Does brushing modify the source values?

Highlighting alone does not; separate editing actions may.

Must every view show the same axes?

No. Linking is useful precisely because the same records can be examined through different variables.

Is a brushed pattern proof of causation?

No. It is an observation that may motivate further investigation.

AI Glossary / Statistics and probability / Advanced

Brushing

Definition

Brushing is an interactive data-exploration technique in which a user selects and highlights observations in a chart. When views are linked, the same observations are highlighted in other charts or a data table, helping the user examine how a subgroup behaves across several variables.

What it means

A scatterplot shows only a few dimensions of a dataset at once. Brushing lets an analyst point to an interesting cluster and ask where those same records appear elsewhere. It is useful when a visible pattern raises a question about variables that are not shown on the original axes.
Selection creates a temporary analytical focus. It does not, by itself, change measured values, prove that the selected points form a meaningful statistical group, or remove records from the dataset. Some applications offer separate actions to filter, export, or delete a selection; those actions should be distinguished from highlighting.

How it works

The user marks points individually or draws a selection region, such as a rectangle. The application identifies the corresponding observations and records their selection state. Linked displays use that identity information to highlight the matching observations, even when their positions differ across views.
The selection can be moved or redefined to explore another subgroup. A useful interface makes it clear whether a new brush replaces, adds to, or intersects an earlier selection. Linking depends on the relationship between records, not merely on points looking similar on screen.

Three practical examples

A model evaluator brushes cases with large prediction errors and examines their input lengths in a linked chart. The highlighted group suggests questions about difficult cases that can be tested separately.
An operations analyst selects unusually slow requests and checks where they fall by workload and processing route. The analyst can distinguish an apparent route pattern from a concentration of demanding requests.
A data-quality reviewer highlights a suspicious cluster and inspects its source rows. Duplicate identifiers, unusual units, or collection dates may become visible without manually searching the entire table.

Think of it this way

Imagine placing colored stickers on several cards in a collection. You can rearrange the cards by date, price, or category and still recognize the same marked cards. Brushing supplies the stickers; linked views provide different arrangements of the collection.

Worked example

Consider six service requests with columns for identifier, input length, processing time, and route. R1 has length 100, time 1, and route A. R2 has 200, 2, and A. R3 has 300, 5, and B. R4 has 400, 6, and B. R5 has 500, 3, and A. R6 has 600, 7, and B.
A scatterplot places input length on the horizontal axis and processing time on the vertical axis. The analyst draws a rectangle covering lengths from 250 through 650 and times from 4 through 8. R3, R4, and R6 fall inside it. R5 is outside because its time is only 3, despite its input length being within the selected range.
The linked table highlights those three identifiers. A linked route display shows that all three selected requests use B. The selected mean time is (5 plus 6 plus 7)/3 = 6. The remaining requests have times 1, 2, and 3, averaging 2.
This four-unit difference is descriptive. The analyst selected records partly because their times were high, so rediscovering a higher selected mean is not independent evidence that the route causes delay. Workload composition and other differences still need investigation.
Now the analyst brushes input lengths from 450 through 650, regardless of time. The selection becomes R5 and R6: one A request and one B request. Their average time is 5. The linked route display changes because the selected record identities changed, not because either request changed route.
The first selection contained three of six requests, or 50 percent. The second contains two of six, approximately 33.3 percent. If the interface filters out unselected requests, the analyst must preserve the original denominator when describing those proportions. A chart showing only selected points is not the complete dataset.

Illustrative case study

Fictional company Maple Insights uses linked plots to investigate an apparent pocket of poor model performance. An analyst brushes the high-error region and checks the highlighted records in a table and a separate plot of input characteristics.
The team discovers that the selection overlaps strongly with long inputs, but it treats this as a hypothesis. It records the selection rule, checks data quality, and evaluates the proposed relationship on additional observations. The dashboard retains an easy way to clear selections and return to the complete dataset.
The investigation produces a reproducible question rather than an unexplained screenshot. This fictional case illustrates how visual exploration can guide subsequent analysis without turning an interactively chosen pattern into a confirmed finding.

Common misconceptions and mistakes

Brushing is not automatically clustering. The user may select an arbitrary region rather than a group identified by an algorithm.
Highlighting is not necessarily filtering. Unselected observations may remain visible and may still contribute to statistics, depending on the application.
A selected subgroup is not a random sample. Selection based on visible outcomes can strongly influence the patterns observed afterward.
A dense point may represent several overlapping records. The analyst should check the selected count and record table rather than assuming one visible mark means one observation.
Linked charts can disagree if they use different aggregation levels, filters, or missing-value rules. Check what each mark represents.

Business use

Use brushing to connect visual anomalies with concrete records and to formulate focused follow-up questions. Record the dataset version, selection conditions, selected count, and relevant filters when the exploration informs a decision. A colleague should be able to reconstruct the subgroup without repeating a mouse gesture. Preserve the distinction between exploratory findings and later validation.

Check your understanding

Why is R5 excluded from the first brush?

Answer: Its processing time falls below the rectangle's lower boundary.

Which records appear in the second selection?

Answer: R5 and R6.

Why is the selected mean of six not proof against route B?

Answer: High processing time was part of the selection rule, and other differences were not controlled.

Related terms

Scatterplot matrix
Exploratory data analysis
Selection bias
Filtering
Linked views
interactive visualization
data provenance

Learn next

Explore coordinated multiple views, brushing versus filtering, and reproducible subgroup analysis. Study how data aggregation and missing values affect what a chart selection represents.

Sources

NIST/SEMATECH, statistical glossary, brushing: https://www.itl.nist.gov/div898/handbook/glossary.htm . MathWorks, brush documentation: https://www.mathworks.com/help/matlab/ref/brush.html . JMP, rectangular point selection documentation: https://www.jmp.com/support/help/en/19.2/jmp/select-a-rectangular-area-of-points-in-a-jmp-graph.shtml . Request data and company scenario are original illustrations.

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