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## Analyzing Variance in Multi-Degree-of-Freedom Movements: Uncovering Structure versus Extracting Correlations

An important aspect of the study of multi-degree-of-freedom motor control is the analysis of high-dimensional variance data. Through the “uncontrolled manifold” (UCM) approach the structure in such data can be discovered and interpreted. The covariation by randomization (CR) approach provides nonlinear and potentially multi-dimensional measures of covariance. We critically examine these two approaches and compare them relative to the three fundamental issues of choice of variables, choice of model, and adoption of either a geometrical or a correlational view of variance. The UCM approach is a geometrical approach that seeks to discover the structure of variance in multi-degree-of-freedom task spaces in which all degrees of freedom have a common metric. The structure of variance in that space is interpreted in terms of its meaning for task variables. The CR approach seeks to uncover correlations between interpretable elemental variables. It requires a defined and common metric in the space of task variables, but not the elemental variables. Although the CR approach is better suited for systems with strong nonlinearities, variance structure that is not caused by correlation but by different amounts of variance in the different elemental variables is undetected by this approach.

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## The Number of Trials Required to Obtain a Representative Movement Pattern During a Hurdle Hop Exercise

When reporting a subject’s mean movement pattern, it is important to ensure that reported values are representative of the subject’s typical movement. While previous studies have used the mean of 3 trials, scientific justification of this number is lacking. One approach is to determine statistically how many trials are required to achieve a representative mean. This study compared 4 methods of calculating the number of trials required in a hopping movement to achieve a representative mean. Fifteen males completed 15 trials of a lateral hurdle hop. Range of motion at the trunk, pelvis, hip, knee, and ankle, in addition to peak moments for the latter 3 joints were examined. The number of trials required was computed using a peak intraclass correlation coefficient method, sequential analysis with a bandwidth of acceptable variance in the mean, and a novel method based on the standard error of measurement (SEMind). The number of trials required across all variables ranged from 2 to 12 depending on method, joint, and anatomical plane. The authors advocate the SEMind method as it demonstrated fewer limitations than the other methods. Using the SEMind, the required number of trials for a representative mean during the lateral hurdle hop is 6.

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## Within-Participant Variance in Multiplanar Breast Kinematics During 5 km Treadmill Running

More and more studies are emerging reporting breast kinematics. These studies rarely present effect sizes, power, and variance in the data. Important inferences are drawn from these data, including applications to product design, breast pain assessment, sports performance effects, and more. The aim of the study was to explore the within-participant variance in breast kinematic data during a 5 km run. Multiplanar breast kinematics and within-participant variance, defined by the coefficient of variation, for 10 female participants wearing a low and high level breast support were calculated during a 5 km run. Greater within-participant variance was reported in the high level (mean = 15%) breast support compared with the low level (mean = 12%). Within-participant variance in breast kinematics did not change over the 5 km run. Differences in the magnitude of within-participant variance in breast kinematics were reported between directions of breast movement, with greater levels in the anteroposterior direction compared with mediolateral and vertical. It is important for the progression of this research area that the presence and sources of within-participant variance in breast kinematics are quantified and acknowledged, ensuring that the margin for meaningful differences can be reported.

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## Pedometer Variance in Adults With Down Syndrome During Free Walking: A Generalizability Study

### Background:

Pedometers are a common instrument used to measure walking activity, yet reliability evidence in disability populations, particularly Down syndrome (DS), has received little attention. There may be systematic and random sources of error that could influence reliability under natural walking conditions. The purpose of this study was to examine the sources of variance and estimate reliability coefficients of spring-levered (SL) and piezoelectric (PZ) pedometers for adults with DS during a free-walking bout.

### Methods:

Seventeen adults with DS and 23 adults without a disability walked continuously for a 20-minute period wearing 2 types of pedometers, SL and PZ. Step counts were analyzed using Generalizability theory to partition and quantify variance components and calculate reliability coefficients.

### Results:

The largest variance component was due to individual participant differences. Adults with DS demonstrated greater intraindividual variability, but also had relatively low proportions of residual variance, or unexplained error. The SL pedometer showed problems with interunit variance while the PZ pedometer demonstrated little systematic error. Reliability coefficients were consistently higher for the PZ pedometer.

### Conclusions:

This study found minimal systematic error and moderate reliability evidence for the PZ pedometer. This type of pedometer may be used in future research for adults with DS.

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## Determinants of Variance in the Habitual Physical Activity of Overweight Adults

### Background:

The number of days of data and number of subjects necessary to estimate total physical activity (TPA) and moderate-to-vigorous physical activity (MVPA) requires an understanding of within- and between-subject variances, and the influence of sex, body composition, and age.

### Methods:

Seventy-one adults wore accelerometers for 7-day intervals over 6 consecutive months.

### Results:

Body fat and sex influenced TPA and MVPA. The sources of subject-related variation for TPA and MVPA were within-subject (48.4% and 54.3%), between-subject (34.3% and 31.8%), and calendar effects (17.3% and 13.9%). Based on within-subject variances, the error associated with estimating TPA and MVPA by collecting 1 to 7 days of data ranged from 28.2% to 13.3% for TPA and 62.0% to 28.6% for MVPA. Based on between-subject variances, detecting a 10% difference between 2 groups at a power of 90% requires approximately 200 and 725 subjects per group for TPA and MVPA, respectively.

### Conclusions:

Estimates of MVPA are more variable than TPA in overweight adults, therefore more days of data are required to estimate MVPA and larger sample sizes to detect treatment differences for MVPA. Log-transforming data reduces the need for additional days of data collection, thereby improving chances of detecting treatment effects.

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## Three-Dimensional Model to Predict Muscle Forces and Their Relation to Motor Variances in Reaching Arm Movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.

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## Intraindividual Movement Variability Within the 5 m Water Polo Shot

The purpose of this study was to explore movement variability of throwing arm and ball release parameters during the water polo shot and to compare variability between successful (hit) and unsuccessful (miss) outcomes. Seven injury free, subelite, females completed 10 trials of the 5 m water polo penalty shot. Intraindividual coefficient of variation percentage (CV%) values were calculated for elbow and wrist angular displacement, wrist linear velocity and ball release parameters (height, angle and velocity). Coordination variability (elbow/wrist angular displacement) was calculated as the CV% of the mean cross-correlation coefficient. Elbow and wrist displacement variability decreased to 80% of throwing time then increased toward release. Wrist linear velocity variability reduced toward release. Individual CV% values ranged between 1.6% and 23.5% (all trials), 0.4% and 20.6% (hit), and 0.4% and 27.1% (miss). Ball release height and velocity variability were low (< 12%; all trials) whereas release angle variability was high (>27%; all trials). Cross-correlation results were inconclusive. Roles of the elbow and wrist in production of stable ball release height and velocity and control of the highly variable release angle in the water polo shot are discussed and suggested for further study. Optimal levels of variability warrant future investigation.

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## Parameterized Estimation of Long-Range Correlation and Variance Components in Human Serial Interval Production

Repetitive movements lead to isochronous serial interval production which exhibit inherent variability. The Wing-Kristofferson model offers a decomposition of the interresponse intervals in tapping tasks based on a cognitive component and on a motor component. We suggest a new theoretical and fully parametric approach to this model in which the cognitive component is modeled as a long-memory process and the motor component is treated as a white noise process, mutually independent. Under these assumptions, we obtained the autocorrelation function and the spectral density function. Furthermore, we propose an estimator based on the maximization of the frequency-domain representation of the likelihood function. Finally, we conducted a simulation study to assess the properties of this estimator and performed an experimental study involving tapping tasks with two target frequencies (1.250 Hz and 0.625 Hz).

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## The Variance Needed to Accurately Describe Jump Height from Vertical Ground Reaction Force Data

In functional principal component analysis (fPCA) a threshold is chosen to define the number of retained principal components, which corresponds to the amount of preserved information. A variety of thresholds have been used in previous studies and the chosen threshold is often not evaluated. The aim of this study is to identify the optimal threshold that preserves the information needed to describe a jump height accurately utilizing vertical ground reaction force (vGRF) curves. To find an optimal threshold, a neural network was used to predict jump height from vGRF curve measures generated using different fPCA thresholds. The findings indicate that a threshold from 99% to 99.9% (6–11 principal components) is optimal for describing jump height, as these thresholds generated significantly lower jump height prediction errors than other thresholds.

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## Maturity Associated Variance in Physical Activity and Health-Related Quality of Life in Adolescent Females: A Mediated Effects Model

### Background:

This study tested a mediated effects model of psychological and behavioral adaptation to puberty within the context of physical activity (PA).

### Methods:

Biological maturity status, physical self-concept, PA, and health-related quality of life (HRQoL) were assessed in 222 female British year 7 to 9 pupils (mean age = 12.7 years, SD = .8).

### Results:

Structural equation modeling using maximum likelihood estimation and bootstrapping procedures supported the hypothesized model. Maturation status was inversely related to perceptions of sport competence, body attractiveness, and physical condition; and indirectly and inversely related to physical self-worth, PA, and HRQoL. Examination of the bootstrap-generated bias-corrected confidence intervals representing the direct and indirect paths between suggested that physical self-concept partially mediated the relations between maturity status and PA, and maturity status and HRQoL.

### Conclusions:

Evidence supports the contention that perceptions of the physical self partially mediate relations maturity, PA, and HRQoL in adolescent females.