Reliable Change & Reliable Change Index (RCI) Calculator

You can use this online tool to calculate the Reliable Change Index (RCI) and determine the minimum change in a score that indicates reliable change (RC).

All you need to do is enter the pre-test and post-test scores, the standard deviation, select your desired confidence level, and enter the test-retest reliability coefficient.

Reference

Test scores will vary from one administration to another due to imperfect reliability. To test whether the change in scores is greater than would be expected from random variation alone, many researchers advocate the use of the Reliable Change Index Statistic.

If the change score exceeds the Reliable Change Index (which is calculated based on the reliability of the measure), then the patient can be said to show a significant change (improvement or deterioration depending on the scale direction), meaning that the observed change would be expected by chance alone at a probability of less than 5% (for a 95% confidence level).

Formulas

Pre-post Score Difference: Difference = X_post − X_pre , where X_post = post-test score, X_pre = pre-test score

Standard Error of Measurement (SE_M): SE_M = SD × √(1 − r_xx) , where SD = standard deviation of the measure at baseline, r_xx = test-retest reliability

Standard Error of Difference (SE_DIFF): SE_DIFF = √2 × SE_M , where SE_M = standard error of measurement

Z-value for Selected Confidence Level: z = qnorm(1 − (1 − CL)/2) , where qnorm = quantile function of the normal distribution

Reliable Change (RC): RC = z × SE_DIFF , where: z = value for selected confidence level (e.g., 1.96 for 95%), SE_DIFF = standard error of difference

Reliable Change Index (RCI): RCI = (X_post − X_pre) / SE_DIFF , where SE_DIFF = standard error of difference

More References

1. Jacobson, N. S., & Truax, P. (1991). Clinical significance: A statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59, 12-19.

2. Bauer S., Lambert M.J., Nielsen S.L. (2004) Clinical significance methods: a comparison of statistical techniques. Journal of Personality Assessment, 82, 60–70.