I was recently asked to examine some single-case study data and ended up using the method described by Mueser, Yarnold, and Foy (1991). In order to use this method, your data must comprise a minimum of four assessment points at equally spaced intervals (e.g., baseline, 12-weeks, 24-weeks, and 36-weeks).

This method is based on classical test theory and the steps involved are as follows:

- Calculate ipsative z-scores for the participant
- Calculate the 1-lag autocorrelation factor
- Calculate the critical difference (CD)
- For each assessment point, we calculate the difference between the corresponding z-score and the z-score at baseline.
- If the absolute value of this difference score is greater than the CD value, then it is statistically significant.

## Function

## Example

The following is weekly weight data for patient with anorexia nervosa undergoing a weight-restoration program:

- 40.12
- 40.50
- 41.20
- 42.00

The function conducts pairwise comparisons for each of the data points. A one-tailed test is used because we are testing whether the patient has **increased** their weight.

The results suggest significant increases in weight for each of the six pairwise comparisons:

> weight <- c(40.12, 40.50, 41.20, 42.00) > single.case(weight, level = .05, two.sided = F) Single-case data analysis X1 X2 delta(X) Z(X1) Z(X2) delta(Z) Pr(Z>|z|) 1 vs 2 40.12 40.50 0.38 -1.01 -0.55 0.46 * 1 vs 3 40.12 41.20 1.08 -1.01 0.30 1.30 * 1 vs 4 40.12 42.00 1.88 -1.01 1.26 2.27 * 2 vs 3 40.50 41.20 0.70 -0.55 0.30 0.85 * 2 vs 4 40.50 42.00 1.50 -0.55 1.26 1.81 * 3 vs 4 41.20 42.00 0.80 0.30 1.26 0.97 * ACF(1) = 0.99 Critical Difference = 0.30

Please leave a comment if you have any questions or suggested improvements to the code.

## Reference

Mueser, K. T., Yarnold, P. R., & Foy, D. W. (1991). Statistical Analysis for Single-Case Designs Evaluating Outcome of Imaginal Exposure Treatment of Chronic PTSD. *Behavior Modification, 15*(2), 134-155.