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.

## Example

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

1. 40.12
2. 40.50
3. 41.20
4. 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

```