An independent study reference written by Dr Phuc V. Nguyen. It is not official subject material — for assessment requirements always follow your subject outline and vUWS.

Visual Communicationintermediate

Visual variables

Q: A chart must let readers compare fifteen branch profits and also show which state each branch sits in. Which channel assignment is strongest?

Profit on bar length against a common baseline, state on colour hue. Profit is the quantity that has to be compared precisely, so it belongs on the most accurate magnitude channel available, which here is position along a common scale read as bar length. State is a category with no natural ordering, so it belongs on an identity channel such as hue. The other options put the precise quantity on area, lightness or angle, all of which are read far less accurately.

Q: A designer doubles a value in a bubble chart and doubles the circle radius to match. How much area is drawn for the doubled value, compared with the original circle?

Four times the area, because area grows with the square of the radius. Area is proportional to the square of the radius, so doubling the radius draws four times the area for a value that has only doubled. What the reader takes from that is a further step removed. Under a power law with an exponent near seven tenths, four times the area reads as roughly two point six times the original, so the bubble still overstates a doubling even though area is itself under-read. The correct construction scales the radius with the square root of the value.

A chart works by mapping data onto visual channels: position, length, angle, area, colour hue, colour lightness, shape, orientation and texture. Bertin catalogued these as the visual variables available to a designer. Cleveland and McGill then showed that the channels are not interchangeable. Readers judge position along a common scale most accurately, then length, then angle and slope, then area, then volume, then colour intensity. The practical rule follows directly. Put the quantity you most need read correctly on the most accurate channel available, and spend the weaker channels on categories, grouping and emphasis.

Why it matters

Every channel has a resolution, like a ruler with marks of different fineness. Position is a fine ruler, and people read it to within a few per cent. Area is a coarse one, and people routinely under-read it. If the number that decides the meeting is encoded as bubble size, you have handed the reader a blunt ruler and asked for a precise answer. Match the channel to how much precision the message actually needs.

Before you read on — recall

A chart must let readers compare fifteen branch profits and also show which state each branch sits in. Which channel assignment is strongest?

Formulas

Stevens power law for perceived magnitude

\psi = k \, \phi^{\beta}

Perceived magnitude

\psi

grows as a power of physical magnitude

\phi

. When the exponent

\beta

is close to one, the channel reads almost true, which is roughly the case for line length. When

\beta

falls below one the channel is systematically under-read, which is the case for area. At an exponent near seven tenths, doubling the area of a circle raises its perceived size by only about sixty per cent, so a bubble carrying twice the value does not look twice as big.

Sizing a circle by value, correctly

r_i = r_{\max} \sqrt{\dfrac{v_i}{v_{\max}}}

Area, not radius, should be proportional to the value, so the radius has to scale with the square root of the value. Setting the radius proportional to the value instead means a doubled value is drawn with four times the area, because area grows with the square of the radius. That single slip is one of the most common quantitative errors in published bubble charts, and it compounds with the under-reading of area rather than cancelling it.

Worked examples

Scenario

A regional manager presents market share for eight territories as a bubble map, then asks the room which two territories are closest in share.

Solution

Nobody can answer reliably. Area is one of the weakest channels, and readers under-read it, so two bubbles differing by fifteen per cent look nearly identical. Redrawing the same eight values as a bar chart sorted from largest to smallest puts every value on position along a common scale, the most accurate channel available. The comparison question is then answered by reading two adjacent bar ends. Keep the map only if geography is itself part of the message, and if so, pair it with the sorted bars rather than replacing one with the other.

Scenario

A team wants a chart showing monthly revenue for four product lines, where the total matters and the individual lines also matter.

Solution

Assign the channels by what has to be read accurately. Revenue goes on vertical position against a common scale, month goes on horizontal position, and the four product lines go on colour hue, which is an identity channel rather than a magnitude channel. That gives four lines, each of which can be traced and compared at any month. Four separate lines do not draw the total, so add a second panel directly above them, on the same time axis and aligned to it, carrying the total as a single line. A stacked area chart does show the total as its top edge, but it puts three of the four series on shifting baselines, a much weaker channel, so only the bottom band and the total stay readable.

Common mistakes

✗Colour is a good way to show a quantity. Colour lightness carries a rough ordering, and hue carries none at all. Both sit near the bottom of the accuracy ranking, so colour belongs on categories, grouping and emphasis, with quantities on position or length.
✗Any channel will do as long as the chart is labelled. Labels let a reader recover exact values one at a time, but the point of a chart is the comparison the eye makes without reading labels. A weak channel degrades that comparison even when every value is printed.
✗Three dimensions carry more information than two. Adding depth adds a volume channel, which is even less accurate than area, and it introduces occlusion and perspective distortion. It reduces what a reader can extract rather than increasing it.
✗The accuracy ranking is a strict rule. It is an ordering of average reading accuracy for magnitude judgements. Other goals can outrank accuracy, for instance when geography, part-to-whole structure or a large number of series makes a weaker channel the only workable option. The ranking tells you what you are giving up, not that you may never give it up.

Revision bullets

•Bertin visual variables: position, size, shape, value, hue, orientation, texture
•Accuracy order: common-scale position, non-aligned position, length, angle, area, volume, colour intensity
•Put the decisive quantity on the most accurate channel available
•Hue is an identity channel, lightness is a weak ordering channel
•Circle radius scales with the square root of the value, never with the value
•Depth adds distortion, not information

Quick check

A chart must let readers compare fifteen branch profits and also show which state each branch sits in. Which channel assignment is strongest?

A designer doubles a value in a bubble chart and doubles the circle radius to match. How much area is drawn for the doubled value, compared with the original circle?

Connected topics

Measures & Dimensions Purpose of Visuals Choosing a Chart Dashboards Visual Mistakes Truncated Axes

More in Visual Communication

Data Storytelling Chart Ethics

Sources

Bertin (1983)
Bertin, J. Semiology of Graphics: Diagrams, Networks, Maps. Translated by W. J. Berg. University of Wisconsin Press, 1983. Originally published as Semiologie graphique, 1967.
The original catalogue of the visual variables available to a chart designer.
Cleveland & McGill (1984)
Cleveland, W. S., & McGill, R. "Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods." Journal of the American Statistical Association, 79(387), 531-554, 1984.
The experimental ranking of elementary perceptual tasks that underpins channel choice.
Heer & Bostock (2010)
Heer, J., & Bostock, M. "Crowdsourcing Graphical Perception: Using Mechanical Turk to Assess Visualization Design." Proceedings of CHI 2010, 203-212.
Replicated and extended the Cleveland and McGill ranking on a much larger participant pool.
Stevens (1957)
Stevens, S. S. "On the Psychophysical Law." Psychological Review, 64(3), 153-181, 1957.
Source of the power-law relationship between physical and perceived magnitude.

How to cite this page

Dr. Phil's Quant Lab. (2026). Visual variables. Derivatives Atlas. https://phucnguyenvan.com/concept/ba-visual-variables