Smoothing can systematically bias small samples of one-dimensional biomechanical continua

Area of Science:

• Biomechanical data analysis
• Statistical modeling
• Computational science

Background:

• Mean-square error (MSE) is commonly used to assess smoothing algorithm performance but fails to detect localized errors.
• Smoothing noisy data can introduce systematic bias, which is not captured by traditional error metrics like MSE.

Purpose of the Study:

• To quantify the systematic bias introduced by smoothing algorithms in 1D data.
• To introduce and utilize the false positive rate (FPR) as a metric for assessing smoothing-induced bias.
• To evaluate the impact of smoothing parameters, sample size, and noise amplitude on FPR.

Main Methods:

• A simulation study involving six 1D datum continua and four smoothing algorithms.
• Systematic manipulation of smoothing parameters, sample size, and noise amplitude.
• Calculation of FPR at α=0.05 based on dataset smoothness over approximately ten million iterations.

Main Results:

• False positive rates (FPRs) were significantly higher than the expected α=0.05, often approaching 100%.
• Highest FPRs were observed with aggressive smoothing, large sample sizes, and low noise amplitudes.
• The observed bias was independent of the specific smoothing algorithm and the nature of the 1D datum.

Conclusions:

• Smoothing 1D biomechanical data frequently introduces statistical bias.
• The high FPR suggests that smoothing can lead to erroneous conclusions, particularly when small data changes have significant biomechanical implications.
• Researchers should exercise caution and consider smoothing-induced bias when interpreting results from smoothed 1D biomechanical data.