Market research method
Perceptual maps from survey data with correspondence analysis
A perceptual map places brands and the attributes people associate with them on one chart, so brands with similar images sit close together and each brand sits near the attributes that describe it best. From survey data the usual method is correspondence analysis of a brand × attribute grid — how many respondents linked each brand with each attribute.
How results are checked
Named statistical review pending. Selected automated reference cases are published on the validation page.Make a perceptual map — free, no signup
Paste a brand × attribute table or open respondent-level pick-any data, add supplementary brands such as an ideal, and get the map with inertia, quality and contributions. Free and browser-local.
Make a perceptual map →From an association grid to a map
The classic input is a pick-any brand image question: “Which of these coffee shops would you describe as… good value? modern? friendly?” Count the ticks and you get a table with brands in the rows and attributes in the columns.
Correspondence analysis compares the profiles of that table — each brand's mix of attributes relative to its own total — rather than raw counts, so a big brand that gets more ticks on everything is not pulled to every attribute at once. It then finds the two dimensions that show most of the differences between profiles.
The method
Formula
S = D_r^(−½) (P − r cᵀ) D_c^(−½) = U Σ Vᵀ total inertia = χ² / n = Σ σₖ²
where
- P
- the grid divided by its grand total n; r and c are its row and column masses (margins)
- σₖ
- the singular values; σₖ² is the inertia (variance) the k-th dimension explains
- principal coordinates
- rows: D_r^(−½) U Σ; columns: D_c^(−½) V Σ — the positions plotted in a symmetric map
- quality (cos²)
- the share of a point's inertia shown on the two plotted dimensions; low-quality points are poorly represented
Worked example
The synthetic coffee-chain image study that the perceptual-map tool loads as sample data asked 500 respondents which of five fictional coffee chains — and their ideal coffee shop — fit each of 8 attributes. The ideal is a supplementary row: it is placed on the map but does not shape it.
| Good value | Fast service | Modern | Premium | Great taste | Sustainable | Friendly staff | Traditional | |
|---|---|---|---|---|---|---|---|---|
| Brewline | 389 | 418 | 185 | 65 | 57 | 62 | 115 | 39 |
| Copper Kettle | 83 | 40 | 47 | 115 | 300 | 58 | 241 | 275 |
| Daybreak | 318 | 151 | 54 | 41 | 105 | 32 | 282 | 129 |
| Harbor Roast | 51 | 69 | 153 | 267 | 246 | 140 | 77 | 78 |
| Summit | 95 | 142 | 256 | 185 | 120 | 147 | 56 | 46 |
| My ideal coffee shop | 111 | 99 | 132 | 180 | 253 | 111 | 159 | 159 |
The association is strong (χ² = 2423.4, df = 28, p < .001; total inertia 0.423). The first dimension explains 53.7% of the inertia and the second 41.0%, so the two-dimensional map shows 94.7% of the differences between brand profiles.
| Brand | Dimension 1 | Dimension 2 | Quality | Mass |
|---|---|---|---|---|
| Brewline | 0.68 | -0.12 | 0.97 | 0.232 |
| Copper Kettle | -0.51 | 0.50 | 0.97 | 0.202 |
| Daybreak | 0.30 | 0.47 | 0.91 | 0.194 |
| Harbor Roast | -0.50 | -0.35 | 0.94 | 0.189 |
| Summit | -0.11 | -0.54 | 0.92 | 0.183 |
| My ideal coffee shop (supplementary) | -0.33 | 0.02 | 0.98 | — |
Synthetic coffee-chain image study · 500 respondents · the same data as “Use sample data”.
Reading it. Dimension 1 runs from Good value and Fast service (where Brewline sits) to Great taste (Copper Kettle and Harbor Roast). Dimension 2 separates Friendly staff and Traditional (Copper Kettle and Daybreak) from Modern and Premium (Summit). The ideal coffee shop lands closest to Harbor Roast, and every brand is well represented (quality 0.91 or higher).
Using it well
When to use it
Use it when
- Use: Brand image and positioning studies with a brand × attribute association grid.
- Use: Showing competitive white space: attributes no brand owns, or where an ideal sits away from every brand.
- Use: Tracking how a brand's position moves between waves (with the same brands and attributes).
Not the right tool when
- Avoid: Reading the distance between a brand point and an attribute point literally in a symmetric map — only directions and relative positions are safe.
- Avoid: Maps whose two dimensions show only a small share of the inertia; look at the third dimension or report the table instead.
- Avoid: Grids with very few respondents per brand, where small counts swing the profiles.
How to interpret it
Rule of thumb
Brands close together have similar profiles; attributes close together are used for the same brands. A brand is associated with attributes that lie in its direction from the centre. Check the map share and each point's quality before interpreting a position, and name the dimensions from the points that contribute most to them.
Symmetric or asymmetric map?
The symmetric map (rows and columns both in principal coordinates) is the market research default and the most readable, but distances between a brand and an attribute are not defined in it. In an asymmetric (row-principal) map the attributes are drawn as vertices and each brand is the weighted average of them, which makes brand–attribute relations exact at the cost of a crowded centre. The Crosstabs tool offers symmetric, row-principal and column-principal maps.
Supplementary points
An ideal brand, a past wave or a new concept can be projected onto an existing map as a supplementary point without changing the axes. That keeps the map about the real competitive set while still showing where the ideal or the concept would sit — here the ideal's quality is 0.98.
Questions
Frequently asked questions
What is a perceptual map in marketing?
A chart that positions brands or products by how customers perceive them, usually in two dimensions. Brands near each other are seen as similar; the attributes plotted with them show what drives the differences.
How do you make a perceptual map from survey data?
Ask a brand × attribute association question, count how many respondents link each brand with each attribute, and run correspondence analysis on that table. Plot the first two dimensions, and check how much of the inertia they explain.
What does inertia mean in correspondence analysis?
Inertia is the chi-square statistic of the table divided by its grand total: a measure of how far the brand profiles are from the average profile. Each dimension explains a share of it; the map's share is the sum for the dimensions plotted.
Can I read the distance between a brand and an attribute?
Not literally in a symmetric map. Interpret direction from the centre instead: a brand is associated with attributes lying in its direction. For exact brand–attribute relations use an asymmetric map.
What is a supplementary brand?
A row (or column) that is placed on the map using the axes computed from the other points, without influencing them. It is the usual way to add an ideal brand, a concept or a previous wave.
Sources and next steps
References & further reading
- [1]Greenacre, M. (2017). Correspondence Analysis in Practice (3rd ed.). Chapman & Hall/CRC.
Make a perceptual map — free, no signup
Paste a brand × attribute table or open respondent-level pick-any data, add supplementary brands such as an ideal, and get the map with inertia, quality and contributions. Free and browser-local.
Make a perceptual map →