Small Multiples and Heterogeneity

The executive question: is the national pattern broad-based or region-specific?

The atlas card for small multiples describes the form in one line. This section is the argument for when to spend the space, because faceting is not free — four panels take four times the room and ask the reader to hold four comparisons at once. That cost is worth paying under exactly one condition: the managerial question is itself about heterogeneity. Whether a pattern holds everywhere, whether one segment is doing all the work, whether a single national number is safe to build a policy on — none of those can be answered by a national line, no matter how carefully it is drawn.

The soup case has four census regions: East, Midwest, South, and West. The national indexed chart said Progresso raises price into a seasonal demand trough. That is a claim about the average. Figure 1 asks whether it is a claim about the business.

Figure 1 gives managers two findings at once, and they point in opposite directions. First, the price seasonality is not a single-market artifact — it appears in all four regions, which makes the national headline more credible, not less. Second, the share level differs sharply by region: the East is a much stronger Progresso market than the South or the Midwest. A national pricing memo that carried the first finding while ignoring the second would turn a visual average into an operational mistake.

That combination — the pattern is broad, the levels are not — is the most common real result, and it is precisely the result a national chart cannot express. It is also why "we checked and the pattern holds" is an incomplete sentence. Holds where, at what level, and how strongly are three separate answers.

The same-scale rule

Small multiples work because the eye compares panels directly. That mechanism depends entirely on the panels being comparable, which means three things stay fixed across every panel and only the data varies:

• The scale. Identical y-axes. If each panel is auto-scaled to fill its own frame, a tiny swing and an enormous swing look the same, and the reader concludes the regions behave alike when they do not. This is a correctness failure, not a cosmetic one.
• The window. Identical time ranges. A panel that starts in a different month has a different story built into its left edge.
• The order. A stable, meaningful panel order — by size, by geography, or by the metric itself — so the reader is not hunting for the pattern in a random arrangement.

Each of those is easy to violate by accident, because most plotting libraries default to free scales when they facet. "Let each region breathe" is how the mistake is usually described, and it is the single most common way a small-multiple chart quietly stops being one.

Small multiples as model preparation

Faceting also does something the rest of the book depends on: it previews regression. A regression with one coefficient asks for one summary relationship across the whole dataset. A small-multiple chart asks whether that one summary is likely to be stable across groups — which is the same question a heterogeneity analysis asks formally in Chapter 7, many chapters before the machinery arrives.

Figure 2 makes the preview concrete by plotting log(Progresso volume) against log(Progresso price), separately by region. The downward trend line is an elasticity-style visual: a one percent increase in price is associated with some percent change in volume. We are not yet claiming a causal elasticity. We are teaching the eye to see a slope before it has to read an equation.

Figure 3 turns those visual slopes into numbers with intervals — a bridge view that is still descriptive but already moving toward the statistical graphics of the next section.

Figure 3 should not replace Figure 2, and the reason generalizes well beyond this case. The table makes the slopes precise; the scatterplots show whether that precision comes from a clean pattern or from compressing a messy one into a single number. A steep slope through a tight cloud and a steep slope through a shapeless scatter produce identical table rows and deserve very different levels of trust. Managers need both views before deciding whether a national elasticity estimate is useful at all.