Ground reaction force adaptations during cross-slope walking and running

Though transversely inclined (cross-sloped) surfaces are prevalent, our understanding of the biomechanical adaptations required for cross-slope locomotion is limited. The purpose of this study was to examine ground reaction forces (GRF) in cross-sloped and level walking and running. Nine young adult males walked and ran barefoot along an inclinable walkway in both level (0°) and cross-slope (10°) configurations. The magnitude and time of occurrence of selected features of the GRF were extracted from the force plate data. GRF data were collected in level walking and running (LW and LR), inclined walking and running up-slope (IWU and IRU), and down-slope (IWD and IRD), respectively. The GRF data were then analyzed using repeated measures MANOVA. In the anteroposterior direction, the timing of the peak force values differed across conditions during walking (p=.041), while the magnitude of forces were modified across conditions for running (p=.047). Most significant differences were observed in the mediolateral direction, where generally force values were up to 390% and 530% (p<.001) larger during the cross-slope conditions compared to level for walking and running, respectively. The maximum force peak during running occurred earlier at IRU compared to the other conditions (p≤.031). For the normal axis a significant difference was observed in the first maximum force peak during walking (p=.049). The findings of this study showed that compared to level surfaces, functional adaptations are required to maintain forward progression and dynamic stability in stance during cross-slope walking and running.     

Lower limb mechanics during moderate high-heel jogging and running in different experienced wearers

The aim of this study is to investigate the differences in lower limb kinematics and kinetics between experienced (EW) and inexperienced (IEW) moderate high-heel wearers during jogging and running. Eleven experienced female wearers of moderate high-heel shoes and eleven matched controls participated in jogging and running tests. A Vicon motion analysis system was used to capture kinematic data and a Kistler force platform was used to collect ground reaction force (GRF). There were no significant differences in jogging and running speed respectively. Compared with IEW, EW adopted larger stride length (SL) with lower stride frequency (SF) at each corresponding speed. During running, EW enlarged SL significantly while IEW increased both SL and SF significantly. Kinematic data showed that IEW had generally larger joint range of motion (ROM) and peak angles during stance phase. Speed effect was not obvious within IEW. EW exhibited a significantly increased maximal vertical GRF (F_z2) and vertical average loading rate (VALR) during running, which was potentially caused by overlong stride. These suggest that both EW and IEW are at high risk of joint injuries when running on moderate high heels. For wearers who have to do some running on moderate high heels, it is crucial to control joint stability and balance SL and SF consciously.     

Variability of a “force signature” during windmill softball pitching and relationship between discrete force variables and pitch velocity

This study assessed reliability of discrete ground reaction force (GRF) variables over multiple pitching trials, investigated the relationships between discrete GRF variables and pitch velocity (PV) and assessed the variability of the “force signature” or continuous force-time curve during the pitching motion of windmill softball pitchers. Intraclass correlation coefficient (ICC) for all discrete variables was high (0.86–0.99) while the coefficient of variance (CV) was low (1.4–5.2%). Two discrete variables were significantly correlated to PV; second vertical peak force (r(5) = 0.81, p = 0.03) and time between peak forces (r(5) = −0.79; p = 0.03). High ICCs and low CVs support the reliability of discrete GRF and PV variables over multiple trials and significant correlations indicate there is a relationship between the ability to produce force and the timing of this force production with PV. The mean of all pitchers’ curve-average standard deviation of their continuous force-time curves demonstrated low variability (CV = 4.4%) indicating a repeatable and identifiable “force signature” pattern during this motion. As such, the continuous force-time curve in addition to discrete GRF variables should be examined in future research as a potential method to monitor or explain changes in pitching performance.     

Sample size planning for composite reliability coefficients: accuracy in parameter estimation via narrow confidence intervals

Composite measures play an important role in psychology and related disciplines. Composite measures almost always have error. Correspondingly, it is important to understand the reliability of the scores from any particular composite measure. However, the point estimates of the reliability of composite measures are fallible and thus all such point estimates should be accompanied by a confidence interval. When confidence intervals are wide, there is much uncertainty in the population value of the reliability coefficient. Given the importance of reporting confidence intervals for estimates of reliability, coupled with the undesirability of wide confidence intervals, we develop methods that allow researchers to plan sample size in order to obtain narrow confidence intervals for population reliability coefficients. We first discuss composite reliability coefficients and then provide a discussion on confidence interval formation for the corresponding population value. Using the accuracy in parameter estimation approach, we develop two methods to obtain accurate estimates of reliability by planning sample size. The first method provides a way to plan sample size so that the expected confidence interval width for the population reliability coefficient is sufficiently narrow. The second method ensures that the confidence interval width will be sufficiently narrow with some desired degree of assurance (e.g., 99% assurance that the 95% confidence interval for the population reliability coefficient will be less than W units wide). The effectiveness of our methods was verified with Monte Carlo simulation studies. We demonstrate how to easily implement the methods with easy-to-use and freely available software.     

Evaluation of key points in the sit-to-stand movement using two force platforms

Three key points of the sit-to-stand (STS) movement were confirmed as aspects of the ground reaction force (GRF): the onset, maximum GRF, and seat-off. 46 healthy subjects (M age = 22.2 yr., SD = 4.4) participated. During the STS movement, two vertical force platforms were used to measure the resultant GRF, defined as the whole-body force, and its two components, the buttock and leg GRFs. The onsets of the component GRFs identified the sequence of the important time points in the STS movement more precisely than the onset of the resultant GRF. Data showed that the maximum whole-body GRF, the maximum GRF of both legs, and seat-off appeared in sequence and not simultaneously.     

Ankle kinetics and plantarflexor morphology in older runners with different lifetime running exposures

Running promotes better cardiovascular health and has positive effects on the musculoskeletal system in older adults. However, older adults have lower ankle plantarflexor torques and positive powers during running, and exhibit changes in plantarflexor morphology than young adults. Since older runners who run as much as younger runners exhibit youthful ankle mechanical outputs, running exposure may preserve the locomotor factors that mediate running speed. The purpose of this study was to compare ankle mechanical output during running and plantarflexor morphological characteristics between older runners who have low or high lifetime running exposure. Ten older runners with low lifetime running exposure and nine older runners with high lifetime running exposure performed over-ground running trials at 3.0 m/s (±5%) while kinematic and ground reaction force (GRF) data were collected and used to compute joint angular kinetics. Right medial gastrocnemius morphological characteristics were assessed using ultrasonography at rest and during isometric contractions. Ankle torques, powers, and plantarflexor morphology were compared between groups. Older runners with different lifetime running exposures ran with similar ankle mechanical output (i.e. no effect of running exposure) (p > .05) and exhibited similar medial gastrocnemius morphology during isometric testing. The findings from this study demonstrate that lifetime running exposure does not appear to influence ankle mechanical output or plantarflexor morphology in middle-aged runners.     

Rhythmic performance during a whole body movement: dynamic analysis of force-time curves

The purpose of this study was to investigate rhythmic performance during two-legged hopping in place. In particular, it was tested whether (a) timing control is independent of force control, (b) a dynamic timer model explains rhythmic performance, and (c) it is a force related parameter that carries the timing information. Eleven participants performed two-legged hopping at their preferred hopping frequency (PHF) and at two hopping frequencies set by an external rhythmic stimulus as lower (LHF) and higher (HHF) than their PHF, respectively. A force plate was used to record the ground reaction force (GRF) time curves during two-legged hopping. The primary temporal and force related parameters determined from the GRF-time curves were the durations of the cycle of movement (t(cycle)), of the contact phase (t(contact)), of the flight phase (t(flight)), the magnitude of peak force (Fz(peak)) and the rate of peak force development (RFD). Control of t(cycle) was independent of force control as shown by the non-significant correlations between t(cycle) and the force parameters of the GRF-time curve. Lag 1 autocorrelations of t(cycle) were not significant in any of the HF, thereby a dynamic timer model is considered to explain the timing of t(cycle) during two-legged hopping. RFD varied more than any other GRF-time curve parameter, exhibited consistent significant strong correlations with the GRF-time curve parameters and significant negative lag 1 autocorrelations in PHF, thus, it was highlighted as the potent timing control parameter. Finally, we provide a practical application for the optimization of rhythmic performance.     

Large-sample confidence intervals for validity and reliability coefficients

Large-sample confidence intervals (CI) for reliability, validity, and unattenuated validity are presented. The CI for unattenuated validity is based on the Bonferroni inequality, which relies on one CI for test-retest reliability and one for validity. Covered are four reliability-validity situations: (a) both estimates were from random samples; (b) reliability was from a random sample but validity was from a selected sample; (c) validity was from a random sample but reliability was from a selected sample; and (d) both estimates were from selected samples. All CIs were evaluated by using a simulation. CIs on reliability, validity, or unattenuated validity are accurate as long as selection ratio is at least 20% and selected sample size is 100 or larger. When selection ratio is less than 20%, estimators tend to underestimate their parameters.     

Minimum Sample Size Recommendations for Conducting Factor Analyses

There is no shortage of recommendations regarding the appropriate sample size to use when conducting a factor analysis. Suggested minimums for sample size include from 3 to 20 times the number of variables and absolute ranges from 100 to over 1,000. For the most part, there is little empirical evidence to support these recommendations. This simulation study addressed minimum sample size requirements for 180 different population conditions that varied in the number of factors, the number of variables per factor, and the level of communality. Congruence coefficients were calculated to assess the agreement between population solutions and sample solutions generated from the various population conditions. Although absolute minimums are not presented, it was found that, in general, minimum sample sizes appear to be smaller for higher levels of communality; minimum sample sizes appear to be smaller for higher ratios of the number of variables to the number of factors; and when the variables-to-factors ratio exceeds 6, the minimum sample size begins to stabilize regardless of the number of factors or the level of communality.     

Single leg landing movement differences between male and female badminton players after overhead stroke in the backhand-side court

Females showed higher anterior cruciate ligament (ACL) injuries rate on the opposite side of dominant hand compared with males during single leg landing in the backhand-side court after overhead stroke. The purpose of this study was to conduct biomechanics testing including kinematics and kinetics to provide some insights on the ACL injuries risks during single leg landing in the backhand-side court after overhead stroke between females and males. Twenty collegiate badminton players (10 females, 10 males) voluntarily participated in this study. Sagittal plane kinematic and kinetic data of the lower limb, and their ground reaction forces during the single leg landing in the backhand-side court after overhead stroke were collected. Results shown that, at the peak posterior ground reaction force (GRF) moment, the ankle dorsiflexion, knee and hip flexion angles of the female were lower than that of male. Meantime, the knee extension moment of the female was lower than that of males but the hip extension moment of the female was larger compared to males at the peak posterior GRF moment. The peak vertical and posterior GRF of female badminton players were larger than that of males. Decreased hip, knee, and ankle flexion angles at the peak posterior GRF moment and greater peak vertical and posterior GRF may expose female badminton players to the higher risk ACL injuries compared to males during single leg landing after overhead stroke in the backcourt-side. Preventative training programs designed to prevent the ACL injuries rate of female badminton players should take these factors into consideration.     

Study samples are too small to produce sufficiently precise reliability coefficients

In a survey of journal articles, test manuals, and test critique books, the author found that a mean sample size (N) of 260 participants had been used for reliability studies on 742 tests. The distribution was skewed because the median sample size for the total sample was only 90. The median sample sizes for the internal consistency, retest, and interjudge reliabilities were 182, 64, and 36, respectively. The author presented sample size statistics for the various internal consistency methods and types of tests. In general, the author found that the sample sizes that were used in the internal consistency studies were too small to produce sufficiently precise reliability coefficients, which in turn could cause imprecise estimates of examinee true-score confidence intervals. The results also suggest that larger sample sizes have been used in the last decade compared with those that were used in earlier decades.     

单维测验合成信度元分析

元分析是根据现有研究对感兴趣的主题得出比较准确和有代表性结论的一种重要方法,在心理、教育、管理、医学等社会科学研究中得到广泛应用。信度是衡量测验质量的重要指标,用合成信度能比较准确的估计测验信度。未见有文献提供合成信度元分析方法。本研究在比较对参数进行元分析的三种模型优劣的基础上,在变化系数模型下推出合成信度元分析点估计及区间估计的方法;以区间覆盖率为衡量指标,模拟研究表明本研究提出的合成信度元分析区间估计的方法得当;举例说明如何对单维测验的合成信度进行元分析。     

A functional modulation for timing a movement: a coordinative structure in baseball hitting

In baseball hitting, a powerful bat-swing needs to be produced by utilizing ground reaction force (GRF) and it should also be temporally coordinated relative to the flight of the pitch. The temporal organization of hitting movements associated with these task requirements was investigated by analyzing GRF during hitting slow and fast pitches. The timing of stepping with a front foot and shifting weight forward was modulated relative to the pitch's speed. The temporal relation between successive motion phases was compensatory and timing variability progressively reduced up to ball-bat contact. These results demonstrated the coordinative structure of the hitting movement for timing the bat-swing relative to the pitch's flight.     

认知诊断属性分类一致性信度区间估计三种方法

摘要：引入了三种可以估计认知诊断属性分类一致性信度置信区间的方法：Bootstrap法、平行测验法和平行测验配对法。用模拟研究验证和比较了这三种方法的表现,结果发现,平行测验法和Bootstrap法在被试量比较少、题目数量比较少的情况下,估计的标准误和置信区间较接近,但是随着被试量的增加,Bootstrap法的估计精度提高较快,在被试量大和题目数量较多时基本接近平行测验配对法的结果。Bootstrap法的所需时间最少,平行测验配对法计算过程复杂且用时较长,推荐用Bootstrap法估计认知诊断属性分类一致性信度的置信区间。     

An adaptive psychophysical method for subject classification

In psychophysical experiments, one’s goal is usually to measure some continuous parameter hypothesized to determine the statistical properties of a subject’s responses. Methods are well developed that adaptively manipulate stimulus characteristics in such a way that the reliability of the parameter estimate is maximized. However, such methods are inapplicable in situations in which the goal is to assign subjects to discrete categories, rather than to measure a continuous parameter. This paper introduces a technique that is directly applicable to efficient categorization and that adaptively manipulates stimulus characteristics in such a way that the information obtained from each trial is maximized. This technique is based on the principle of minimum estimated expected entropy, whereby stimulus parameters on each trial are chosen in order to minimize the estimated expected entropy of the a posteriori probability distribution that expresses how likely a subject is to belong to each of a group of mutually exclusive categories. A sample implementation of the technique—the classification of infant subjects according to their audiograms—is then described and evaluated via computer simulation.     

单维测验合成信度三种区间估计的比较

已有许多研究建议使用合成信度来估计测验信度, 并报告其置信区间。有三种方法或途径可以计算单维测验合成信度的置信区间, 包括Bootstrap法、Delta法和直接用统计软件(如LISREL)输出的标准误进行计算。本文通过模拟研究进行比较, 发现Delta法与Bootstrap法得到的置信区间相当接近, 但用LISREL输出的标准误计算的与Bootstrap法得到的结果相差很大。推荐用Delta法估计合成信度的置信区间(使用Mplus容易实现), 但不能直接用LISREL输出的标准误来计算。举例说明了如何计算单维测验的合成信度以及用Delta法计算其置信区间。     

Effects of Differential Item Functioning on Examinees' Test Performance and Reliability of Test

Simulations were conducted to examine the effect of differential item functioning (DIF) on measurement consequences such as total scores, item response theory (IRT) ability estimates, and test reliability in terms of the ratio of true-score variance to observed-score variance and the standard error of estimation for the IRT ability parameter. The objective was to provide bounds of the likely DIF effects on these measurement consequences. Five factors were manipulated: test length, percentage of DIF items per form, item type, sample size, and level of group ability difference. Results indicate that the greatest DIF effect was less than 2 points on the 0 to 60 total score scale and about 0.15 on the IRT ability scale. DIF had a limited effect on the ratio of true-score variance to observed-score variance, but its influence on the standard error of estimation for the IRT ability parameter was evident for certain ability values.     

Combining wearable sensor signals,machine learning and biomechanics to estimate tibial bone force and damage during running

There are tremendous opportunities to advance science, clinical care, sports performance, and societal health if we are able to develop tools for monitoring musculoskeletal loading (e.g., forces on bones or muscles) outside the lab. While wearable sensors enable non-invasive monitoring of human movement in applied situations, current commercial wearables do not estimate tissue-level loading on structures inside the body. Here we explore the feasibility of using wearable sensors to estimate tibial bone force during running. First, we used lab-based data and musculoskeletal modeling to estimate tibial force for ten participants running across a range of speeds and slopes. Next, we converted lab-based data to signals feasibly measured with wearables (inertial measurement units on the foot and shank, and pressure-sensing insoles) and used these data to develop two multi-sensor algorithms for estimating peak tibial force: one physics-based and one machine learning. Additionally, to reflect current running wearables that utilize running impact metrics to infer musculoskeletal loading or injury risk, we estimated tibial force using a commonly measured impact metric, the ground reaction force vertical average loading rate (VALR). Using VALR to estimate peak tibial force resulted in a mean absolute percent error of 9.9%, which was no more accurate than a theoretical step counter that assumed the same peak force for every running stride. Our physics-based algorithm reduced error to 5.2%, and our machine learning algorithm reduced error to 2.6%. Further, to gain insights into how force estimation accuracy relates to overuse injury risk, we computed bone damage expected due to a given loading cycle. We found that modest errors in tibial force translated into large errors in bone damage estimates. For example, a 9.9% error in tibial force using VALR translated into 104% error in estimated bone damage. Encouragingly, the physics-based and machine learning algorithms reduced damage errors to 41% and 18%, respectively. This study highlights the exciting potential to combine wearables, musculoskeletal biomechanics and machine learning to develop more accurate tools for monitoring musculoskeletal loading in applied situations.     

Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach

The accuracy in parameter estimation approach to sample size planning is developed for the coefficient of variation, where the goal of the method is to obtain an accurate parameter estimate by achieving a sufficiently narrow confidence interval. The first method allows researchers to plan sample size so that the expected width of the confidence interval for the population coefficient of variation is sufficiently narrow. A modification allows a desired degree of assurance to be incorporated into the method, so that the obtained confidence interval will be sufficiently narrow with some specified probability (e.g., 85% assurance that the 95 confidence interval width will be no wider than to units). Tables of necessary sample size are provided for a variety of scenarios that may help researchers planning a study where the coefficient of variation is of interest plan an appropriate sample size in order to have a sufficiently narrow confidence interval, optionally with somespecified assurance of the confidence interval being sufficiently narrow. Freely available computer routines have been developed that allow researchers to easily implement all of the methods discussed in the article.     

How Many Subjects Does It Take To Do A Regression Analysis

Numerous rules-of-thumb have been suggested for determining the minimum number of subjects required to conduct multiple regression analyses. These rules-of-thumb are evaluated by comparing their results against those based on power analyses for tests of hypotheses of multiple and partial correlations. The results did not support the use of rules-of-thumb that simply specify some constant (e.g., 100 subjects) as the minimum number of subjects or a minimum ratio of number of subjects (N) to number of predictors (m). Some support was obtained for a rule-of-thumb that N ≥ 50 + 8 m for the multiple correlation and N ≥104 + m for the partial correlation. However, the rule-of-thumb for the multiple correlation yields values too large for N when m ≥ 7, and both rules-of-thumb assume all studies have a medium-size relationship between criterion and predictors. Accordingly, a slightly more complex rule-of thumb is introduced that estimates minimum sample size as function of effect size as well as the number of predictors. It is argued that researchers should use methods to determine sample size that incorporate effect size.