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Zero- vs. one-dimensional, parametric vs. non-parametric, and confidence interval vs. hypothesis testing procedures

Todd C Pataky1, Jos Vanrenterghem2, Mark A Robinson2

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Summary

For biomechanics, using 1D (one-dimensional) methods is crucial for trajectory analysis, not just parametric versus non-parametric choices. 1D methods, like bootstrap confidence intervals (CIs), offer accurate results, unlike biased 0D approaches.

Keywords:
Bootstrap confidence intervalGround reaction forceKinematicsRandom field theoryStatistical parametric mappingTime series analysis

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Area of Science:

  • Biomechanics
  • Statistical analysis
  • Data science

Background:

  • Biomechanical processes often generate one-dimensional (1D) data trajectories.
  • Traditional zero-dimensional (0D) statistical methods can introduce bias when analyzing 1D data.
  • One-dimensional bootstrap confidence intervals (CIs) are increasingly used in biomechanics.

Purpose of the Study:

  • To emphasize the importance of distinguishing between 0D and 1D statistical methods for biomechanics datasets.
  • To demonstrate a parametric alternative to 1D bootstrap CIs using random field theory (RFT).
  • To analyze the impact of 0D vs. 1D and parametric vs. non-parametric methods on trajectory data.

Main Methods:

  • Analysis of six biomechanics datasets (force and kinematic trajectories).
  • Comparison of 1D bootstrap CIs, other 1D non-parametric CIs, random field theory (RFT) CIs, and 0D CIs.
  • Evaluation of parametric and non-parametric hypothesis testing for 1D data across various designs (one-sample, paired, two-sample, regression).

Main Results:

  • 1D non-parametric CIs (bootstrap, RFT) were qualitatively identical and significantly different from 0D CIs.
  • 1D parametric and non-parametric hypothesis testing yielded qualitatively identical results for all datasets.
  • 1D CIs were shown to be complex, design-dependent, and non-generalizable.

Conclusions:

  • Biomechanical analyses of 1D data using 0D models are generally biased unless 0D variables are pre-identified.
  • Parametric and non-parametric 1D hypothesis testing provide a clear framework for analyzing entire 1D trajectories.
  • The choice between 1D and 0D methods is more critical than parametric vs. non-parametric for 1D biomechanics data.