Effect Size Rules of Thumb for One-Dimensional Functional Data With an Application to Gait Analysis

Area of Science:

• Biomechanics
• Statistics

Background:

• One-dimensional (1D) functional data, such as joint angles in human movement, are commonly analyzed using scalar (0D) effect size rules of thumb (e.g., Cohen/Sawilowsky).
• Existing rules may overestimate effect sizes for functional data due to its inherent smoothness and greater probability of occurrence.

Purpose of the Study:

• To propose new, probabilistically consistent functional effect size rules of thumb for 1D human movement data.
• To develop a framework for adapting these interpretations to various experimental designs and data characteristics.

Main Methods:

• Developed functional effect size guidelines based on a benchmark two-sample scenario.
• Created a framework to adjust interpretations for different experimental designs (e.g., paired designs).
• Applied both standard and proposed methods to a total hip arthroplasty gait dataset.

Main Results:

• Standard Cohen/Sawilowsky rules yielded 'medium' and 'less than very small' interpretations for post-surgery gait data.
• Proposed functional rules initially suggested 'less than very small' effect sizes.
• Adapting the framework to the specific experimental case (n=52, smooth residuals) resulted in a 'very large' effect size interpretation.

Conclusions:

• Standard effect size guidelines are inadequate for functional data and arbitrary experimental scenarios.
• A single set of rules cannot be universally applied; context-specific interpretation is crucial.
• The proposed framework offers probabilistically consistent and more meaningful cross-study interpretations, especially for post hoc analysis.