Comparative evaluation of two superior stopping rules for hierarchical cluster analysis

A split-sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by Milligan and Cooper (1985) in their comparison of 30 different procedures. The number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping-rule validity. Equal and unequal population base rates were also considered. Both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space. The replication criterion, which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set, was superior as the degree of overlap in population distributions increased. Neither method performed adequately when overlap obliterated visually discernible density nodes.This research was supported in part by NIMH grant 5R01 MH 32457 14.     

The Flow-Clutch Scale: Development and preliminary validation in sport and exercise

ObjectivesThe Integrated Model of Flow and Clutch States describes two overlapping psychological states that underlie exceptional performance and rewarding exercise experiences. However, research based on this model is currently hampered because no validated measure has yet been developed. Therefore, the aim of this multi-study paper was to develop and provide preliminary validation of the Flow-Clutch Scale in sport and exercise.DesignUsing two independent adult samples (n = 280; n = 264), three studies were conducted to develop and establish preliminary validity of the Flow-Clutch Scale.MethodIn Study 1, we developed an initial version of the scale and established content validity using an expert panel. In Study 2, we employed exploratory factor analysis to: identify the most appropriate factor structure; examine the scale’s internal consistency; test whether the scale differentiated between individuals who experience flow, clutch, or neither state; and examine relationships with the Flow State Scale-2. In Study 3, we aimed to replicate findings of Study 2 with an independent sample, and employed confirmatory factor analysis to confirm the factor structure, internal consistency, and relationships with the Flow State Scale-2.ResultsThe results provide preliminary validation of the four-factor, 22-item Flow-Clutch Scale.ConclusionsThese studies indicate the Flow-Clutch Scale represents a useful scale for researchers interested in examining flow and/or clutch states in sport and exercise. Recommendations are provided for further research to continue testing, and accumulating evidence for, the validity and reliability of the Flow-Clutch Scale.     

Stability criteria

Three approaches to the determination of behavioral stability were examined. In the first, a learning curve was fit to acquisition data (from Cumming and Schoenfeld, 1960), and the “experiment” stopped when the data approached sufficiently close to the theoretical asymptote. In the second, the data were analyzed for variability and linear and quadratic trend. In the third, the experiment was stopped when the magnitude of the daily changes in the data fell below a criterion. Accuracy was measured as deviation between the average value of the dependent variable when the experiment was stopped, and the average value over the last 100 sessions. The first approach was most accurate, but at the cost of requiring the most sessions and being the most difficult to apply. Both the second and third approaches provided acceptable criteria with a reasonable cost-accuracy tradeoff. The second approach permits a continuous adjustment of the criteria to accommodate the variability intrinsic in the experimental paradigm. The third, nomothetic, approach also takes into account the decreasing marginal utility of extended training sessions.     

Stopping rules for multi-category computerized classification testing

Computerized classification testing (CCT) aims to classify persons into one of two or more possible categories to make decisions such as mastery/non-mastery or meet most/meet all/exceed. A defining feature of CCT is its stopping criterion: the test terminates when there is enough confidence to make a decision. There is abundant research on CCT with a single cut-off, and two common stopping criteria are the sequential probability ratio test (SPRT) statistic and the generalized likelihood ratio statistic (GLR). However, there is a relative scarcity of research extending the SPRT to the multi-hypothesis case for when there is more than one cut-off. In this paper, we propose a new multi-category GLR (mGLR) statistic as well as a stochastically curtailed version of the CCT with three or more categories. A simulation study was conducted to show that the mGLR statistic outperformed the existing stopping rules by generating shorter average test length without sacrificing classification accuracy. Results also revealed that the stochastically curtailed mGLR successfully increased test efficiency in certain testing conditions.     

A cautionary note on using internal cross validation to select the number of clusters

A highly popular method for examining the stability of a data clustering is to split the data into two parts, cluster the observations in Part A, assign the objects in Part B to their nearest centroid in Part A, and then independently cluster the Part B objects. One then examines how close the two partitions are (say, by the Rand measure). Another proposal is to split the data into k parts, and see how their centroids cluster. By means of synthetic data analyses, we demonstrate that these approaches fail to identify the appropriate number of clusters, particularly as sample size becomes large and the variables exhibit higher correlations.The authors express their thanks to the Sol C. Snider Entrepreneurial Center, Wharton School, for support of this project.     

A unified approach for revealing multiple balance recovery strategies

In human balance recovery, different strategies have been proposed with generally overlooked knee motions but extensive focus on the ankle, hip, and step strategies. It is not well understood whether maintaining balance is regulated at the lower “muscular–articular” level of coordinating segment joints or at a higher level of controlling whole body dynamics. Whether balance control is to minimize joint degrees of freedom (DOF) or utilize all the available DOF also remains unclear. This study aimed to use a realistic musculoskeletal human model to identify multiple balance recovery strategies with a single optimization criterion. Movements were driven by neural excitations (which activated muscle force generation) and were assumed to be symmetric. Balance recoveries were simulated with forward-inclined straight body postures as the initial conditions. When the position of the toes was fixed, balance was regained with virtually straight knees and mixed ankle/hip strategies. Under a severely perturbed condition, use of the forward hop strategy after releasing the fixed-toes constraint indicated spontaneous recruitment or suppression of DOF, which mimicked functions of optimally computed CNS commands in humans. The results also indicated that increase/decrease in the number of DOF depends on the imposed perturbation intensity and movement constraints.     

Optimal versus heuristic planning of object manipulations: A review and a computational model of the continuous end-state comfort effect

Human beings select actions that facilitate the execution of later actions. For example, humans tend to select grasps that ensure that forthcoming object manipulations end in a comfortable posture (“end-state comfort effect”). Basic experimental results and their explanation within the optimal control framework are reviewed. I conclude that the discrete grasp selection tasks, which are commonly used to study anticipatory planning, leave room for alternative explanations. Moreover, the results of seven experiments employing a continuous grasp selection task seem incompatible with the optimal control (of end-state comfort) account. I introduce the weighted integration of multiple biases (WIMB) model, which accounts for many aspects of the selection of human grasp orientations in continuous tasks. Additionally, it accounts for the precision effect and hysteresis effect. The model shows that the brain may rely on a simple heuristic and does not actually has to anticipate the end-state of a movement to select effective grasps for object manipulations.     

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.     

“Look around while running!” Attentional focus effects in inexperienced runners

While attentional focus effects on running economy have been shown in different settings for trained athletes, it is unclear how attentional instructions should be formulated to improve running economy for inexperienced runners. The present study was designed to fill this gap and test attentional focus effects in runners with little running experience. An experimental design was implemented and participants ran 4 × 6 min at a slow and fixed running pace with different attentional instructions for each block (video, breathing, running movement, no instruction), while oxygen consumption was measured continuously. The results showed best running economy (lowest oxygen consumption) in the video compared with the breathing and movement condition which goes in line with effects for trained runners. Therefore, inexperienced runners can also profit from directing their attention externally and commonly taught principles such as focusing on the coordination of breathing and stride patterns should be reconsidered.     

Focusing attention on circular pedaling reduces movement economy in cycling

Previous research has shown that focus of attention affects movement economy in endurance tasks. This experimental study was designed to take a closer look at how focusing attention on special characteristics of endurance cycling actions can influence metabolic energy costs. Twenty-five trained cyclists completed 4 × 6 min time trials at submaximal intensity on a cycling ergometer. For each of the four time trials, they were instructed to adopt a different focus of attention: (1) circular pedaling, (2) force production of quad muscles, (3) head position, (4) stimuli in a cycling video. The order of conditions was counterbalanced. The main dependent measure was movement economy (i.e., oxygen consumption at a given workload). The results show that a focus on the circular pedaling action leads to reduced economy than a focus on the video (p = 0.001). Focusing on smooth and circular pedaling includes a continuous monitoring of the cycling action, which could disturb the rhythmical nature of movement execution, thereby leading to detriments in movement economy.