An ABA data interquartile range is Q3 minus Q1 after the observations are ordered and a quartile convention is declared. It summarizes the spread of the middle half of the values. Report the sample size, method, Q1, median, Q3, IQR, endpoints, and raw ordered data because software can use different quartile conventions for small samples.

Start with a compatible, traceable sample

IQR answers how spread out the middle half of an ordered sample is. Define the target, operational definition, unit, phase, setting, observation rule, dates, and analysis unit before calculating. Wes's worksheet uses eight compatible latency observations measured in seconds. The denominator is eight observed values. Each value remains linked to its source date and record.

Confirm expected, observed, excluded, corrected, and missing records. A missing observation stays missing; it does not become zero. Mixed units, duplicate entries, copied graph values, phase errors, and changed measurement definitions require correction or separate analysis before quartiles are calculated.

Declare the quartile method

Software packages and hand methods can return different quartiles, especially for small samples. The worksheet must name the convention, software and version when applicable, and rounding rule. This example uses the median-of-halves convention. With an even sample of eight values, split the ordered data into a lower half and an upper half, then find the median of each half.

Do not change methods between phases because another option produces a preferred result. If an earlier report omitted the method, reproduce the calculation when possible and label any uncertainty. Preserve full precision through intermediate steps and round once for presentation.

Calculate Wes's five-number summary

The ordered observations are 2, 3, 4, 5, 7, 8, 9, and 12 seconds.

  1. Minimum = 2 seconds.
  2. Lower half = 2, 3, 4, 5. Q1 = (3 + 4) / 2 = 3.5 seconds.
  3. Median = (5 + 7) / 2 = 6 seconds.
  4. Upper half = 7, 8, 9, 12. Q3 = (8 + 9) / 2 = 8.5 seconds.
  5. Maximum = 12 seconds.
  6. IQR = Q3 minus Q1 = 8.5 minus 3.5 = 5 seconds.

The complete five-number summary is 2, 3.5, 6, 8.5, and 12 seconds. Retaining those values makes the IQR reproducible and shows what the single number omits.

Review edge cases before interpreting

Ties are valid observations and remain in the ordered sample. Small samples can produce quartiles that change noticeably when one value is added. When only a few observations exist, raw data and a graph may be more informative than a stable-sounding IQR. If every observation is identical, Q1 and Q3 match and the IQR is zero; verify measurement sensitivity and context before describing performance as stable.

IQR reduces the influence of extremes without making them irrelevant. Investigate unusual values through source records and context. NIST's outlier guidance advises investigation before deletion. State any predeclared exclusion rule and show how the result changes if a corrected record alters the sample.

Graph the raw sequence and quartiles

Plot Wes's observations in date order with phase and condition annotations. A box plot can display the five-number summary, but it removes time order and should accompany the time-series graph. NIST's box-plot page provides the quartile and IQR structure. Label the quartile method in the figure note when different software conventions could matter.

Review the graph for level, trend, variability, immediacy, overlap, and consistency using an appropriate protocol. Lobo and colleagues and Wolfe, Barton, and Meadan provide relevant single-case and visual-analysis context. A moving average, described separately by NIST, smooths time-ordered values and does not answer the same question as IQR.

Write a reproducible report sentence

For eight compatible latency observations, Wes's median was 6 seconds. Using the median-of-halves convention, Q1 was 3.5 seconds, Q3 was 8.5 seconds, and the IQR was 5 seconds. Observations ranged from 2 to 12 seconds.

Add phase dates, setting, measurement definition, missing-state result, source version, and any context that affected exposure or access. Do not describe the middle half as half of all future performance. The result summarizes these eight observations under the declared method.

Keep the outcome meaningful and accessible

Review the summary with Wes through an accessible communication method and with the responsible clinician. Maintain AAC, interpreters, mobility supports, food, water, bathroom use, prescribed care, rest, relationships, and emergency access throughout measurement and review. ASHA supports continuous access to AAC tools or devices.

Ask whether latency is useful to Wes, whether observation conditions changed, and whether spread relates to comfort, participation, risk, or ordinary life. Pair IQR with treatment-integrity or implementation evidence, the time-series pattern, and client feedback before making a clinical decision.

Keep the source set in scope

The BACB ethics hub and CASP public summary provide professional context. The BCBA Test Content Outline identifies measurement and data-based decision topics as examination content. NIST's distribution page distinguishes location, spread, and shape. These sources support careful description; they do not set a universal IQR threshold for changing ABA care.

Clinician review checklist

For an ABA data interquartile range review, confirm the question, operational definition, unit, phase, eligible records, missingness, source lineage, ordered values, quartile convention, software version, Q1, median, Q3, IQR arithmetic, rounding, five-number summary, graph, access, client perspective, implementation evidence, interpretation, decision owner, and review date. Recalculate if the data, method or sample changes.

Limits of IQR

IQR does not show time order, trend, endpoints, rare events, measurement validity, treatment integrity, client benefit, future variability or cause. Different quartile conventions can yield different results. A narrow IQR can coexist with a clinically important extreme, and a wide IQR does not identify why values differ. Keep the ordered data and full graph available. Use IQR as one description of a defined sample, never as a stand-alone treatment rule.

Related resources

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