Tau-U Effect Size Analysis
Single-Case Experimental Design (SCED) Phase Comparisons
SUMMARY
Effect Size Summary (A vs B+C)
TAU-U: Mean RMSSD
Large0.638
Large effect | p<0.001 (trend-corrected)
A vs B+C | NAP=93.1%
TAU-U: Lowest Heart Rate
Large0.632
Large effect | p<0.001 (trend-corrected)
A vs B+C | NAP=92.0%
TAU-U: Average Heart Rate
Large0.604
Large effect | p<0.001 (trend-corrected)
A vs B+C | NAP=91.0%
TAU-U: Sleep Efficiency
Moderate0.467
Moderate effect | p<0.001 (trend-corrected)
A vs B+C | NAP=79.7%
RESULTS
Tau-U Results: All Comparisons
| Comparison | Metric | nA | nB | MeanA | MeanB | Dir | Tau-U | 95% CI | p-value | Effect | NAP | Note |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A vs B (Jakavi Effect) | Mean RMSSD | 67 | 22 | 10.0 | 10.9 | ▼ | -0.192 * | [-0.471, +0.088] | p<0.001 | weak | 62.7% | ⚠ corrected |
| A vs B (Jakavi Effect) | Lowest Heart Rate | 64 | 19 | 76.7 | 72.9 | ▼ | -0.114 * | [-0.411, +0.184] | p=0.046 | weak | 69.7% | ⚠ corrected |
| A vs B (Jakavi Effect) | Average Heart Rate | 64 | 19 | 85.2 | 81.4 | ▼ | -0.162 * | [-0.459, +0.136] | p=0.005 | weak | 69.1% | ⚠ corrected |
| A vs B (Jakavi Effect) | Sleep Efficiency | 64 | 19 | 78.6 | 79.9 | ▼ | -0.018 | [-0.316, +0.279] | p=0.749 | weak | 62.4% | ⚠ corrected |
| B vs C (BB Marginal Effect) | Mean RMSSD | 22 | 144 | 10.9 | 28.6 | ▲ | +0.943 * | [+0.683, +1.000] | p<0.001 | very large | 97.1% | |
| B vs C (BB Marginal Effect) | Lowest Heart Rate | 19 | 141 | 72.9 | 60.1 | ▲ | +0.856 * | [+0.579, +1.000] | p<0.001 | very large | 92.8% | |
| B vs C (BB Marginal Effect) | Average Heart Rate | 19 | 141 | 81.4 | 69.1 | ▲ | +0.835 * | [+0.557, +1.000] | p<0.001 | very large | 91.7% | |
| B vs C (BB Marginal Effect) | Sleep Efficiency | 19 | 141 | 79.9 | 83.0 | ▲ | +0.500 * | [+0.223, +0.778] | p<0.001 | moderate | 75.0% | |
| A vs B+C (Combined Post) | Mean RMSSD | 67 | 166 | 10.0 | 26.2 | ▲ | +0.638 * | [+0.474, +0.802] | p<0.001 | large | 93.1% | ⚠ corrected |
| A vs B+C (Combined Post) | Lowest Heart Rate | 64 | 160 | 76.7 | 61.6 | ▲ | +0.632 * | [+0.464, +0.800] | p<0.001 | large | 92.0% | ⚠ corrected |
| A vs B+C (Combined Post) | Average Heart Rate | 64 | 160 | 85.2 | 70.6 | ▲ | +0.604 * | [+0.436, +0.772] | p<0.001 | large | 91.0% | ⚠ corrected |
| A vs B+C (Combined Post) | Sleep Efficiency | 64 | 160 | 78.6 | 82.7 | ▲ | +0.467 * | [+0.299, +0.635] | p<0.001 | moderate | 79.7% | ⚠ corrected |
DESCRIPTIVE
Phase Descriptive Statistics
| Phase | Metric | n | Mean | SD | Min | Max |
|---|---|---|---|---|---|---|
| A | Mean RMSSD | 67 | 10.0 | 2.4 | 5.0 | 18.4 |
| A | Lowest Heart Rate | 64 | 76.7 | 5.7 | 64.0 | 96.0 |
| A | Average Heart Rate | 64 | 85.2 | 6.8 | 69.8 | 113.9 |
| A | Sleep Efficiency | 64 | 78.6 | 3.4 | 71.0 | 91.0 |
| B | Mean RMSSD | 22 | 10.9 | 2.2 | 6.9 | 17.7 |
| B | Lowest Heart Rate | 19 | 72.9 | 4.0 | 67.0 | 84.0 |
| B | Average Heart Rate | 19 | 81.4 | 4.2 | 76.4 | 96.4 |
| B | Sleep Efficiency | 19 | 79.9 | 4.0 | 69.0 | 87.0 |
| C | Mean RMSSD | 144 | 28.6 | 8.5 | 8.0 | 55.4 |
| C | Lowest Heart Rate | 141 | 60.1 | 7.4 | 35.0 | 86.0 |
| C | Average Heart Rate | 141 | 69.1 | 7.4 | 58.1 | 97.8 |
| C | Sleep Efficiency | 141 | 83.0 | 6.1 | 58.0 | 92.0 |
METHODOLOGY
Methodology & Interpretation
Methodology
Tau-U (Parker, Vannest, Davis & Sauber, 2011) is the recommended effect size for single-case experimental designs (SCED). It quantifies the degree of nonoverlap between phases while optionally correcting for baseline trend.
Interpretation Scale
|Tau| < 0.20 = Weak
0.20 – 0.60 = Moderate
0.60 – 0.80 = Large
> 0.80 = Very large
Key Details
- Positive Tau = improvement (direction-adjusted per metric)
- Baseline correction: If Phase A shows a significant trend (Kendall tau, p<0.05), Tau-U is corrected by subtracting the baseline S statistic. A ⚠ symbol marks corrected values.
- NAP (Nonoverlap of All Pairs) is a complementary measure: probability that a random Phase B observation exceeds a random Phase A observation (after direction adjustment). NAP > 0.93 = large, 0.66–0.92 = medium, < 0.66 = weak (Parker & Vannest, 2009).
- * = statistically significant at p < 0.05
Phases
- Phase A (Pre-treatment): Jan 08 – Mar 15, 2026
- Phase B (Jakavi only): Mar 16 – Apr 07, 2026
- Phase C (Jakavi + Beta-blocker): Apr 08, 2026 – present