Comparison between the Functional Mean and the Deepest Curve in Biomechanical Curves
Bibliographic record
Abstract
Functional Data Analysis (FDA) is a branch of statistics that extends the concepts of classical statistics to functions.However, as with classical statistics, where sometimes the mean of a data set is not very representative, the functional mean may not be always the best option in FDA.This is because if the curves are not similar or aligned, this mean may not be very representative.Therefore, the concept of the deepest curve, similar to a functional median, is proposed in this submission.So, we want to reflect on the convenience of using a functional mean or the deepest curve and on which occasions it may be more acceptable to use one versus the other.The analysis is done on a set of data from Biomechanics, where in the literature reviewed, no works have been found that previously discuss this issue.A database of 56 subjects is used to measure the three components of the ground reaction force.Each subject performs six repetitions, so the mean and the deepest curve of these repetitions will be calculated to obtain a representative curve for each subject.Then, starting from these curves, the mean and deepest curves of the entire sample are calculated.In this way, they can be compared visually to find differences.Also, some characteristic values of the curves are calculated for each subject, and a paired t-test is performed to analyze whether there are significant differences between the mean and the deepest curve.This submission concludes that if the subsequent statistical analysis only considers values as maximum or minimum, the use of the mean or the deepest curve is analogous.However, if the entire curve is going to be used, as in FDA, then the deepest curve may be more advisable, especially if the curves present much variability.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".