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

Download Code

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

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.

Category:
Single-case research
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