Before you start
You will be able to
- Explain what a perceptual map shows (customers’ average perceptions of brands relative to each other) and what it can’t show.
- Build a two-attribute map from brands’ mean ratings and read each brand’s nearest rivals on it.
- Interpret a map made with principal components: the dimensions’ shares of the variance, the loadings drawn as arrows, the brands’ positions and how well each attribute is represented.
- Calculate the distance on the map from a segment’s ideal point to each brand, and find each segment’s nearest brand.
- Evaluate whether a gap on a map is a market opportunity, and state a map’s limits: small bases, the attributes asked and averages that hide segments.
Review first
- Profiling segments — The five segments and their names come from module 2; here each gets an ideal point on the map.
- Competitive advantage — Positioning, the place an offer holds in customers’ minds relative to rivals, is what a perceptual map draws.
- Questionnaire design — The brand ratings are rating-scale items; how they were asked decides what they can mean.
- Normalisation and standardisation — The attributes are standardised across the brands before the map is built, as in B02.
- Confidence intervals — A brand’s mean rating is an estimate; its standard error and interval show how far a small base can be trusted.
Fictional case A fictional coffee business founded by Ana Lim. It starts as a catering and barista-training service, opens its own cafés and an online shop for beans, and plans a canned cold brew.
The idea
Fictional case
In May 2027 Ana’s needs study asked each of its 640 coffee drinkers to rate three of the six brands they knew on the same eight attributes as their needs, from 1 to 7, and then to rate their ideal coffee the same way. Module 2 turned the needs ratings into five segments. This lesson turns the brand ratings into a picture of the market as these coffee drinkers see it: where Lantern stands against Summit Brew, Daily Grind RTD, Arcadia Coffee, Harbour Basics and Corner Cup, and which segment each brand sits closest to.
A perceptual map is a chart that places competing brands by how customers perceive them, so that brands seen as alike sit close together and brands seen as different sit far apart. OpenStax’s Principles of Marketing describes it as a visual diagram of how the average target consumer perceives a product relative to its competitors. Two words in that description carry the weight. Perceives: the map shows beliefs, which may differ from what a blind taste test or a price check would find. Average: each point is a mean over many people, so the map is only as good as the ratings behind it.
A map is how positioning becomes visible. M01 defined positioning as the place a business wants its offer to hold in target customers’ minds, relative to competing offers; a perceptual map shows the place it actually holds today. The gap between the two is what the rest of this module works on.
The simplest map: two attributes
Choose two attributes that matter to the purchase, plot each brand’s mean rating on one against its mean rating on the other, and read the picture. OpenStax calls these determinant attributes: the attributes customers use in making their purchase decision. The study’s price attribute asks how far a brand offers “a low price”, so a high rating means cheap.
| Brand | Rated by | Taste and quality | A low price | Convenience |
|---|---|---|---|---|
| Lantern | 61 | 5.92 | 3.41 | 3.15 |
| Summit Brew | 289 | 5.29 | 3.31 | 5.41 |
| Daily Grind RTD | 406 | 3.52 | 5.83 | 6.08 |
| Arcadia Coffee | 270 | 4.71 | 3.73 | 3.91 |
| Harbour Basics | 438 | 3.04 | 6.29 | 5.98 |
| Corner Cup | 456 | 4.66 | 4.28 | 6.15 |
Each respondent rated three brands they knew, so each brand has its own base. Opt-in panel with quotas on age band (fictional).
The brands fall along a band from cheap but plain (Harbour Basics, Daily Grind RTD) to tasty but dear (Summit Brew, Lantern), with Corner Cup and Arcadia Coffee in between. Across the six brands the two ratings have a correlation coefficient of −0.96: these coffee drinkers see taste and a low price as a trade-off. On this map Lantern’s nearest rival is Summit Brew, √((5.92 − 5.29)² + (3.41 − 3.31)²) = 0.64 rating points away.
A two-attribute map is quick to build and easy to explain, but the two attributes you pick decide what you see. Swap the low price for convenience and Summit Brew moves well away from Lantern: it is rated 5.41 on convenience against Lantern’s 3.15. The study measured eight attributes, and a map that uses them all needs a way of summarising them.
A map from many ratings
With eight attributes each brand is a point in eight dimensions, which nobody can draw. Principal components analysis (PCA) finds the two directions that show as much as possible of how the brands differ. It starts by standardising each attribute across the brands, as B02 taught: subtract the six brands’ mean rating and divide by their standard deviation. Without that step the attribute on which brands differ most in raw points (local and independent, with a standard deviation of 1.65 across the brands) would outweigh one on which they differ least (energy, 0.78).
Dimension 1 is the direction along which the six brands are most spread out. Dimension 2 is the direction, at right angles to it, that captures most of what is left. Each brand’s position on a dimension, its score, is a weighted sum of its standardised ratings, with the weights chosen by the analysis. On the two-attribute map above, the dashed line is Dimension 1 of just two ratings: because taste and a low price are so closely (negatively) related across the brands (r = −0.96), that one line carries 98% of the differences between the brands.
Each dimension carries a share of the variance: the differences between the brands’ standardised ratings. For Lantern’s six brands Dimension 1 carries 68% and Dimension 2 21%, 90% together. The flat map therefore shows about nine-tenths of how the six brands’ average ratings differ, and leaves out a tenth.
Each attribute is drawn as an arrow from the centre. Its coordinates are the attribute’s loadings: its correlation with each dimension. The arrow points towards brands rated high on the attribute, and its length, at most 1, shows how well the two dimensions represent it. A chart that shows the brands as points and the attributes as arrows on the same axes is a biplot, a display introduced by Gabriel (1971). Strictly, as Greenacre (2010) explains, this map is not a biplot in the full sense: it draws the brands by their scores and the arrows by their correlations, a common choice in marketing maps that makes a brand’s position along an arrow only a rough guide.
| Attribute | Dimension 1 | Dimension 2 | Share on the map |
|---|---|---|---|
| Taste and quality | 0.87 | 0.48 | 99% |
| A low price | −0.86 | −0.41 | 90% |
| Convenience | −0.93 | 0.22 | 92% |
| Sustainability | 0.96 | −0.24 | 97% |
| Energy | −0.49 | 0.82 | 91% |
| Health | 0.82 | −0.46 | 89% |
| Local and independent | 0.80 | −0.01 | 64% |
| Novelty | 0.79 | 0.58 | 96% |
The share on the map is the sum of the two squared loadings. Dimension 1 carries 68.4% of the variance and Dimension 2 21.5%.
The loadings give the dimensions their meaning. Dimension 1 runs from a low price (−0.86) and convenience (−0.93) to sustainability (0.96), taste (0.87), health (0.82), local (0.80) and novelty (0.79): call it cheap and everywhere against crafted and ethical. Dimension 2 runs from health (−0.46) and a low price (−0.41) to energy (0.82), novelty (0.58) and taste (0.48): light and plain against a kick and something new. The names are interpretations, as segment names were in module 2; the loadings are what the data say.
Ideal points: where each segment would like a brand to be
Every respondent also rated their ideal coffee on the eight attributes. Average a segment’s ideal ratings, standardise them with the brands’ means and standard deviations, and weight them as the brands were weighted: the result is the segment’s ideal point, on the same map as the brands. A brand near a segment’s ideal point is close to what that segment says it wants, and the distance between them on the map measures how close.
| Segment (respondents) | Ideal point | Nearest brand | Distance | Lantern’s distance |
|---|---|---|---|---|
| Value routine (152) | (−1.24, −1.17) | Harbour Basics | 1.15 | 4.67 |
| On the go (146) | (−1.21, 1.09) | Corner Cup | 0.57 | 4.48 |
| Explorers (129) | (1.12, 0.68) | Summit Brew | 1.03 | 2.12 |
| Craft and local (109) | (2.48, −0.03) | Lantern | 0.79 | 0.79 |
| Mindful (104) | (2.09, −2.00) | Arcadia Coffee | 0.48 | 2.54 |
The segments are module 2’s five k-means segments of the 640 respondents.
Each segment’s nearest brand is a different brand, and that is itself a finding: the market is already divided, and every segment has a brand that sits close to what it wants. Lantern is nearest the Craft and local ideal, 0.79 away, and far from On the go (4.48) and Value routine (4.67), whose ideals lie on the other side of the map near Corner Cup and Harbour Basics.
Gaps on the map
A gap is a region of the map with no brand in it. OpenStax notes that a map can reveal holes or gaps that may signal an opportunity, and the word “may” matters. A gap is worth acting on only when three things hold: people want what would sit there, shown by the ideal point of a large enough segment nearby; the firm can deliver it credibly, at a cost its price covers; and nothing explains the emptiness except that nobody has tried.
On the two-attribute map the tasty and cheap corner is empty for a reason: better coffee costs more to buy and make, so a brand that sat there would struggle to cover its costs, and customers might not believe it. On the full map the space around the Explorers’ ideal, between Lantern and Summit Brew, is more interesting. The Explorers’ nearest brand is Summit Brew at 1.03, a longer distance than three other segments have to travel to theirs; only Value routine is further from its nearest brand (Harbour Basics, 1.15), and that segment fits Lantern badly. That makes the Explorers’ space worth investigating, not yet worth acting on.
In depth
Where the ratings come from, and how far to trust them
The brand ratings are rating-scale items of the kind M04 designed, asking how well each of the eight attributes describes the brand, from 1 to 7. Respondents rated only brands they knew, because a rating of an unknown brand would be a guess. Each brand’s mean is therefore based on a different number of people, its base.
The bases run from 456 ratings of Corner Cup to only 61 of Lantern. Only 89 of the 640 respondents (14%) knew Lantern, and 61 of them were asked to rate it. A small base makes a mean less precise. Lantern’s convenience ratings have a standard deviation of 0.96, so the standard error of their mean is 0.96 ÷ √61 = 0.12, and a 95% confidence interval runs from 2.90 to 3.39. Summit Brew’s mean, from 289 ratings, has a standard error of 0.05.
Large gaps survive a small base. Lantern’s taste rating is 0.63 points above Summit Brew’s, with a Welch t of 5.46, far beyond chance. Smaller ones need checking before they are used: Arcadia’s sustainability rating is 0.36 points above Lantern’s (t = −3.07, p = 0.003), so the difference is real but not large. Test a difference of a few tenths of a point involving Lantern, as here, before building a claim on it. Both tests treat the two sets of ratings as independent, although 18 people rated both Lantern and Summit Brew and 17 both Lantern and Arcadia; one person’s ratings of two brands usually move together, so ignoring the overlap tends to make the tests cautious rather than bold.
Who rated a brand matters as much as how many. 18 of Lantern’s 61 raters (30%) are in the Craft and local segment, which is 17% of the sample; only 6 (10%) are in Value routine, which is 24%. Lantern’s point shows how the people who know it see it, and they lean towards its natural customers. The 86% who don’t know Lantern have no perception of it to map, which is a finding in its own right.
How principal components build the map
- Brand means. Average each brand’s ratings on each attribute: a table of brands by attributes (six by eight here).
- Standardise across the brands. For each attribute, subtract the brands’ mean and divide by their standard deviation, so every attribute has mean 0 and standard deviation 1 across the brands.
- Find the directions. The analysis looks at how the attributes vary together across the brands (their correlations) and finds the direction with the most variance, then the next at right angles to it, and so on. The variance each direction carries is its eigenvalue; with standardised attributes the eigenvalues add up to the number of attributes.
- Place the brands. Each brand’s score on a dimension is a weighted sum of its standardised ratings, with that dimension’s weights.
- Draw the arrows. Each attribute’s loading on a dimension is its correlation with the brands’ scores on that dimension.
- Place anything else with the same recipe. An ideal point, or a brand you are planning, is standardised with the brands’ means and standard deviations and weighted with the same weights, so it lands on the same axes without moving anyone else.
For Lantern’s six brands the eigenvalues are 5.47, 1.72, 0.59, 0.18, 0.04, and the last three are zero: six points can spread in at most five directions. Each share is an eigenvalue divided by 8, so Dimension 1 carries 5.47 ÷ 8 = 68.4%. Note what the 90% is a share of: the differences between six brands’ averages, not between 640 people. Individual ratings vary far more than averages do, and the map shows none of that spread.
With so few brands, two dimensions carry a large share even of random ratings. In 2,000 simulated maps of six brands rated at random on eight attributes, two dimensions carried 70% on average and 80% or less in 95% of them; none reached Lantern’s 90%. Lantern’s map shows real structure, but a share of 70–80% from a handful of brands would show very little.
Reading a biplot
- Position along an arrow. Drop a line from a brand to the line through an arrow: the further along the arrow it lands, the higher, roughly, the brand is rated on that attribute compared with the other brands. This map, like many marketing maps, draws brands by their scores and arrows by their correlations, so the reading is a rough guide, and rougher the more the two eigenvalues differ (5.47 and 1.72 here): check the table of means. Lantern lies furthest along the sustainability arrow, yet Arcadia is rated higher on sustainability (6.00 against 5.64). Across the eight attributes the order of the brands along each arrow matches the order of their means with a rank correlation of only 0.83 to 0.94.
- Angles between arrows. Arrows that point the same way belong to attributes that rise and fall together across these brands; arrows pointing in opposite directions are traded off; arrows at right angles are unrelated. Convenience and sustainability point almost opposite ways (their correlation across the six brands is −0.95), while energy and novelty are nearly at right angles (0.04).
- Arrow length. An arrow’s squared length is the share of that attribute’s differences the map shows. Local and independent has the shortest arrow, with 64% on the map: Lantern’s lead on local (6.30 against at most 3.11 for any rival) is understated by the picture.
- The axes have no fixed direction. The analysis decides each dimension’s sign arbitrarily; flipping an axis changes nothing. “Right” is not better than “left”, and the names belong to whoever reads the loadings.
- Distances are in standardised units on two dimensions. Compare them within one map. A distance of 1 on this map and 1 on another map built from other brands or attributes mean different things.
Ideal points and their assumptions
Reading the distance from an ideal point as appeal assumes that a segment prefers whichever brand is closest to its ideal, with both dimensions counting equally. That is a model, and three cautions apply. Ideal ratings can drift high on everything desirable (an ideal coffee that tastes great and costs little), which pushes ideal points towards the edge of the map rather than among the brands. A segment’s average ideal hides how much its members disagree. And the distance uses only the two dimensions drawn.
The 90% is a share of the brands’ variance, not of each ideal point’s. An ideal profile can lie partly off the map: only 42% of the Explorers’ standardised ideal lies in the map’s plane, against 67% of Craft and local’s and 98% of Mindful’s. Part of what Explorers want is invisible on the map, so read their distances with particular care.
The all-respondent ideal sits at (0.42, −0.22), near the centre-right of the map. A business that positions for that average ideal is positioning for nobody in particular: no segment’s ideal sits close to it (the nearest, the Explorers’, is 1.14 away), which is the argument for segmenting in the first place.
Other kinds of map, in outline
This lesson’s map is attribute-based: customers rate brands on named attributes, and the map summarises those ratings. Factor analysis and discriminant analysis are related ways of building such maps. A similarity-based map asks customers only how alike pairs of brands are, and multidimensional scaling places the brands so that the distances on the map match the judgements; the dimensions are named afterwards, which captures attributes nobody thought to ask about but makes naming harder. When the data are counts of yes/no associations (“Which of these brands is friendly?”), correspondence analysis draws a similar picture. Each method answers a slightly different question, and none of them shows more than the data put in.
What a map cannot tell you
- Attributes nobody asked about. The map has eight attributes because the questionnaire did. If something else drives choice (whether a brand is sold at the office, say), it isn’t on the map. The list of attributes should come from qualitative research before the survey, as M04 described.
- People nobody asked. The study is an opt-in panel with quotas on age band, not a probability sample, and each brand was rated only by people who knew it.
- Differences between segments. A brand’s mean averages over everyone who rated it. Craft and local and On the go may see Lantern differently, but Lantern’s 61 ratings split into five segments leave between 6 and 18 per segment: too few to map each segment’s view.
- Change. A map is a snapshot of May 2027. Whether a position is moving shows only in a repeated survey, the subject of this module’s last lesson.
- Choice. Closeness to an ideal suggests appeal; it doesn’t measure purchase. Price, availability and habit also decide what people buy.
Formulas
Distance on the map between an ideal point and a brand
- The straight-line distance on the map between the brand and the ideal pointmap units
- The brand’s coordinates on Dimensions 1 and 2map units
- The ideal point’s coordinates on Dimensions 1 and 2map units
Assumes. Both points are on the same map, built from the same brands and attributes. On a two-attribute map the coordinates are mean ratings and the distance is in rating points.
The same formula gives the distance between two brands. Shorter means closer to what the segment says it wants, on the two dimensions drawn.
Share of the variance a dimension carries
- The eigenvalue of dimension k: the variance it carries across the brands
- The number of standardised attributes (the eigenvalues add up to p)attributes
Assumes. The attributes are standardised across the brands, so each contributes a variance of 1.
The two-dimensional map shows Share₁ + Share₂ of the differences between the brands’ average ratings.
Share of an attribute shown on a two-dimensional map
- The communality: the share of attribute a’s variance across the brands that the two dimensions represent (0 to 1)
- Attribute a’s loadings on Dimensions 1 and 2: its correlations with the brands’ scores
Assumes. Loadings are correlations, as in a map of standardised attributes.
The arrow’s length is the square root of the communality. A short arrow means the map hides much of how brands differ on that attribute.
Worked examples
Fictional figures
A survey in a market town (fictional) asked book buyers to rate five places that sell books on two attributes from 1 to 7, and to rate their ideal bookshop the same way. Students’ ideal is (range 5, low prices 6.2); people buying books as gifts want (4.8, 3). Which seller is nearest each group’s ideal, and what does the map say to the independent bookshop?
| Seller | Range of titles | Low prices |
|---|---|---|
| The chain bookshop | 5.8 | 4.0 |
| The independent bookshop | 4.4 | 2.6 |
| The supermarket’s book aisle | 2.2 | 6.0 |
| The online retailer | 6.6 | 5.8 |
| The charity shop | 3.0 | 6.6 |
- Plot the five sellers with range across and low prices up. The online retailer sits top right, rated high on both; the supermarket and the charity shop sit top left (cheap, narrow range); the chain bookshop sits right of centre and the independent bottom centre (dearer, middling range).
- Distance from the students’ ideal, √((range − 5)² + (low prices − 6.2)²): the chain 2.34, the independent 3.65, the supermarket 2.81, online 1.65 and the charity shop 2.04. Nearest: the online retailer.
- Distance from the gift buyers’ ideal: the chain 1.41, the independent 0.57, the supermarket 3.97, online 3.33 and the charity shop 4.02. Nearest: the independent bookshop.
- Read the gaps. No seller sits near the bottom left (narrow range and dear), and nobody should want to. The top right is occupied by the online retailer alone, which is why it is nearest the students.
Answer. The online retailer is nearest the students (1.65 rating points); the independent bookshop is nearest the gift buyers (0.57).
What it means. The independent can’t win students on these two attributes without matching the online retailer on price, which it almost certainly can’t afford. It already sits close to gift buyers, so its question is how many of them there are and what else they value (advice, wrapping, a pleasant shop), none of which this two-attribute map shows.
Fictional figures
Tarnley Fitness (fictional) surveyed local gym-goers, who rated five gyms they knew on six attributes. The principal components of the five gyms’ mean ratings give eigenvalues 3.90, 1.72, 0.29, 0.09, 0 and 0. The table gives the loadings; the gyms’ scores are Tarnley (−0.28, 0.62), the budget chain (2.95, 0.30), the boutique studio (−2.31, −0.89), the leisure centre (0.65, −1.69) and the hotel club (−1.02, 1.66). Two segments’ ideal points, projected on the same map, are busy professionals (0.54, 1.43) and class lovers (−0.72, −1.47). How good is the map, what do its dimensions mean, and is there a gap Tarnley should look at?
| Attribute | Dimension 1 | Dimension 2 |
|---|---|---|
| Low price | 0.93 | −0.29 |
| Equipment | −0.45 | 0.88 |
| Classes | −0.76 | −0.62 |
| Opening hours | 0.80 | 0.55 |
| Friendly staff | −0.90 | −0.13 |
| Not crowded | −0.90 | 0.40 |
- How much the map shows. Six standardised attributes give eigenvalues adding to 6, so Dimension 1 carries 3.90 ÷ 6 = 64.9% and Dimension 2 1.72 ÷ 6 = 28.6%: 93.6% together. That looks high, but with only five gyms two dimensions carry 80% on average even for random ratings, and 1.5% of 2,000 simulated random maps of this size reach 93.6%. So the map shows more than chance, but with five gyms a high share is easy to reach: read it as a useful sketch of these gyms, not as proof of strong structure.
- Name the dimensions from the loadings. Dimension 1 runs from friendly staff (−0.90), not crowded (−0.90) and classes (−0.76) to a low price (0.93) and opening hours (0.80): personal and spacious against cheap and always open. Dimension 2 runs from classes (−0.62) to equipment (0.88): classes against kit.
- Check each attribute’s share on the map (the communality, loading² + loading²). Friendly staff is lowest: −0.90² + −0.13² = 0.83, so 17% of how the gyms differ on friendliness is off the map. The others are between 0.94 and 0.97.
- Distances from the class lovers’ ideal: Tarnley 2.14, the budget chain 4.08, the boutique studio 1.69, the leisure centre 1.39, the hotel club 3.14. From the busy professionals’ ideal: Tarnley 1.15, the budget chain 2.66, the boutique studio 3.68, the leisure centre 3.12, the hotel club 1.58.
- Judge the gap. The class lovers’ ideal sits between the boutique studio and the leisure centre with no gym closer than 1.39, while Tarnley is the busy professionals’ nearest gym (1.15, with the hotel club next at 1.58). The class lovers are the less closely served segment, but Tarnley would have to move towards classes, away from where its own nearest customers want it.
Answer. The map shows 93.6% of the differences; its dimensions are personal and spacious against cheap and always open, and classes against kit. Tarnley is nearest the busy professionals; the class lovers’ ideal is a thinly served space, 1.39 from the nearest gym and 2.14 from Tarnley.
What it means. The map points to a question rather than an answer: is the class lovers’ segment big enough, and could Tarnley add classes credibly without losing the busy professionals it already suits? The last lesson of this module shows how to plan such a move on the map before paying for it.
Fictional figures
Ana wants to know three things before she drafts Lantern’s positioning: where Lantern sits on the map, which segments’ ideals it is near and far from, and how much weight its own point can bear. Use the map, the ideal points and the bases.
- Lantern’s position. Its score is (3.20, 0.29): the furthest of any brand towards the crafted and ethical end of Dimension 1 and a little above the centre on Dimension 2. Its nearest brands are Arcadia Coffee (2.10 away, lower on Dimension 2: healthier and plainer) and Summit Brew (3.09, further towards the cheap and everywhere end and higher on Dimension 2: more convenient and more of a kick).
- Which ideals it is near. Craft and local is the only segment whose nearest brand is Lantern (0.79); Arcadia is next for that segment at 1.52. Explorers are 2.12 from Lantern and 1.03 from Summit Brew. Mindful are 2.54 from Lantern and only 0.48 from Arcadia.
- Which ideals it is far from. On the go (4.48) and Value routine (4.67) sit on the far side of the map. On the go’s nearest brand is Corner Cup (0.57), then Summit Brew (1.50) and Daily Grind RTD (1.59).
- How much weight Lantern’s point can bear. It rests on 61 ratings, 30% of them from Craft and local, against bases of 270 to 456 for the rivals. Its big differences (taste, local and independent, convenience) are well beyond sampling error; small ones are not. And it is a rating of Lantern as a brand, which raters know from its cafés and beans, not a rating of the can of Cold Brew.
Answer. Lantern holds a distinct crafted and ethical position nearest the Craft and local ideal (0.79), with Arcadia and Summit Brew its nearest rivals on either side; it is far from On the go (4.48) and Value routine (4.67). The point rests on 61 ratings from people who know Lantern.
What it means. The map gives Ana her competitive set for each segment: Arcadia for Craft and local and Mindful drinkers, Summit Brew for Explorers, Corner Cup and Summit Brew for On the go. It also shows the tension the next two lessons work on. Cold Brew’s top-two intent is highest in Craft and local (46%) and On the go (38%), two segments at opposite sides of the map.
Explore
Common mistakes
“The map shows where the brands really are.”
It shows how the people surveyed perceive them. Lantern’s convenience rating of 3.15 is a belief held by people who know Lantern, and it may lag behind what Lantern actually offers. That is why a map is a positioning tool: the place in customers’ minds is the thing being managed.
“Every empty space on the map is an opportunity.”
A gap is an opportunity only if a large enough segment wants what would sit there, the firm can deliver it credibly at a cost its price covers, and the space isn’t empty for a reason. The tasty and cheap corner of the two-attribute map is empty because good coffee costs more, not because nobody has noticed it.
“A long arrow means customers care about that attribute.”
An arrow’s length shows how well the two dimensions represent how the brands differ on that attribute. How much customers care comes from the needs ratings and the segment profiles. An attribute everyone cares about but on which all brands are rated alike has a short arrow, or barely shapes the map at all.
“Every brand’s point is equally reliable.”
Each point is a mean with its own base. Lantern’s rests on 61 ratings, Corner Cup’s on 456. Report the bases with the map, and treat small differences involving a small base as uncertain.
“Brands close together on Dimension 1 are similar.”
Read both dimensions, and remember that the map leaves out a tenth of the differences. Two brands close on the map may still differ on an attribute the map represents poorly, such as local and independent here. Check the table of means before claiming two brands are seen alike.
“The right-hand end of a dimension is the good end.”
The direction of each axis is arbitrary; the analysis could flip it without changing anything. The ends mean whatever the loadings say, and whether a position is good depends on which segment you want to be near.
Guided practice
Work through these with hints when you need them. Every hint and every worked solution is there to be used.
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On your own
No hints this time. Answer, check, and read the feedback; the solution appears once you have answered or if you ask for it. Your first answers count toward mastery.
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In practice
A brand manager uses a perceptual map as a position review, before anyone writes a positioning statement or plans a campaign. The review asks four questions in order: where are we, and who is near us; which rival is nearest each segment we might serve; what would have to change for us to be nearer the segment we want; and how good is the evidence. The answers become the inputs to the next two lessons.
Fictional case
Ana’s review for Lantern. Lantern holds the crafted and ethical end of the map alone, nearest the Craft and local ideal. That segment is 109 of the 640 respondents but spends the most per head ($76.61 a month) and has the highest Cold Brew intent (46% top-two). Its nearest rival for Craft and local is Arcadia Coffee, which holds the Mindful drinkers more closely than Lantern does. Summit Brew sits between Lantern and the convenient brands, nearest the Explorers, and is the brand Cold Brew will be compared with on the shelf.
| Question | What the map says | What it can’t say |
|---|---|---|
| Where is Lantern? | The crafted and ethical end of Dimension 1, alone | How Lantern Cold Brew, which the survey didn’t rate, will be seen |
| Who is it near? | Craft and local (0.79); Explorers next (2.12) | How each segment sees Lantern: too few ratings per segment |
| Who are the rivals? | Arcadia for Craft and local and Mindful; Summit Brew for Explorers; Corner Cup for On the go | Rivals on attributes the survey didn’t ask about |
| How good is the evidence? | 61 ratings of Lantern; 90% of the differences on the map | Whether people who don’t know Lantern would see it the same way |
Two decisions follow from the review, and both belong to the lessons ahead. The first is what Lantern should claim, and against whom: the frame of reference, the points of parity and the points of difference that make up a positioning statement. The second is whether Lantern should try to move on the map, towards the On the go drinkers who like the idea of canned cold brew, and what such a move would cost in credibility with the Craft and local drinkers who already see Lantern as theirs.
The same review works for any business with rivals customers can compare: a gym deciding whether to add classes, a bank checking whether its new app has changed how it is seen, a travel company comparing itself with online booking sites. In each case the map is only as good as the attributes asked, the people asked and the number of ratings behind each point, so the review starts by stating those limits.
Knowledge check
Six questions, one attempt each, no hints. Score 80% or more to complete the lesson; you can take it again at any time.
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Summary
- A perceptual map places brands by how customers perceive them: alike brands close, different brands far apart. It shows perceptions, not facts.
- A two-attribute map plots mean ratings directly; it is quick but shows only the two attributes chosen, and a different pair can change the picture.
- A principal-components map summarises many standardised ratings in two dimensions. Each dimension carries a share of the variance (its eigenvalue ÷ the number of attributes); Lantern’s map carries 68% and 21%, 90% together.
- Loadings, drawn as arrows, are each attribute’s correlations with the dimensions: an arrow points roughly towards brands rated high on it, and its squared length (the communality) is the share of that attribute the map shows.
- Ideal points place each segment’s ideal on the same map; the distance from an ideal point to a brand measures how close the brand is to what the segment says it wants. Lantern is nearest the Craft and local ideal.
- A gap is an opportunity only if a large enough segment wants it, the firm can deliver it credibly and profitably, and it isn’t empty for a reason.
- State the limits beside any map: the bases (Lantern’s 61 ratings), who rated each brand, the attributes asked, the averages that hide segments, and the share of the differences left off the map.
Key formulas
- Distance on the map between an ideal point and a brand
- Share of the variance a dimension carries
- Share of an attribute shown on a two-dimensional map
Terms introduced
- Perceptual map
- A chart that places competing brands by how customers perceive them, so that brands seen as alike sit close together; built from customers’ ratings or similarity judgements.
- Determinant attributes
- The attributes customers use in making a purchase decision, and so the ones worth putting on a perceptual map.
- Principal components analysis
- A method that summarises many correlated variables in a few uncorrelated dimensions, the first carrying the most variance, the second the most of what is left, and so on. On a perceptual map it is applied to brands’ standardised mean ratings.
- Eigenvalue
- In principal components analysis, the variance a dimension carries. With standardised variables the eigenvalues add up to the number of variables, so each divided by that number is the dimension’s share of the variance.
- Loadings
- In principal components analysis of standardised variables, the correlations between each variable and each dimension; on a perceptual map they are drawn as arrows.
- Communality
- The share of a variable’s variance that the retained dimensions represent; on a two-dimensional map, the sum of its two squared loadings.
- Biplot
- A chart that shows the rows of a data table as points and its columns as arrows on the same axes, such as brands and attributes on a perceptual map.
- Ideal point
- The position on a perceptual map of the profile a customer or segment says it would most like; brands nearer it are closer to what that customer or segment wants.
Sources
- Gomez Albrecht, M., Green, M. & Hoffman, L. (2023). Principles of Marketing, section 5.6, “Product Positioning” (perceptual maps, determinant attributes, gaps). OpenStax. Read in the LibreTexts copy of the same edition. biz.libretexts.org/Bookshelves/Marketing/Principles_of_Marke…
- Greenacre, M. (2010). Biplots in Practice, chapter 6, “Principal Component Analysis Biplots” (form and covariance biplots; showing both rows and columns in principal coordinates “is not a biplot”, and projections degrade when the two singular values differ). Bilbao: Fundación BBVA. fbbva.es/wp-content/uploads/2017/05/dat/greenacre_c06_2010.p…
- Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58(3), 453–467. Citation and abstract confirmed from the bibliography of Greenacre (2010); the paper itself was not consulted. fbbva.es/wp-content/uploads/2017/05/dat/greenacre_ap0B_2010.…
- NIST/SEMATECH (2012). e-Handbook of Statistical Methods, section 6.5.5.2, “Principal Components: Numerical Example” (eigenvalues of the correlation matrix, cumulative proportions, communalities). itl.nist.gov/div898/handbook/pmc/section5/pmc552.htm