Does an intervention work for one person? (single-case analysis)

In brief

One person (or a few) is measured repeatedly over a longer time: first without intervention (phase A, baseline), then with intervention (phase B). The question is whether the values in B lie differently - usually better - than in A. Group tests do not fit here because the measurements follow each other and are related. Statable instead compares the phases with NAP (main index), Tau-U, baseline-corrected Tau and PND, and draws the usual time-series chart.

When does it fit?

• Diagnostic assessment and evaluation of an intervention for a child or young person, e.g. reading rate per week before and after a reading intervention begins.
• Several people with the same design (multiple baseline): one chart per person and a mean across the people.

What the table looks like

One row per measurement occasion. You need the column with the measure (a number) and a column that tells baseline and intervention phase apart (exactly two values, e.g. “A” and “B”). Optional: a column with the measurement occasion (number or date; otherwise the order of the rows applies) and, for several people, a column that tells them apart.

Requirements and limits

• At least 3 data points per phase, preferably 5 (What Works Clearinghouse). With fewer, Statable shows a note.
• First all baseline measurements, then all intervention measurements (A-B). Alternating phases (A-B-A-B) are not yet calculated by Statable.
• A trend already during baseline is reported; NAP and PND do not take it into account, Tau-U (“minus trend A”) and baseline-corrected Tau do.
• Consecutive measurements are often similar (autocorrelation). Statable shows a note if it is noticeable (lag 1 from .30); the p values are then too optimistic.
• An A-B design alone does not show a cause: maturation, chance or other events may be behind it.

Reading the result

• NAP is the share of pairs of one A and one B measurement in which B is better (a tie counts half). 0.5 means no difference, 1 means complete separation. Rule of thumb (Parker and Vannest 2009): up to .65 weak, up to .92 medium, from .93 strong.
• Tau-U and baseline-corrected Tau also lie between −1 and +1; grouping after Vannest and Ninci (2015): up to .20 small, up to .60 moderate, up to .80 large, above that very large.
• PND is the share of B values above the best A value; it depends on a single value and is shown for comparison with older work.
• If a lower value counts as better (e.g. errors), switch the direction in the result. The chart can show a mean or trend line per phase.

NAP = .97, 95% CI [.70, 1.00], p = .003; Tau-U = .93, p = .002; Tau-BC = .59, p = .002; PND = 87%

For specialists

Own code, checked against R (scan 0.68.1: nap, tau_u(method = "parker"), corrected_tau, pnd; SingleCaseES::NAP; wilcox.test). NAP interval after Newcombe (score interval for the AUC), p from the Mann-Whitney test with normal approximation (two-sided). Tau-U after Parker et al. (2011): (pairs B better − pairs B worse [− Kendall S of A over time]) / (nA · nB); p from Kendall S with tie correction. Baseline-corrected Tau after Tarlow (2017): trend test in A with Kendall τb (α = .05); with a significant trend the Theil-Sen line of A is subtracted, then τb between residuals and phase. Occasions count as equally spaced (1…n). With several cases the means are simple averages of the case indices, unweighted.

Typical examples

• One child reads for one minute each day: words per minute before and during the intervention (NAP, Tau-U).
• One pupil: how often does she disrupt per hour, without and with a reinforcement plan?