Market research tool
Brand perceptual map (correspondence analysis)
How results are checked
Named statistical review pending. Selected automated reference cases are published on the validation page.Shown by a 2-D map
94.7%of inertia
Dimension 1 contrasts Good value and Fast service with Great taste
5 brands × 8 attributes · dimension 1 53.7%, dimension 2 41.0%
A perceptual map shows which brands are described by which words. Correspondence analysis turns a brand × attribute table — how many respondents linked each attribute to each brand — into a map whose first two dimensions capture as much of the association as possible. Brands near each other have similar images; the share of inertia on each axis says how much of the table the map shows.
Make a perceptual map from your data
Paste a brand × attribute table of counts or percentages, or open a respondent-level file with a pick-any grid ("Which of these words describe …?") and the tool counts the associations for you. Everything runs in this browser tab — free, no account, and the file is never uploaded. "Load example table" and "Use sample data" load a synthetic coffee-chain image study.
Brands in rows, attributes in columns, names in the first row and column. Paste from Excel or Google Sheets, or type comma- or semicolon-separated values. Blank cells count as 0.
Symmetric or asymmetric map?
The symmetric map draws brands and attributes in principal coordinates. It is the most common perceptual map because both clouds are spread out to the same scale, but only distances within each set are defined: brand to brand, attribute to attribute. A brand that sits next to an attribute is not necessarily strongly linked to it; read links by direction from the centre and check them in the "What each brand stands for" list.
The asymmetric (row-principal) map keeps brands in principal coordinates and draws the attributes at their standard coordinates — the vertices of the space. Each brand is then the weighted average of the attribute points, so a brand is pulled toward the attributes that describe it and brand–attribute distances can be read. For a brand image grid this is the map to use when the question is "what does each brand own?". To compare segments of respondents rather than brands, crosstab the grid in the workspace.
The method
Formula
S = D_r^−½ (P − r cᵀ) D_c^−½ = U Σ Vᵀ; F = D_r^−½ U Σ, G = D_c^−½ V Σ
where
- P
- the table divided by its grand total N; r and c are its row and column masses (marginal shares)
- S
- standardized residuals; its singular value decomposition gives the dimensions
- λ_k = σ_k²
- principal inertia of dimension k; the total inertia Σ λ_k equals χ² ÷ N
- F, G
- principal coordinates of rows (brands) and columns (attributes); standard coordinates divide by σ_k
- contribution
- mass × standard coordinate², the share of a dimension’s inertia due to a point
- cos²
- principal coordinate² ÷ squared χ² distance to the centre: how well a dimension shows the point
- supplementary
- passive points placed with the transition formula (profile × standard coordinates of the other set)
Worked example
In the synthetic sample, 500 respondents ticked which of eight words describe five fictional coffee chains and their ideal coffee shop. Dimension 1 explains 53.7% of the inertia and dimension 2 41.0%, so the map shows 94.7% of the brand–attribute association — a faithful summary.
Dimension 1 contrasts Good value, Fast service and Brewline with Great taste, Copper Kettle and Harbor Roast; dimension 2 contrasts Friendly staff, Traditional, Copper Kettle and Daybreak with Modern, Premium and Summit. Brewline over-indexes on Fast service (index 220) and Good value (index 179).
The ideal coffee shop is a supplementary row: it does not shape the map but is projected onto it. It lands on the great taste side, closest to Harbor Roast, and over-indexes on Great taste, Traditional and Premium. The action: those are the associations to build.
Using it well
When to use it
Use it when
- Use: Brand image or brand association grids: which words fit which brands.
- Use: Any two-way table of counts — products × usage occasions, stores × reasons for choice, segments × answers.
- Use: Projecting an 'ideal brand', a new wave or a competitor onto an existing map as a supplementary point.
Not the right tool when
- Avoid: Ratings on a scale (means per brand) — use a crosstab of means or principal components instead.
- Avoid: Very sparse tables: rare brands or words with tiny totals are placed unreliably; make them supplementary.
- Avoid: Reading a symmetric map as if brand–attribute distances meant something — they do not.
How to interpret it
Rule of thumb
Check how much inertia the first two dimensions explain (below about 60% the map hides a lot), then read which points contribute most to each axis to name it. Interpret only points with good quality (cos² summed over the two dimensions above about 0.5), and confirm brand–attribute links in the over-indexing list or an asymmetric map.
Questions
Frequently asked questions
What is inertia in correspondence analysis?
Inertia is the chi-square statistic of the table divided by the grand total: a measure of how far the brand profiles are from the average profile. Each dimension carries part of it (its principal inertia), and the share on the first two dimensions tells you how much of the table the map shows.
Can I read the distance between a brand and an attribute?
Not in a symmetric map, where both sets are in principal coordinates and only brand–brand and attribute–attribute distances are defined. In an asymmetric (row-principal) map brands are weighted averages of the attribute points, so a brand lies toward the attributes that describe it and brand–attribute distances can be interpreted.
Should I paste counts or percentages?
Counts if you have them. Percentages of the grand total give exactly the same map, because correspondence analysis only uses proportions, but the chi-square test needs counts. Row percentages give every brand the same weight, which changes the map; that can be intended when brands differ a lot in size.
What are supplementary brands and attributes?
Points that are placed on the map after it is built, using the same transition formulas, without influencing the axes. Typical uses are an 'ideal brand' row, last year's wave, or rare words that would otherwise dominate a dimension.
Is the chi-square test valid for pick-any brand grids?
Only roughly. In a pick-any grid one respondent can tick several words for several brands, so the cells are not independent observations and the p-value is too optimistic. Use the map descriptively; the test is meaningful for tables where each count is a separate respondent or event.
Sources and next steps
References & further reading
- [1]Greenacre, M. (2017). Correspondence Analysis in Practice (3rd ed.). CRC Press.
- [2]Greenacre, M. J. (1984). Theory and Applications of Correspondence Analysis. Academic Press.
- [3]Benzécri, J.-P. (1973). L’Analyse des Données. Tome 2: L’Analyse des Correspondances. Dunod.
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