The analysis of errors in short-term motor memory research using trial profiles

In the past, researchers have debated the problem of selecting the most appropriate error measure (e.g., CE, VE, AE, or E) for use as the dependent variable when analyzing the results of their experiments in short-term motor memory research (Gessaroli & Schutz, 1982; Henry, 1974; Safrit, Spray, & Diewert, 1980; Schutz, 1977; Schutz & Roy, 1973). This paper suggests that the subjects' error scores, recorded over a series of trials, are analyzed individually, using repeated measures (RM) ANOVA. This analysis divides the total error sum of squares into recognizable components that, when identified, adequately explain the subjects' performance. The between-subjects sources of variation will indicate any differences in CE bias between the levels of each factor in the experiment. Similarly, any VE differences between the levels of each factor will be identified by significant trial-by-factor interactions. However, not all significant trial-by-factor interactions will necessarily indicate differences in VE performances. Nevertheless by plotting the group's perceived mean trial profiles for any significant trial-by-factor interactions, valuable insight can be gained into difference performance responses in trial adaptation for each level of the factors in the experimental design.     

Minimizing error in measurement of error: a proposed method for calculation of error in a two-dimensional motor task

Traditional one-dimensional error scores are still consistently used in research on motor learning to quantify two-dimensional error; however, the inherent differences in two-dimensional tasks render that application inappropriate and often misleading. Consequently, the purpose of this paper was to propose a novel method of presenting errors, which more precisely represents the accuracy, direction, and variability of error in two-dimensional settings. Although closely related to several alternatives for representing errors, the methodology used and the results obtained provide a more accurate procedure for pinpointing critical trends in what have been commonly referred to as AE (absolute error), VE (variable error), CE (constant error), and E (total variability). The proposed measurements of AVE (adjusted variable error), DE (directional error), TSE (total spread of error), and RE (radial error) provide composite error scores carrying a variety of information about performance on two-dimensional tasks. Formulas and examples are provided to facilitate computation and enhance understanding of the proposed scores.     

Methodological issues in short-term motor memory research

Four methodological issues identified and studied by short-term motor memory researchers were examined in this paper: (a) the distributions of three commonly used measures of error (AE, CE, and VE); (b) statistical analysis of these scores as dependent measures in an experiment; (c) within-cell and experiment-wise estimates of the reliability of CE; and (d) the power of the statistical test with CE as the dependent measure. The first two sub-problems were explored theoretically, while the latter two were subjected to empirical examination using four data sets from previously published experiments. The distributions of AE and VE scores were described as non-normal under certain conditions, while the CE score distribution was shown to be normal. Therefore analyses of these three dependent measures may require different statistical procedures. In light of this information, the assumptions affecting estimates of reliability and power in an experimental framework were examined. Based on an analysis of the four data sets, a strategy was proposed in which a relatively small number of subjects could be utilized in an experiment without sacrificing desired experimental controls.     

Variable Error

The degree to which blocked (VE) data satisfies the assumptions of compound symmetry required for a repeated measures ANOVA was studied. Monte Carlo procedures were used to study the effect of violation of this assumption, under varying block sizes, on the Type I error rate. Populations of 10,000 subjects for each of two groups, the underlying variance-covariance matrices reflecting a specific condition of violation of the homogeneity of covariance assumptions, were generated based on each of three actual experimental data sets. The data were blocked in various ways, VE calculated, and subsequently analyzed by a repeated measures ANOVA. The complete process was replicated for four covariance homogeneity conditions for each of the three data sets, resulting in a total of 22,000 simulated experiments. Results indicated that the Type I error rate increases as the degree of heterogeneity within the variance-covariance matrices increases when raw (unblocked) data are analyzed. With VE, the effects of within-matrix heterogeneity on the Type I error rate are inconclusive. However, block size does seem to affect the probability of obtaining a significant interaction, but the nature of this relationship is not clear as there does not appear to be any consistent relationship between the size of the block and the probability of obtaining significance. For both raw and VE data there was no inflation in the number of Type I errors when the covariances within a given matrix were homogeneous, regardless of the differences between the group variance-covariance matrices.     

Variable error: variance-covariance heterogeneity, block size and type L error rates

The degree to which blocked (VE) data satisfies the assumptions of compound symmetry required for a repeated measures ANOVA was studied. Monte Carlo procedures were used to study the effect of violation of this assumption, under varying block sizes, on the Type l error rate. Populations of 10,000 subjects for each of two groups, the underlying variance-covariance matrices reflecting a specific condition of violation of the homogeneity of covariance assumptions, was generated based on each of three actual experimental data sets. The data were blocked in various ways, VE calculated, and subsequently analyzed by a repeated measures ANOVA. The complete process was replicated for four covariance homogeneity conditions for each of the three data sets, resulting in a total of 22,000 simulated experiments. Results indicated that the Type l error rate increases as the degree of heterogeneity within the variance-covariance matrices increases when raw (unblocked) data are analyzed. With VE, the effects of within-matrix heterogeneity on the Type l error rate are inconclusive. However, block size does seem to affect the probability of obtaining a significant interaction, but the nature of this relationship is not clear as there does not appear to be any consistent relationship between the size of the block and the probability of obtaining significance. For both raw and VE data there was no inflation in the number of Type l errors when the covariances within a given matrix were homogeneous, regardless of the differences between the group variance-covariance matrices.     

Absolute Error

School of Physical Education and Recreation The University of British Columbia The purpose of this investigation was to re-examine the measures of algebraic error (CE), absolute error (AE), and within-S variance (VE). in an attempt to arrive at unambiguous definitions regarding the statistical and logical meanings of these three performance variables. Under the assumption of a normal distribution, the statistic AE is completely dependent on CE and VE and thus can be predicted from them. This shows that all information contained in the term AE is contained in either CE (when the ratio $$\text{C}\text{E}/\sqrt{\text{V}\text{E}} > \text{2}\text{.0}$$), or in VE (when CE ? 0.0) or in a weighted combination of both CE and VE (when $$0<\text{C}\text{E}/\sqrt{\text{V}\text{E}}<2.0$$). Examples are provided to show the type of errors made in interpreting significant findings when AE is the dependent variable.     

Response Timing Accuracy as a Function of Movement Velocity and Distance

In two experiments, patterns of response error during a timing accuracy task were investigated. In Experiment 1, these patterns were examined across a full range of movement velocities, which provided a test of the hypothesis that as movement velocity increases, constant error (CE) shifts from a negative to a positive response bias, with the zero CE point occurring at approximately 50% of maximum movement velocity (Hancock & Newell, 1985). Additionally, by examining variable error (VE), timing error variability patterns over a full range of movement velocities were established. Subjects (N = 6) performed a series of forearm flexion movements requiring 19 different movement velocities. Results corroborated previous observations that variability of timing error primarily decreased as movement velocity increased from 6 to 42% of maximum velocity. Additionally, CE data across the velocity spectrum did not support the proposed timing error function. In Experiment 2, the effect(s) of responding at 3 movement distances with 6 movement velocities on response timing error were investigated. VE was significantly lower for the 3 high-velocity movements than for the 3 low-velocity movements. Additionally, when MT was mathematically factored out, VE was less at the long movement distance than at the short distance. As in Experiment 1, CE was unaffected by distance or velocity effects and the predicted CE timing error function was not evident.     

Response Timing Accuracy as a Function of Movement Velocity and Distance

In two experiments, patterns of response error during a timing accuracy task were investigated. In Experiment 1. these patterns were examined across a full range of movement velocities, which provided a test of the hypothesis that as movement velocity increases, constant error (CE) shifts from a negative to a positive response bias, with the zero CE point occurring at approximately 50% of maximum movement velocity (Hancock & Newell, 1985). Additionally, by examining variable error (VE), timing error variability patterns over a full range of movement velocities were established. Subjects (N = 6) performed a series of forearm flexion movements requiring 19 different movement velocities. Results corroborated previous observations that variability of timing error primarily decreased as movement velocity increased from 6 to 42% of maximum velocity. Additionally, CE data across the velocity spectrum did not support the proposed timing error function. In Experiment 2, the effect(s) of responding at 3 movement distances with 6 movement velocities on response timing error were investigated. VE was significantly lower for the 3 high-velocity movements than for the 3 low-velocity movements. Additionally, when MT was mathematically factored out. VE was less at the long movement distance than at the short distance. As in Experiment 1, CE was unaffected by distance or velocity effects and the predicted CE timing error function was not evident.     

Factor analysis; some effects of chance error

Ignorance concerning the standard error of individual factor loadings and their differences has been a major obstacle to the proper interpretation of factorial results. The effects of three types of experimental error (selection of variables, selection of subjects and selection of scores) are here reported. In order to handle the errors of rotation systematically, it has been necessary to introduce a new semi-analytical criterion for the attainment of simple structure. Variability in results which may theoretically be eliminated is discussed under the heading of non-essential error.     

Joint position error after neck protraction-retraction movements in healthy office workers: a cross-sectional study

Since the upper cervical spine (UCS) has been regarded to be distinct from the lower cervical spine (LCS), joint position error (JPE) needs to be tested separately for both regions. The purpose of this study was to investigate the JPE after cervical protraction/retraction movements, involving opposite movements of extension and flexion for the UCS and LCS. These movements are frequently performed during office work.Cervical JPEs were tracked in thirty healthy office workers while performing four tests of cervical pro-retraction movements with variations in vision and movement direction, and assessed using the Kinect head tracker (Microsoft Corp), placed in front of each participant. The JPE was expressed in constant (CE), absolute (AE) and variable errors (VE). Multilevel linear models evaluated main and interaction effects of vision, movement direction, cervical region and sex.Slightly larger JPEs have been found in the UCS. Vision showed no effect on any outcome variable. No effect exceeded typical measurement errors reported for the Kinect head tracker.This study showed, that JPEs after pro-retraction movements of the head and neck may differ for UCS and LCS. The differences were small and not beyond measurement error reported for the Kinect.     

The Effect of Interpolated Motor Activity on the Short-Term Retention of Movement Distance and End-Location

The effect of an interpolated movement on the recall of a blind, lever-positioning movement was assessed separately for the reproduction cues of distance and end-location. Both cues showed the context effect of assimilation, that is, the end-location of the interpolated movement caused directional biasing of the algebraic or constant error (CE) for location reproduction while the length of the interpolated movement caused similar directional biasing for distance reproduction. Variability about algebraic error (VE) was used to assess forgetting. There was no change in VE for location reproduction, and an increase in VE for distance reproduction was limited to the relatively large movements. Thus, an interpolated movement that does not have to be remembered does not cause interference with the retention of location information, but does cause some interference with the retention of distance information. The findings are discussed in relation to a model of motor short-term memory which incorporates both CE and VE.     

Sex differences in coincidence-anticipation timing (CAT): a review

Coincidence-anticipation timing (CAT) is the ability to judge when a moving stimulus will arrive at a target. 43 articles were reviewed which investigated sex differences in this skill. Performance was typically recorded as one or more of three error measures, absolute error (AE), constant error (CE), and variable error (VE). Despite many null findings, it is argued that the evidence for a male advantage is strong, particularly for AE and VE. 10 parameters typically associated with CAT studies were analyzed (e.g., knowledge of results, number of trials, stimulus duration, and stimulus speed), but none differentiated clearly between the presence and absence of the sex difference. However, when the mean AE score was used as a measure of task difficulty, a male advantage was reliably associated with lower values of AE (easier tasks) and null findings with higher values (more difficult tasks). An attempt to compare sex difference findings from Bassin timer and real-world tasks was thwarted by the lack of studies using real-world tasks. Given little evidence for the influence of socialization on sex differences in CAT, it is suggested that the difference may have originated from the evolutionary selection of women for gathering and men for hunting.     

Are True Scores and Construct Scores the Same? A critical examination of their substitutability and the implications for research results

Relations between constructs are estimated based on correlations between measures of constructs corrected for measurement error. This process assumes that the true scores on the measure are linearly related to construct scores, an assumption that may not hold. We examined the extent to which differences in distribution shape reduce the correlation between true scores on a measure and scores on the underlying construct they are intended to measure. We found, via a series of Monte Carlo simulations, that when the actual construct distribution is normal, nonnormal distributions of true scores caused this correlation to drop by an average of only .02 across 15 conditions. When both construct and true score distributions assumed different combinations of nonnormal distributions, the average correlation was reduced by .05 across 375 conditions. We conclude that theory‐based scales intended to measure constructs usually correlate highly with the constructs they are constructed to measure. We show that, as a result, in most cases true score correlations only modestly underestimate correlations between different constructs. However, in cases in which the two constructs are redundant, this underestimation can lead to the false conclusion that the constructs are ‘correlated but distinct constructs,’ resulting in construct proliferation.     

The Unhappy Marriage of Care Ethics and Virtue Ethics

The proposal that care ethic(s) (CE) be subsumed under the framework of virtue ethic(s) (VE) is both promising and problematic for feminists. Although some attempts to construe care as a virtue are more commendable than others, they cannot duplicate a freestanding feminist CE. Sander‐Staudt recommends a model of theoretical collaboration between VE and CE that retains their comprehensiveness, allows CE to enhance VE as well as be enhanced by it, and leaves CE open to other collaborations.     

Judgment of line orientation depends on gender, education, and type of error

Visuospatial tasks are particularly proficient at eliciting gender differences during neuropsychological performance. Here we tested the hypothesis that gender and education are related to different types of visuospatial errors on a task of line orientation that allowed the independent scoring of correct responses ("hits", or H) and one type of incorrect responses ("commission errors", or CE). We studied 343 volunteers of roughly comparable ages and with different levels of education. Education and gender were significantly associated with H scores, which were higher in men and in the groups with higher education. In contrast, the differences between men and women on CE depended on education. We concluded that (I) the ability to find the correct responses differs from the ability to avoid the wrong responses amidst an array of possible alternatives, and that (II) education interacts with gender to promote a stable performance on CE earlier in men than in women.     

Effects of precision of knowledge of results on performance of a gross motor coincidence-anticipation task

The purpose of the investigation was to determine the effects from three knowledge of results (KR) precision levels (qualitative; 0.10 sec, 0.001 sec) on the performance of a gross motor coincidence-anticipation task where subjects performed with visual and other sense modality input. Other variables included in the analysis were sex, movement distance, and practice over three blocks of trials. Absolute error (AE), constant error (CE), variable error (VE), and E scores (E) of the subjects from two experiments (N = 90; N = 54) were analyzed with 3 x 2 x 2 x 3 ANOVAs with repeated measures on the last two factors (feedback, sex, movement distance, blocks). Consistent finding from both experiments indicated that, for this gross motor coincidence-anticipation task, the subjects performed as accurately and as consistently when they received qualitative KR as when, in addition, they received more precise KR. Subjects performed with less error on the short as opposed to the long term distance pattern. Males performed with less error on the long movement pattern than females in Experiment 1; however, the only sex difference noted in Experiment 2, when the movement distances were shortened, was that males had a more on-time CE mean score.     

The effect of perceived locomotor constraints on distance estimation

Two experiments were conducted to examine the ways in which the visual estimation of distance to a target is affected by constraints perceived to be placed on the subsequent locomotion to the target without vision. We hypothesized that an appraisal of impending effort would play a role in ascertaining the distance to be walked. In Experiment 1, the amount of resistance to walking was variable and unpredictable. One group of subjects performed against relatively low resistance, whereas another group performed against substantially greater resistance. In the low-resistance condition, no significant differences in CE, VE, time to target, or number of steps to target were found between any of the eight combinations of predictable or unpredictable resistances during walking. In the high-resistance condition, however, significant differences were found for CE and number of strides to target when resistance varied unpredictably during walking. Experiment 2 was similar in design but required subjects to walk with combinations of normal or short steps after they had viewed the target knowing only the gait type that would be used to begin locomotion. No differences in CE, VE, or time to target were found between four different combinations of gait type and predictability, under subjectively controlled conditions. When the step constraints were externally imposed, however, differences were found for CE. None of the results from either experiment, in which the number of strides needed to reach the target or the predictability of gait did not change from normal, supported the hypothesis that motor output requirements are necessary in forming a mental representation of the target position that can be used to walk to the target with eyes closed. Whichever locomotor technique was used to walk the estimated distance in these cases, the representation was able to be used independently. When walking mechanics were altered by externally imposed constraints, however, the success at reaching the estimated target position was reduced. These latter results are consistent with those obtained using up, down, and level walking and support the premise that mental representations used in blind walking are linked to the locomotor mechanics afforded by environmental conditions.     

Average KR schedule in learning of timing: influence of length for summary knowledge of results and task complexity

This experiment investigated the influence of length for average Knowledge of Results (KR) and task complexity on learning of timing in a barrier knock-down task. Participants (30 men and 30 women) attempted to press a goal button in 1200 msec. after pressing a start button. The participant was assigned into one of six groups by two tasks (simple and complex) and three feedback groups (100% KR, Average 3, Average 5). The simple and complex tasks required a participant to knock down one or three barriers before pressing a goal button. After a pretest without KR, participants practiced 60 trials of physical practice with one of the three following groups as a practice phase: one given the result of movement time after every trial (100% KR), a second given the average movement time after every third trial (Average 3), a third given the average movement time after every fifth trial (Average 5). Participants then performed a posttest with no-KR and two retention tests, taken 10 min. and 24 hr. after the posttest without KR. Analysis gave several findings. (1) On the complex task, the absolute constant error (/CE/) and the variable error (VE) were less than those on the simple task. (2) The /CE/ and the VE of the 100% KR and the Average 3 groups were less than those of the Average 5 group in the practice phase, and the VE of the 100% KR and the Average 3 group were less than those of the Average 5 group on the retention tests. (3) In the practice phase, the /CE/ and the VE on Blocks 1 and 2 were higher than on Blocks 5 and 6. (4) On the retention tests, the /CE/ of the posttest was less than retention tests 1 and 2. And, the VE of the 100% KR and the Average 3 groups were less than that of the Average 5 group. These results suggest that the average feedback length of three trials and the given feedback information after every trial are advantageous to learning timing on this barrier knock-down task.     

The relative weightings of visual and nonvisual coding in a simple motor learning task

A linear positioning task was used to examine the effects of visual and nonvisual inputs on motor learning. The experiment had three factors with two levels of each namely: sensory modality (visual-nonvisual), transfer at recall (changed-unchanged), size of movement (25.4 cm, 50.8 com). Three dependent variable were used: absolute error (AE), constant error (CE), and variable error (VE). The results suggest that visual dominance causes disruption of recall in the visual, changed conditions. No disruption of recall was found for the nonvisual condition other than in terms of CE with respect to movement sizes. The results are taken to follow Posner et al.'s (1976) theory of visual dominance, but some account of the spatial qualities of visual and kinesthetic information is needed.     

Stepwise Latent Class Models for Explaining Group-Level Outcomes Using Discrete Individual-Level Predictors

Explaining group-level outcomes from individual-level predictors requires aggregating the individual-level scores to the group level and correcting the group-level estimates for measurement errors in the aggregated scores. However, for discrete variables it is not clear how to perform the aggregation and correction. It is shown how stepwise latent class analysis can be used to do this. First, a latent class model is estimated in which the scores on a discrete individual-level predictor are used to construct group-level latent classes. Second, this latent class model is used to aggregate the individual-level predictor by assigning the groups to the latent classes. Third, a group-level analysis is performed in which the aggregated measures are related to the remaining group-level variables while correcting for the measurement error in the class assignments. This stepwise approach is introduced in a multilevel mediation model with a single individual-level mediator, and compared to existing methods in a simulation study. We also show how a mediation model with multiple group-level latent variables can be used with multiple individual-level mediators and this model is applied to explain team productivity (group level) as a function of job control (individual level), job satisfaction (individual level), and enriched job design (group level).