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Rasch Analysis of the Wrist and Hand Fugl-Meyer

Dimensionality and Item-Level Characteristics

Persch, Andrew C. PhD, OTR/L; Gugiu, P. Cristian PhD; Velozo, Craig A. PhD, OTR; Page, Stephen J. PhD, MOT, OTR/L

Journal of Neurologic Physical Therapy: July 2015 - Volume 39 - Issue 3 - p 185–192
doi: 10.1097/NPT.0000000000000096
Research Articles
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Background and Purpose: Clinical administration of the wrist stability, wrist mobility, and hand items of the upper-extremity Fugl-Meyer (W/H UE FM) may provide a rigorous, easily administered, bedside measure of motor impairment in mildly impaired stroke survivors. The purpose of this study was to evaluate the item structure of the W/H UE FM to better understand its measurement properties using Rasch analysis.

Methods: This was a secondary analysis of W/H UE FM data arising from clinical trials of mildly impaired stroke survivors using latent parallel analysis, ordinal factor analysis, and partial credit model Rasch analyses.

Results: Latent parallel analysis and ordinal factor analysis indicated that all W/H UE FM items represent a single unidimensional construct, wrist and hand motor ability. Rasch analysis of data from 150 mildly impaired stroke survivors (94 men; mean age, 57.1 ± 11.4 years; mean time since stroke, 19.5 months) revealed that the W/H UE FM operated as a reliable, valid, and effective measure of wrist and hand motor ability. These data were compatible with Rasch model assumptions and are consistent with previous W/H UE FM research. Mass flexion and extension movements were the least difficult W/H UE FM items while the radial and hook grasp items were the most difficult.

Discussion and Conclusion: The W/H UE FM is well suited to mildly impaired stroke survivors who exhibit the ability to perform mass flexion and mass extension movements. The full-scale UE FM may be preferable for stroke survivors with lower levels of ability.

Video abstract available for additional insight from the authors (Supplemental Digital Content 1,

Division of Occupational Therapy (A.C.P., S.J.P.), The Ohio State University, Columbus, Ohio; Quantitative Research, Evaluation, and Measurement (P.C.G.), College of Education and Human Ecology, The Ohio State University, Columbus, Ohio; Division of Occupational Therapy, Medical University of South Carolina (CAV), Charleston, South Carolina.

Correspondence: Andrew C. Persch, PhD, OTR/L, Assistant Professor, Division of Occupational Therapy, The Ohio State University, 453 W. 10th Ave, 406 Atwell Hall, Columbus, OH 43210 (

This work was partially supported by grants from the National Institutes of Health (R21AT002110-01; R01AT004454-04).

This work represented herein was presented at a poster at the 2015 ACRM Conference.

The authors declare no conflict of interest. registration number: Data predate the FDAAA 801 requirements.

Supplemental digital content is available for this article. Direct URL citation appears in the printed text and is provided in the HTML and PDF versions of this article on the journal's Web site (

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Upper-extremity (UE) hemiparesis remains one of the most common impairments exhibited among the expanding stroke survivor population,1 and frequently impedes performance of valued activities. Indeed, despite weeks of rehabilitation, 50% of stroke survivors retain some degree of UE weakness2 and up to 70% remain unable to functionally use their paretic UEs3 in the months after stroke.

Developed in 1975, the UE section of the Fugl-Meyer (UE FM)4 remains one of the most established and widely used5 assessments of UE impairment in stroke. Moreover, the UE FM is recommended for use in stroke rehabilitative trials6 and, unlike other measures of paretic UE dysfunction7–9 only requires a few household items to administer, making it especially conducive for clinical use. Using classical test theory techniques, the psychometric reliability10–13 and validity14–18 of the UE FM have been shown, and support its integrated, clinical use for assessing UE impairment after stroke. Recent investigations that employ Rasch analysis also demonstrate the strength of the UE FM items themselves. For example, it is now well established that the majority of UE FM items represent the unidimensional construct of UE motor ability19 and that the UE FM constitutes a useful tool for classifying poststroke UE motor impairment as mild, moderate, or severe.5

The proliferation of UE therapies targeting stroke survivors exhibiting minimal UE impairment20–23 has necessitated the continued development and evaluation of assessment tools, providing high reliability, validity, and clinical utility. Such tools are necessary because (a) clinical time is valuable and (b) recent evidence19,24 demonstrates that the traditional understanding of UE motor recovery (ie, proximal to distal, reflexive then synergistic then isolated) is not absolute. Furthermore, existing measures of wrist and hand motor impairment25–27 may require specialized materials, training, and may take an excessive amount of time. To address the need for a quickly administered, rigorous, bedside measure of active UE motor ability, the wrist stability, wrist mobility, and hand items of the UE FM (W/H UE FM) were administered in a standardized manner to subjects with minimal28 and moderate29 UE impairment. This 12-item subset of the UE FM was recently shown to have high intrarater reliability (intraclass correlation coefficients, 0.95), internal consistency (Cronbach α > 0.80; ordinal α > 0.80), and concurrent validity (Action Research Arm Test correlation > 0.70) in samples of mildly impaired28 and moderately impaired29 stroke survivors. These findings provide strong evidence that the W/H UE FM may prove a viable tool for efficient, reliable, and valid assessment of UE motor ability in persons with stroke who have mild and moderate impairment. Despite these promising results, it remains unclear how individual W/H UE FM items function in the population of stroke survivors exhibiting minimal UE impairment. Because individuals experiencing mild, and even moderate, UE impairment may be at risk for early-supported discharge from rehabilitative services,30–32 it is critical that the psychometric properties of these items be ascertained. Our overall goal was to examine the item-level psychometrics of W/H UE FM items in a population of mildly impaired stroke survivors using Rasch analysis. To accomplish this goal, the specific aims of this study were to (a) determine whether W/H UE FM items represent a unidimensional construct, wrist, and hand motor ability, and (b) determine the Rasch-modeled item structure of the W/H UE FM.

Rasch analysis provides a measurement model for evaluation of categorical data on the basis of the tenet that a total score results from the interaction of (1) person ability and (2) item difficulty.33 The first step in a Rasch analysis is to construct a scalogram. The scalogram is an ordered table of data resulting from measurement of any single attribute (eg, wrist and hand motor ability). People are ordered from the least able to the most able on the basis of on their ability. Thus, person ability is given by the number of items answered correctly or points earned out of the total possible. Similarly, test items are ordered from the least difficult to the most difficult, with item difficulty given as the number of items endorsed out of the total possible. These data are transformed from the ordinal (ie, categorical) level of measurement to an interval scale by means of a log-odds transformation. The resulting logits enable direct, linear, comparison of person abilities and item difficulties, a primary advantage of the Rasch model. Applied to wrist and hand motor ability, as is the case here, the probability of a person's “success for any given item depends on the difference between the ability of the person and the difficulty of the item.”33 Rasch analysis also enables evaluation of individual items using fit statistics, which reflect the alignment of each item to the construct being measured.34 Researchers use these statistics to refine new and existing instruments, examine reliability and validity, and optimize clinical utility for specific populations.

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Study Design

This study was a secondary analysis of data obtained during outpatient, randomized controlled trials approved by the Human Research Protection Program at The Ohio State University. The UE FM was administered on multiple occasions as part of a larger battery of outcome measures. The current study focused solely on pretest data, collected before randomization and to any interventions taking place.

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The battery of measures included frequently used, established, instruments administered to assess both UE impairment (ie, active movement in each UE joint) and function (ie, intersegmental movements put together in sequential fashion to accomplish a functional goal). Licensed therapists, acting as blinded raters at participating rehabilitation centers, administered all outcome measures. All raters were certified and recertified on the outcome measures every 3 months using standardized, live, and video-based interrater reliability checks at the main study center.

The full-scale UE FM4 served as the primary outcome measure for the trials that contributed data to this study. The UE FM is a, 33-item, proximal (eg, shoulder flexion) to distal (eg, hook grasp) assessment of UE motor impairment. Data arise from a 3-point ordinal scale (0 = cannot perform; 1 = can partially perform; and 2 = can perform fully) and are often summed to yield a maximum total score of 66.

The W/H UE FM28 is a 12-item assessment (Table 1) of wrist and hand motor impairment derived from the larger, full-scale, UE FM. Items are scored using the same 3-point ordinal scale as the UE FM. Preliminary evidence supports the intrarater reliability, internal consistency, and concurrent validity of the W/H UE FM28 when used with mildly impaired stroke survivors. Standardized directions for administration of the W/H UE FM are available for scholarly and clinical use.28

Table 1

Table 1

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Psychometric Evaluation

For the current study, the psychometric validity of the W/H UE FM was assessed using Rasch analysis.33,35 Before conducting any analyses employing the Rasch model, the prerequisite unidimensionality of the W/H UE FM was examined using latent parallel analysis36 and ordinal exploratory factor analysis (EFA).37 Latent parallel analysis provides a rigorous method for examining the dimensionality of measures composed of polytomous items38 and is preferred for its accuracy relative to other methods of factor extraction (ie, Kaiser criterion, and scree plot).39,40 Likewise, ordinal EFA offers advantages including utilization of all response data and robustness when data are missing.37,41 The working hypotheses were (a) the W/H UE FM represented a unidimensional construct, wrist, and hand motor ability, and (b) all W/H UE FM items would load onto this single factor.

Rasch analysis conducted on the W/H UE FM used an established methodology.33,35 Specifically, examination of infit and outfit statistics enabled identification of misfitting items and persons. Fit statistics are reported as mean-square residual summary statistics (MNSQ) and reflect the degree to which data fit the Rasch model.33,35 Applied here, fit statistics reveal the extent to which the data (eg, person abilities and item difficulties) contribute to a single construct, such as wrist and hand motor ability. As the W/H UE FM is a clinical tool, MNSQ values between 0.5 and 1.7 (ie, standardized Z values < 2) were considered acceptable.42 Next, using these criteria to direct a process of iterative model building and comparison, misfitting items and people were temporarily removed from the dataset.35,43 When the removal of misfitting items (or persons) improves fit to the Rasch model, a cross-plot of the person measures resulting from each model should show a poor correlation. When the removal of misfitting items (or persons) fails to improve the model, the cross-plot should reveal a strong correlation (eg, Figure 1). In this way, misfitting items and/or persons are systematically removed from the dataset until doing so fails to improve model fit.35,43

Figure 1

Figure 1

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Participants were recruited for the trials from across the Midwestern United States using active and passive recruitment strategies,44 including print advertisements placed in clinics near enrolling sites, in-services to local clinicians, and communications to local stroke support groups. As potential participants came forward, the following screening criteria were applied to determine study eligibility. Inclusion criteria were (a) at least 10° of active flexion in the more affected wrist, and at least 2 fingers of the paretic hand; (b) experienced stroke 12 months or more before study enrollment; (c) Modified Mini-Mental Status Exam score 70 or more45; (d) between age 18 and 75 years; (e) first stroke experienced; and (f) not receiving any form of physical rehabilitation. Exclusion criteria were (a) excessive spasticity in the more affected UE (Modified Ashworth Scale46 score ≥ 3); (b) significant pain in the more affected UE (score ≥5 on a visual analog scale); and (c) enrollment in any rehabilitative trials.

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Participant Demographics

Using the aforementioned study criteria, 150 subjects were determined to be eligible and included in the current analyses (94 males; mean age, 57.1 ± 11.4 years; mean time since stroke, 19.5 months; 121 ischemic strokes; 78 with right hemiparesis; 105 white participants, 40 African American, 2 Hispanic/Latino, 2 Asian-Pacific Islander, and 1 participant of more than 1 race; UE FM mean score, 28.3 ± 12.0; mean W/H UE FM score, 7.34 ± 5.44).

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Latent parallel analysis was conducted on W/H UE FM data for 150 mildly impaired stroke survivors. First, SAS 9.3 software (SAS Version 9.3, SAS Institute Inc, Cary, NC) was used to create a polychoric correlation matrix of the data. The polychoric correlation is appropriate when polytomous data arise from a latent normal distribution, as is the case with the W/H UE FM. Next, the polychoric correlation matrix was used as the input for latent parallel analysis. Ten thousand random datasets that parallel the actual W/H UE FM data (ie, 150 cases; 12 variables; 3-point scale) were created using Monte Carlo simulations in SAS. The latent parallel analysis program then computed eigenvalues for the real dataset and for each of the 10,000 randomly generated datasets. SAS then compared the real eigenvalues with those derived from the random data (Figure 2). Factors were only retained when the real eigenvalues exceeded the randomly generated values. Latent parallel analysis of the W/H UE FM data suggested extracting only 1 factor.

Figure 2

Figure 2

On the basis of the results of latent parallel analysis, the decision was made to proceed to ordinal EFA with a single-factor solution. That is, only one factor was retained and EFA was performed without rotation. The SAS-generated factor pattern (Table 1) indicated that all 12 W/H UE FM items had large positive loadings with the single factor retained. Items 8 and 9 (ie, radial grasp and hook grasp) had the smallest factor loadings (0.477 and 0.624, respectively; Table 1). These findings (ie, latent factor analysis, ordinal EFA) illustrate that the W/H UE FM is unidimensional.

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Rasch Analysis

Having established the prerequisite unidimensionality, WINSTEPS 3.80.1 software (Winsteps, Version 3.80.1, JM Linacre, Beaverton, OR) was used to conduct a partial credit model (PCM)33 Rasch analysis of W/H UE FM items in a sample of mildly impaired stroke survivors. Rasch analysis conducted using the PCM allows for different Rasch-Andrich thresholds for each item. The Rasch-Andrich threshold is the boundary between 2 points on a scale, say 1 and 2, where the probability of selecting either option is 50%. By employing the PCM, this analysis allows for these boundaries to vary item to item (ie, each item has its own rating scale). This iterative, model-building, process35,43 (Table 2) was used to develop the final item-difficulty hierarchy that conforms to the Rasch model.33 That is, items had acceptable fit statistics and are presented from the least difficult to the most difficult.

Table 2

Table 2

Persons and items that attain the minimum measure on an instrument (ie, in the case of persons a score of 0 on all items and in the case of items a score of 0 for all persons) do not contribute to measurement of the construct. Here, a total of 10 stroke survivors received scores of zero on the W/H UE FM and were temporarily removed from the analysis (model 2; 140 people, 12 items).35,43 Model 2 item statistics identified items 6 and 8 as misfitting (outfit MNSQ > 1.742; Table 2). These misfitting items were temporarily removed from the analysis, yielding model 3 (140 people; 10 items). Analysis of the cross-plot (Figure 1; strong correlation) of person measures for models 2 and 3 indicated that the removal of items 6 and 8 was unnecessary. That is, the removal of items 6 and 8 did not influence person measures. Accordingly, these items were returned to the analysis.35,43 Finally, item-difficulty values were anchored43 using model 2 values, and the analysis was rerun using all 150 people (model 4; includes the 10 people previously, temporarily removed). This iterative process allowed for estimation of “clean” item-difficulty and error values (eg, values not influenced by the misfitting items; Table 3).

Table 3

Table 3

The final analysis (model 4; Figure 3; Table 3) incorporates anchored item-difficulty values (model 2) and person ability scores for all 150 stroke survivors.33 Mass flexion (item 6; −3.90 ± 0.27 logits) and mass extension (item 7; −1.01 ± 0.21 logits) were easiest for this sample of mildly impaired stroke survivors to perform. The radial grasp (item 9; 2.10 ± 0.22 logits) and hook grasp (item 8; 1.92 ± 0.21 logits) were most difficult. As W/H UE FM item difficulties exceeded person abilities for much of the sample. Person abilities for 16% of the sample (24 people) were less than −3.90 logits, the mean item-difficulty value for item 6: mass flexion, the easiest W/H UE FM item. Person abilities for another 37% of the sample (56 people) were less than −1.01 logits, the mean item-difficulty value for item 7: mass extension, the second-easiest W/H UE FM item. The standard error associated with the person measures for this group of participants ranged from 0.58 to 2.11, in contrast to values 0.54 or less for participants with higher abilities. Despite these limitations, comparison of the Rasch-modeled expected point-measure correlations with observed correlations (Table 3) failed to reveal any differences more than 0.05. This finding indicates compatibility of the final model (model 4) with Rasch-modeled expectations. Further interpretation of the variable map (Figure 3) is present in the discussion.

Figure 3

Figure 3

Values for the person separation index, number of person strata, and test reliability of person separation of the W/H UE FM (ie, short form) and UE FM (ie, long form) were calculated using Rasch-modeled statistics.35 The person separation index (GP) reflects the spread of persons within the sample in units of test error.47GP for the W/H UE FM was 2.41, whereas it was 3.77 for the full-scale UE FM. The number of person strata (HP) was calculated using the formula

.35 Strata are defined as “statistically distinct levels of person ability ... with centers three measurement errors apart.”35HP for the W/H UE FM was 3.55 and for the UE FM was 5.36. Finally, the test reliability of person separation (RP) was calculated using the formula

. RP reflects the proportion of observed score variance, not do to chance (ie, measurement error), and was 0.85 for the W/H UE FM and 0.93 for the UE FM.

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This study examined the dimensionality and item-level function of W/H UE FM items with stroke survivors exhibiting mild UE impairment. This is a population for whom a number of promising interventions have been developed and for whom easily-administered clinical measures are needed. This psychometric evaluation of the W/H UE FM provides new data that inform usefulness of the W/H UE FM with this important, increasingly prevalent, group.

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Establishing Unidimensionality

Previous research19 had established that a modified, 30-item version of the UE FM functions as a single, unified measure of UE motor ability in stroke survivors exhibiting mild, moderate, or severe impairment. This positive finding supported the construct validity, clinical, and scholarly use of the UE FM with stroke survivors. However, because mildly impaired stroke survivors can usually perform most UE FM items, administration of the full-scale UE FM may prove superfluous. Consequently, the W/H UE FM was developed to address the need for a quick, easy-to-administer screening assessment of active motor ability in stroke survivors. The rigorous implementation of latent parallel analysis and ordinal EFA performed herein confirmed the working hypotheses that (a) W/H UE FM items represent the unidimensional construct, wrist, and hand motor ability, and (b) all W/H UE FM items had large positive loading with this single factor. Specifically, latent parallel analysis indicated that W/H UE FM items contributed to a single-factor solution and ordinal EFA confirmed that W/H UE FM items loaded onto this single factor.

Items 8 and 9 (ie, radial grasp and hook grasp) had the smallest factor loadings, 0.477 and 0.624, respectively (Table 1). These items each test a distinct hand skill. Item 8, the hook grasp, challenges the subject to fully extend digits 2 through 5 at the metacarpophalangeal joint while simultaneously flexing at the proximal and distal interphalangeal joints. Item 9, the radial grasp, asks the subject to flex the thumb toward the second digit in an isolated fashion. Both of these skills are known to be extraordinarily challenging for stroke survivors experiencing UE motor impairment.5,19,28 That these skills are challenging may explain why they contribute the least to the unidimensional construct, wrist, and hand motor ability, especially given the motor impairment levels of subjects comprising the current sample.

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Item Difficulty

Rasch analysis of the W/H UE FM provided several, unique insights related to assessment and clinical care of mildly impaired stroke survivors. Although the W/H UE FM performed adequately for the majority of the sample, analysis of the final, validated Rasch model (ie, model 4) indicated that the W/H UE FM did not precisely measure stroke survivors with relatively lower levels of ability. This finding was unanticipated. When compared with survivors of stroke with moderate and severe impairment, mildly impaired stroke survivors represent a relatively higher functioning cohort of individuals seeking rehabilitation in the weeks and months after stroke. It was expected that these individuals would demonstrate the ability to complete all W/H UE FM items.

Under the Rasch model, a measurement instrument functions best when item difficulties are well matched to the ability levels of the people being measured (ie, mildly impaired stroke survivors). This is not observed in the data (Figure 3). Although all W/H UE FM items were found to have small error values (Table 3), and thus high precision, the measurement error for people increased for those with ability scores below −1.01 logits. That is, the W/H UE FM measured individuals with relatively lower ability levels less precisely. It is not surprising then, that the clinical implication of this finding is that the W/H UE FM is less precise in measuring stroke survivors who are on the lower end of the spectrum herein included (ie, people who met our study criteria but are more moderately impaired). Additional items, targeted at individuals with lower ability levels, would likely enhance the item-level functioning of the W/H UE FM and are recommended for future research. This could likely be accomplished by adding additional items from the UE FM if the individual being tested exhibits more motor impairment than those who were included in this study.

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Separation, Strata, and Reliability

Rasch-modeled statistics were used to calculate the person separation index (GP), number of person strata (HP), and test reliability of person separation (RP).35 The W/H UE FM was able to separate people into 3 distinct strata (HP = 3.55), whereas the UE FM separated people into 5 strata (HP = 5.36). Practically, this means that the UE FM is better able to distinguish mild stroke survivors on the basis of individual differences of UE motor ability than is the W/H UE FM. Similarly, the test reliability of person separation (RP) was greater of the full-scale UE FM (RP = 0.93) than it was for the W/H UE FM (RP = 0.85). These findings make sense for a couple of reasons. First, the modified UE FM5,19 has 18 more items than does the W/H UE FM, all of which measure other aspects of UE motor ability. Second, it is generally accepted that reliability can be expected to increase as the length of a test increases.48

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Implications for Clinical Use and Future Research

This study is the third and most advanced evaluation of the W/H UE FM to date.28,29 The final model (model 4) revealed items 6 and 7 (ie, mass flexion and mass extension) as the easiest W/H UE FM items. This finding is consistent with previous Rasch analyses5,19 of the UE FM, which have identified W/H UE FM items 6 and 7 as easiest to endorse. Thus, it is particularly troubling that these easiest W/H UE FM items remained too difficult for many participants. For survivors of stroke, active finger extension is a powerful predictor of UE motor recovery49,50 and potential to benefit from neurorehabilitation.38 To date, research has failed to examine the potential predictive power of this distal motor skill from a psychometric perspective.

The present analysis is the first, of which we are aware, to reveal that mass extension may be useful from a measurement point of view as well. For example, quick bedside screening for mass extension may provide useful information for researchers and clinicians who make decisions about the need for assessment and potential to benefit from rehabilitation. Although additional studies will be required, we recommend that future psychometric evaluations of the UE FM include designed, item-level analyses of this important item. Although the W/H UE FM has been evaluated for use with survivors of stroke with minimal28 and moderate29 UE impairment, additional research is needed to extend these results to other populations and settings. For example, future research should evaluate the reliability and validity of the W/H UE FM in survivors of stroke who exhibit severe impairment of UE function. Similarly, the clinical utility of measurements made using the W/H UE FM during the acute, subacute, and chronic phases of recovery should be evaluated. It is also important that the convergent and discriminant validity of the W/H UE FM be assessed by administering it in conjunction with other tests of wrist and hand motor ability.

In the interim, we recommend that clinicians and researchers consider using the W/H UE FM with survivors of stroke who exhibit mild and moderate UE impairment. In cases where limited mass flexion and mass extension are observed, we recommend that professionals access the full-scale UE FM to gather a more comprehensive picture of UE function.

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This study is limited by the following factors. The W/H UE FM data analyzed herein were collected as part of larger trials that used the UE FM. Performance may have been affected by the administration of extra items. Next, these data were collected only from stroke survivors exhibiting minimal UE impairment and do not represent the full range of UE abilities in stroke survivors. As such, these findings should be viewed as preliminary.

The limitations of the UE FM are also applicable. First, proximal functions are more heavily weighted than are distal functions, such as the wrist and hand items that compose the W/H UE FM. Second, although the instrument includes hand items, finger movement and function is not specifically assessed, a limitation that is not overcome by the W/H UE FM. Finally, previous research5,19 demonstrates that the UE FM does not always function as a single unidimensional construct. These limitations should be kept in mind when considering use of the UE FM and W/H UE FM.

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The W/H UE FM provides a reliable, valid, rigorous, and easy-to-administer bedside assessment of wrist and hand motor ability for use with mildly impaired stroke survivors. This tool performed well in a sample of mildly impaired stroke survivors exhibiting the ability to perform mass flexion and mass extension movements. Future psychometric studies of the W/H UE FM should include examinations of item 7: mass extension as a potentially powerful predictive tool.

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psychometrics; rehabilitation; stroke; upper extremity

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