Mapping and Perception
This set of concepts forms the foundation of effective data visualization, explaining how we map abstract data to visual elements and, crucially, how the human brain perceives and interprets those elements.
Mappings: Variable Types & Visual Encodings
Effective visualization begins with matching the right type of data variable to the right visual encoding.
Variable Types
Data variables are classified by the mathematical operations that can be performed on them:
Nominal (Categorical): Variables that are simply names or labels with no inherent order (e.g., countries, colors, gender).
Ordinal: Variables with a clear, sequential order, but the distance between values is unknown or inconsistent (e.g., T-shirt sizes: S, M, L; customer satisfaction: Bad, Good, Excellent).
Quantitative (Interval/Ratio): Variables where the difference between values is consistent and meaningful (e.g., temperature in Celsius, price, age).
Jacques Bertin – Encodings (Visual Variables)
The French cartographer Jacques Bertin formalized the language of visual mapping in his 1967 book, Semiology of Graphics.
Position (X, Y)
Size (Length, Area)
Value (Lightness/Darkness)
Color Hue (Red, Green, Blue)
Orientation (Angle)
Shape
Texture
Bertin's work emphasizes that Position is the most effective variable for all data types, especially quantitative data, while variables like Color Hue and Shape are best for nominal (categorical) data.
Perception & Quantitative Mappings
The effectiveness of a visualization is determined by how accurately and quickly the audience can decode the visual element back into its numerical value—a field of study known as Graphical Perception.
Cleveland & McGill – Numeric Encoding Hierarchy
Statisticians William S. Cleveland and Robert McGill (1984) conducted landmark experiments to empirically rank the accuracy of different visual encodings for quantitative data. Their Hierarchy of Elementary Perceptual Tasks shows which visual channels are decoded most accurately by the human eye:
| Rank | Visual Encoding | Example Chart | Accuracy |
| 1 | Position along a common scale | Bar/Dot Plot | Highest |
| 2 | Position along non-aligned scales | Multiple Line Graphs | High |
| 3 | Length | Bar Chart (vertical/horizontal) | Moderate |
| 4 | Angle & Slope | Pie Chart (angle), Line Chart (slope) | Low |
| 5 | Area | Bubble Chart | Lowest |
| 6 | Volume, Color Saturation, Color Hue | 3D Shapes, Heatmaps | Lowest |
Mantra: Always use the highest possible ranking encoding for the most critical quantitative data. For instance, using Length (bar chart) is better than using Area (pie chart slice) for comparing magnitudes.
Gestalt Psychology – Patterns That Pop
Gestalt Psychology provides principles for how the human mind automatically organizes and simplifies visual elements into a coherent whole. Data visualization leverages these principles to make patterns "pop" and groups easy to identify:
Proximity: Objects placed close together are perceived as a group (e.g., clustered bar charts).
Similarity: Objects that share visual characteristics (color, shape, size) are perceived as related (e.g., using the same color for one data category across multiple charts).
Continuity: The eye naturally follows lines and smooth curves, implying a connection or trend (e.g., a line in a line chart).
Closure: The mind fills in missing information to create a complete shape or figure.
Figure/Ground: The ability to distinguish an object (the figure) from its background (the ground).This is used to draw attention to the key data point (figure) against the context (ground).
Psychophysics: It's All Relative
These laws, derived from psychophysics, explain the non-linear relationship between a physical stimulus (the visual encoding) and the perceived sensation (the interpretation).
Weber’s Law – It’s All Relative
Weber's Law states that the ability to perceive a difference between two stimuli is relative to the magnitude of the stimuli.
Visualization Implication: It's easier to detect an absolute difference between two short lines than between two very long lines. This means that at the high end of a scale, a proportionally larger change is needed to be noticed. This principle underlies why stacked charts or pie charts become harder to judge when the base value is large or when segments are small.
Steven’s Power Law – Nonlinearity
Steven's Power Law is an empirical relationship that supersedes Weber's Law for a broader range of stimuli It states that the perceived magnitude is related to the physical intensity by a power function.
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