One-dimensional (1D) kinematic, force, and EMG trajectories are often analyzed using zero-dimensional (0D) metrics like local extrema. Recently whole-trajectory 1D methods have emerged in the literature as alternatives. Since 0D and 1D methods can yield qualitatively different results, the two approaches may appear to be theoretically distinct. The purposes of this paper were (a) to clarify that 0D and 1D approaches are actually just special cases of a more general region-of-interest (ROI) analysis framework, and (b) to demonstrate how ROIs can augment statistical power. We first simulated millions of smooth, random 1D datasets to validate theoretical predictions of the 0D, 1D and ROI approaches and to emphasize how ROIs provide a continuous bridge between 0D and 1D results. We then analyzed a variety of public datasets to demonstrate potential effects of ROIs on biomechanical conclusions. Results showed, first, that

Many biomechanical measurements may be regarded as ‘

In

Recently a variety of 1D methodologies have emerged in the Biomechanics literature including functional data analysis (FDA) (

This paper therefore focusses on SPM, a methodology that was initially developed in the Neuroimaging literature in the 1990s (

Despite the validity of 1D approaches, a variety of conceptual difficulties may arise when attempting to corroborate 0D and 1D approaches. In particular, 0D statistical results are typically tabulated using single numbers for the test statistic and

The primary purpose of this paper was to clarify the theoretical consistency between 0D and 1D techniques as special cases of ROI analysis. To that end we describe 1D ROI theory then validate its predictions using numerical simulations of random datasets with temporal scopes ranging from single points to large 1D continua. The second purpose was to demonstrate how ROIs can be used to augment statistical power in both exploratory and hypothesis-driven experiments. The final purpose was to introduce an open-source software implementation of ROI analysis (in

All analyses were implemented in Python 2.7 (

In classical hypothesis testing the null hypothesis is rejected if the experimentally observed test statistic ^{∗} , which can be computed according to: ^{∗}) is the probability that the test statistic exceeds ^{∗} if the null hypothesis is true.

Datasets A and B are identical except in Dataset B the signal at time = 75% is amplified. Three regions of interest (ROIs) are depicted, centered at time = 75% and spanning time windows of 10%, 20% and 30%, respectively.

For an ROI of size _{max} is the maximum value of the _{0D}(^{∗}) is the probability under the null hypothesis that 0D random Gaussian data will produce a ^{∗}, _{max} > ^{∗}) converges to _{0D}(^{∗}) as ^{∗} must increase as

We computed ^{∗} for a range of ROI sizes (

To validate _{max} , thereby producing one distribution of 100,000 _{max} values for each combination of parameters. We then estimated ^{∗} for each distribution as the 95th percentile of the distribution, then qualitatively compared to the theoretical result (

Datasets A and B (

Dataset C (

(A) Knee kinematics during side-shuffle and v-cut maneuvers (

Dataset D (

Critical thresholds ^{∗} necessary to maintain ^{∗} values for 1D data converged to 0D ^{∗} values as ROI size approached zero (^{∗} values for arbitrary 1D field smoothness values and arbitrary sample sizes. These results emphasize that 0D analyses are a special case of 1D analysis for which ROI size is zero.

(A) Three different degrees of freedom (

In Dataset A, the test statistic exceeded the critical threshold for 0D analysis and also for a narrow ROI of 10%, but failed to reach the thresholds for wider ROIs of 20% and 30%, and also failed to reach the full-field threshold (

“SPM{

For Dataset C, 0D analysis conducted on maximum knee flexion passed the critical threshold, as did a moderately broad ROI of 40% (

“SPM{

For Dataset D the pilot subject’s data were used to identify two relatively narrow ROIs in the vicinity of the first local maximum and the local minimum at mid-stance (

(A) Pilot study’s mean inter-condition VGRF difference (see

The main purpose of this paper was to clarify the theoretical consistency between “0D” and “1D” analyses, and to emphasize that both are actually just special cases of ROI analysis. In particular, the ROI size (

Although ROI analyses are common in biomechanical applications like plantar pressure analysis (

The key theoretical point to consider when implementing ROI analyses is that small ROIs can more readily detect true within-region effects than large ROIs (

An apparent limitation of ROIs is that, since they can create / eradicate statistical significance (

More formally, ROI definitions and procedures should be considered from the perspective of ‘circular analysis’ (

The literature contains a variety of recommendations regarding avoiding bias associated with circularity in ROI analyses, and recent developments in particular show that it is possible to use algorithmic data-driven ROI selection in an unbiased manner to increase statistical power and also maintain control over Type I error rates (

A technical point not addressed in the analyses above is how to handle within-ROI signals that extend beyond the ROI. This situation is observable in

In summary, this paper has introduced and validated an ROI approach for analyzing 1D biomechanical trajectories which clarifies the consistency between common 0D approaches and recent 1D approaches. Since biomechanical interpretations can be sensitive not only to ROI size but also to other data processing particulars like filtering and coordinate system definitions, it is recommended that ROIs be used only when there is adequate

The authors declare there are no competing interests.

The following information was supplied regarding data availability:

All raw data analyzed in this paper are available in the “spm1d” software package available at: