Mosaic plot¶
An area-proportional display of a contingency table that recursively partitions a rectangle by categorical frequencies so each tile represents one combination of levels.
Core Idea¶
Widths and heights encode marginal and conditional proportions, while color or shading can show residuals from independence; category order, empty cells and conditioning sequence strongly affect interpretation. The total rectangle is split by the first variable's proportions, each strip is subdivided by conditional proportions of later variables, and tile area becomes joint frequency or probability. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Mosaic plot belongs to categorical data visualization and is useful where the analyst can specify the typed categorical data visualization carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the contingency table and sampling weights, variables and category order, missing and zero cells, total and margins, recursive split orientation, area normalization, labels, residual or significance shading, independence reference, ordering and collapsing, uncertainty and accessibility are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the contingency table and sampling weights, variables and category order, missing and zero cells, total and margins, recursive split orientation, area normalization, labels, residual or significance shading, independence reference, ordering and collapsing, uncertainty and accessibility are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Mosaic plot. Mosaic plot compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed categorical data visualization carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of categorical data visualization because they reuse the typed categorical data visualization carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, The total rectangle is split by the first variable's proportions, each strip is subdivided by conditional proportions of later variables, and tile area becomes joint frequency or probability., and type the carrier, state every parameter and convention in the definition, test that the contingency table and sampling weights, variables and category order, missing and zero cells, total and margins, recursive split orientation, area normalization, labels, residual or significance shading, independence reference, ordering and collapsing, uncertainty and accessibility are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Mosaic plot Domain-specific
Parents (1) — more general patterns this builds on
-
Mosaic plot is a kind of Representation Prime
The proposed strict upward parent is
prime:representation.
Hierarchy path (1) — routes to 1 parentless root
- Mosaic plot → Representation → Abstraction
Neighborhood in Abstraction Space¶
Mosaic plot sits in a crowded region of the domain-specific corpus (30th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Data Visualization & Geometric Displays (21 abstractions)
Nearest neighbors
- Scatter plot — 0.92
- Area chart — 0.92
- Qualitative variation — 0.91
- Horizon chart — 0.90
- Biplot — 0.90
Computed from structural-signature embeddings · 2026-09-08