ISYS3438 Chap.6 Bivariate Patterns and Comparisons
Bivariate Patterns and Comparisons
Bivariate visualisation begins by pairing the analytical roles of two variables. Two quantitative measures suggest a scatterplot; two categories suggest grouped or stacked comparisons or a heatmap; a quantitative measure split by category calls for grouped distributions or another mixed display. This chapter explains direction, form, strength, clusters and outliers without turning association into cause.
It also separates counts, within-group percentages and exposure rates because each answers a different business question.
What this chapter covers
- 01
variable-pair matrix
- 02
scatterplot patterns
- 03
grouped and stacked bars
- 04
heatmaps
- 05
mixed-type comparisons
- 06
association boundaries
Worked example · free
Interpret a clustered scatterplot
- +1Describe the overall positive association with units.
- +1Identify the subgroup and display vehicle type without obscuring points.
- +1Request load, terrain and traffic evidence before labelling the vehicle inefficient.
Key terms
- Scatterplot
- A scatterplot places two quantitative variables on perpendicular position scales.
- Overplotting
- Overplotting occurs when marks overlap and hide the number or density of records.
- Within-group share
- A within-group share divides each category by its own total to compare composition.
- Binned plot
- A binned plot groups nearby values or points to reveal density when individual marks overlap.
Bivariate Patterns and Comparisons FAQ
Does a trend line prove causation?
No. A trend line summarises association in the plotted records. Causal claims require a design that addresses time order, alternative explanations, selection and other relevant conditions.
When should I use percentage-stacked bars?
Use them to compare composition across groups with different totals. Also disclose the totals because two groups can have identical shares but very different operational workload.
How should I show a quantitative measure across categories?
Use box plots, points or small multiples when spread matters. A bar of means may be sufficient for a narrow summary task, but it should not hide sample size and variation.
Assessment move
Create a two-by-two matrix of categorical and quantitative variable pairs. For each cell, sketch two possible views and state the denominator or aggregation. Practise describing scatterplots with direction, form, strength, subgroup and uncertainty. Remove causal verbs unless you can name the design feature that warrants them. Start with the relationship question and the role of each variable.
Two quantitative measures suggest a scatterplot; a quantitative measure across categories suggests common-scale points, bars or distributions; two categorical attributes suggest counts, proportions or a heatmap. Identify whether the purpose is association, difference, composition or prediction. Keep the observation unit visible because aggregated points can describe groups while the business claim concerns individuals.
For scatterplots, inspect range, clusters, outliers and non-linearity before adding a trend line. Report sample size and consider whether overplotting hides repeated observations. Use transparency, jitter or aggregation carefully, preserving the ability to explain what one mark means. A fitted line summarises association in the displayed records; it does not establish direction or causation.
Name plausible confounders, selection effects and time-order questions that the view cannot resolve. When comparing groups, show distributions or uncertainty when a single mean could hide overlap and tail behaviour. Grouped bars support direct category comparison on a shared baseline, while stacked bars privilege totals and broad composition but make most internal segments harder to compare.
A heatmap can reveal a large matrix of relative values but needs a clear scale and often direct labels for important cells. Normalise by an appropriate denominator before comparing differently sized groups. Practise sensitivity checks by altering one defensible analytical choice at a time: time window, inclusion rule, aggregation, transformation or denominator. Record whether the relationship persists, weakens or reverses.
If a conclusion depends on one convenient setting, describe it as fragile. Finish with a business statement that contains the comparison, magnitude, population and period, followed by an explicit evidence boundary. The recommended action should be an investigation, monitoring step or controlled test unless the design supports a stronger causal claim.
Build a claim table with separate rows for pattern, strength, exception and limitation. Link each row to a mark or comparison in the selected visual. For a scatterplot, note unusual observations and whether the apparent relationship persists within important groups. For categorical comparisons, check both absolute numbers and normalised shares. Remove any row that cannot be reconstructed from the chart and data.
Then ask what action follows if the association is real and what risk arises if it is not. This discipline prevents a visually strong relationship from becoming an unsupported causal story. It also shows which follow-up analysis, experiment or operational check would most efficiently reduce uncertainty. Archive the final visual with a small data extract and the code or worksheet settings needed to recreate it.
Ask a peer to reproduce the reported comparison and note where definitions are unclear. Reproducibility exposes silent filters and ambiguous denominators before they enter the business claim, while the peer's questions often reveal which annotations belong on the view.