Abstract
Motivations: The purpose of this research is to develop adaptive nonparametric statistical methods for 2 × 2 cross over designs with repeated measures. Methods: The statistics and their asymptotic distributions are established for testing: (1) the equality for carry-over effects; (2) direct treatment effect when carry-over effects are equal; (3) equality of carry-over effect over time; (4) equality of direct treatment effect over time when carry-over effect over time is equal; (5) the average response for carry-over effects; and (6) the average response for direct treatment effects when average response for carry-over effects are equal. Findings: The methods are applied to the slopes of systolic and diastolic pressures in the study regarding to sleep apnea severity. Implications: Using the sleep apnea severity study as an example, we show that adaptive procedures had advantage of detecting the significance of test while the ranks-only based methods by Johnson and Grender (1993) failed to detect such significant result.
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