Equal-interval graph

Equal differences receive equal space

On an equal-interval vertical axis, the visual distance from 5 to 10 equals the distance from 50 to 55. Both are five-unit increases. The first value doubled, while the second rose by 10%. A linear scale highlights the shared additive change and gives less visual emphasis to the different proportional changes.

The horizontal axis can also be equal interval. If it represents calendar days, equal physical spaces should represent equal elapsed time. If it represents sessions, the label should say so because five session spaces may cover very different calendar periods.

Additive and proportional questions differ

An equal-interval graph is often useful when absolute change matters. Examples include minutes engaged, number of completed steps, percentage points, or occurrences per fixed observation period.

A semilogarithmic chart gives equal space to equal ratios. On that display, 5 to 10 and 50 to 100 occupy the same vertical distance because both are ×2. It cannot place zero on an ordinary logarithmic axis.

Neither scale is inherently more honest. The chosen display should match the question, disclose its rules, preserve raw values, and avoid exaggerating an effect.

A fictional tutoring example

Priya’s correct responses per one-minute timing rise from 5 to 10 in one week. A second skill rises from 50 to 55. Both increased by five responses per minute.

An equal-interval graph gives both changes the same vertical rise. That display answers, “How many responses per minute were added?” The proportional changes differ: the first is ×2, while the second is ×1.1. A ratio chart would make that contrast much clearer.

The team retains both raw series and selects the graph that fits the decision. If the goal concerns ten additional correct responses per minute, additive distance is relevant. If the goal concerns weekly multiplication of frequency, proportional display may help.

Scale range shapes the picture

A vertical axis from 0 to 100 can make a five-point change look small. An axis from 40 to 60 makes the same change occupy more space. Readers need the minimum, maximum, interval, and unit to interpret the visual honestly.

Starting at zero is useful for many count and percentage displays, though a restricted range can be defensible when small changes matter. If zero is omitted, disclose that choice prominently and avoid bar lengths that imply a false baseline.

Aspect ratio matters too. Stretching a graph vertically makes trends appear steeper; stretching it horizontally makes them appear flatter. Keep dimensions stable when comparing panels, people, or phases.

Percentages need denominators

A line at 80% can represent 8 of 10, 80 of 100, or 4 of 5. Show or retain the numerator, eligible denominator, and observation rule. Unequal or tiny denominators can produce visible movement unrelated to a meaningful change in count.

When opportunities differ greatly, consider displaying the denominator or pairing the percentage graph with counts. A graphing choice cannot repair an unstable measurement system.

Transformations need labels as well. A value shown as “change from baseline,” a rolling average, or a standardized score is no longer the raw measure. Name the transformation, preserve its formula, and keep the original values available. Equal spacing then applies to the transformed units, which may answer a different question from the source data.

Avoid silent axis breaks

A scale break marks a deliberate discontinuity. It can compress a large unused range or accommodate a rare outlier, but it also disrupts the ordinary equal-interval reading. Use a visible break symbol, label both segments, and explain the decision.

When the broken segments use different spacing, readers cannot compare slopes across the break in the usual way. A separate panel or inset may be clearer.

Audit the graph against the source

Check:

• axis variable, unit, minimum, maximum, and interval
• equal physical spacing for equal numerical differences
• observation order and elapsed-time rule
• complete labels, legends, and phase changes
• raw-value agreement
• missing, zero, and ineligible states
• consistent dimensions across comparisons

Report graph accuracy as required graph elements matching the approved specification divided by elements due for review. Visual appeal is separate from data integrity.

The BACB BCBA Test Content Outline, sixth edition includes graphing and visual analysis. A comparison of linear and ratio graphs shows why scale format can influence what change looks most prominent. Neither source supplies a universal graph choice for every clinical decision.