
• Split cards: If a card has moderate agreement with two different clusters, it may need to appear in both places or be labelled more clearly.

Thresholds depend on your sample size. With 30+ responses, 60-70% is a useful cutoff. With 15-29 responses, use 50-60%. Below 15, the data is exploratory only.

Step 3: Read the Dendrogram

A dendrogram visualises hierarchical clustering. Cards that join at the top of the tree have the strongest agreement; cards that join lower down have weaker agreement.

How to interpret it:

• Early merges (high agreement): Form your main navigation categories. In the example, "Home + About + Team + Careers" is a strong company info cluster; "Services + Portfolio" is a strong work cluster.
• Late merges (low agreement): May be statistical artifacts rather than meaningful patterns. The final merge at 35% suggests these two clusters should stay separate in navigation.
• Single-card branches: Cards that don't merge until very late are outliers. Check whether they were unclear or genuinely don't fit anywhere.

Different clustering algorithms (average linkage, complete linkage, Ward's method) produce slightly different dendrograms. Most tools default to average linkage, which balances sensitivity and stability for under 30 participants.

Closed Sorts: The Placement Matrix

In a closed sort, you measure placement agreement: what percentage of participants put each card into each predefined category.

What to look for:

• Cards with high agreement (70%+) in one category: Good fit.
• Cards with split placement: Participants disagree on where it belongs. Either the card label is unclear, or your categories overlap.
• Cards that don't fit anywhere: Often placed in "Other" or spread thinly across categories. These cards may need clearer labelling or a new category.
• Categories with very few cards: May be too narrow, or your content set doesn't support them.

Turn Clusters Into Navigation

Once you've identified strong clusters, design your navigation structure:

1. Main categories from strong clusters. Use the top-level merges in your dendrogram or the highest-agreement groupings in your matrix.
2. Subcategories from mid-level clusters. If a main category is large, check for subclusters at 50-60% agreement.
3. Clear, consistent labels. Use the most common category names from participants, adjusted for clarity and your brand voice.
4. Validate with a tree test. Card sorting reveals mental models; tree testing checks whether your navigation design actually helps users find things. Run a tree test with different participants to measure success rates and directness.

Worked Example

The diagrams above show a card sort for a small agency website. Here's what the analysis reveals:

• Company info cluster (85% agreement): Home, About, Team, Careers. This becomes an "About" or "Company" navigation section.
• Work cluster (85% agreement): Services, Portfolio. This becomes a "Work" or "What We Do" section.
• Content cluster (70% agreement): Blog, Contact. Weaker than the others, but still a reasonable pairing for a "Resources" or "Connect" section.
• Weak final merge (35%): Don't merge all three clusters into one mega-category. Keep them separate in the navigation.

Proposed navigation: About, Work, Blog, Contact. Tree test this structure to see if users can find specific pages reliably.

Automatic vs Manual Analysis

You can analyse card sort results manually in a spreadsheet: count placements, calculate co-occurrence percentages, build a similarity matrix, and draw a dendrogram. This works for 5-10 participants but becomes error-prone and time-consuming beyond that.

Automated tools (like Free Card Sort) generate the matrix and dendrogram from your data in seconds, letting you focus on interpretation rather than calculation. For most projects, automation is faster and more accurate.