Jacobson & Truax (1991) proposed two questions every psychotherapy outcome must answer: did the client change more than measurement error alone could explain, and did they end up statistically closer to a healthy population than a clinical one?
Standard error of measurement: SEM = σ·√(1 − r_xx)
Standard error of difference: SE_diff = SEM·√2
Reliable Change Index: RCI = (post − pre) / SE_diff
|RCI| ≥ 1.96 → reliably changed (p < .05, not just noise)
|RCI| < 1.96 → change indistinguishable from measurement error
Clinically significant cutoff (functional/dysfunctional crossover):
c = (σ_clin·μ_norm + σ_norm·μ_clin) / (σ_clin + σ_norm)
- Top panel — the probability-density curves of the clinical (red) and normative (green) reference populations plotted analytically over the 0–63 symptom scale, with the client's pre (amber) and post (blue) scores and the clinically-significant cutoff (purple dashed) marked as vertical lines.
- Bottom panel — the actual hypothesis-test object: the sampling distribution a truly unchanged client's difference score would follow, Normal(0, SE_diff). The shaded tails mark |z| ≥ 1.96 (p < .05, two-tailed); the vertical marker is the client's observed difference (post − pre). If it lands in a shaded tail, the change is reliable.
- rxx — the measure's test–retest reliability. A noisier instrument (lower rxx) inflates measurement error, widens the bottom curve, and makes the same raw change less reliable.
- σ — the standard deviation of scores in the general population, the other input to measurement error.
- Real-world relevance: this is the standard statistic clinical trials and single-case practitioners use to separate genuine treatment response from random fluctuation in self-report measures — required reporting in most psychotherapy efficacy research.