### Design

This research was a clinical measurement and cross-sectional study. Participants received GS tests twice; more specifically, the first test was administered on Friday and we carried out the second test on the following Monday.

### Participants

Patients with upper extremity dysfunction due to traumatic occupational injuries were recruited in a rehabilitation center. All patients were receiving inpatient rehabilitation services in the rehabilitation center when they were recruited. The following inclusion criteria were applied: (1) aged 18 years or above; (2) having a traumatic injury in unilateral upper extremity; (3) being capable of being evaluated for GS, confirmed by an occupational therapist experienced in hand therapy; (4) remaining dysfunction in injured upper extremities; and (5) having good compliance with occupational therapists’ daily treatment instructions. The following exclusion criteria were applied: (1) having concurrent injuries in any other parts of the body; (2) experiencing pain when performing maximal isometric GS (visual analogue scale > 3); and (3) not being able to attend the second GS test.

All participants signed an informed consent form in accordance with the Declaration of Helsinki, and the study was approved by the medical ethics committee of the rehabilitation center.

### Procedures

In this rehabilitation center, all patients receive rehabilitation services five days per week, from Monday to Friday. During weekends, they usually go home or stay in wards and do not receive any formal rehabilitation services from clinical practitioners. The aim of this study was to estimate the test-retest reliability and the range of measurement errors of GS test. To avoid any bias from interventions, we arranged the first test on Friday and the second test on the following Monday. Therefore, we hypothesized that because no effective interventions were delivered in the short interval between the two tests, none of the participants would have experienced a real change in GS. After signing the consent form, demographic data including gender, marital status, age, height, body weight, and dominant hand were collected from each participant. In addition, injured sides, injury sites, and the number of days since injuries were confirmed.

### GS test

Prior to starting the first test, participants were instructed to sit on a chair and maintain the posture recommended by the American Society of Hand Therapy [16] and Roberts et al. [17]. The participants sat with their feet flat on the floor, the shoulder adducted 0 degree, the elbow flexed at 90 degrees, the forearm in a neutral position, and the wrist extended to 30 degrees. The dynamometer used in this study was a calibrated Jamar Hydraulic Hand Dynamometer (model SH5001, Saehan Corp, Masan, Korea) which was the most commonly used one and showed excellent reliability for the measurement of GS in previous studies [17]. Verbal instructions and demonstration about how to perform GS test were provided to each participant prior to the test. Once everything was ready, the participants were instructed to exert maximum grip at the second handle position and to maintain the contraction for five seconds. Three consecutive trials were performed with both injured and healthy upper extremities and there was 15 s of rest period among trials to prevent muscle fatigue. All participants started the test with their healthy hands. The value at which the needle of the dynamometer stopped was recorded for each trial. The second test followed the above procedures and used the same dynamometer for all patients. In the current study, the same occupational therapist experienced in hand therapy was responsible for all participants’ GS tests.

### Statistical analysis

Descriptive statistics were computed to illustrate participants’ demographic characteristics. Both the one-sample Kolmogorov-Smirnov test and histogram plot were applied to check for the normality of continuous variables. We used the data of the first trial, the mean of the first two trials (mean_{2}), and the mean of the three trials (mean_{3}) to estimate the test-retest reliability and the measurement error of GS of injured and healthy upper extremities. ICC_{2,1} as well as their 95% confidence intervals (CI) were calculated [5]. An ICC value higher than 0.9 was considered excellent. In addition, a paired *t*-test was applied to verify if there was any systematic bias between the first and second tests. The MDC_{95} and standard error of measurement (SEM) were calculated using the following formulas [18]:

$$ {\mathrm{MDC}}_{95}=1.96\times \sqrt{2}\times \mathrm{SEM} $$

(1)

$$ \mathrm{SEM}=\mathrm{SD}\times \sqrt{1- ICC} $$

(2)

To verify whether there were any other relationships between GS and measurement errors, the Bland-Altman plots were created based on the values of mean_{3}. A systematic error is confirmed if the 95% CI for the mean value of differences does not include 0. The LoA_{95} was calculated by using the Bland-Altman plots which present the scatter of differences between the first and second tests (y-axis) against the average of the first and second GS tests (average GS) (x-axis) [19]. If the differences are normally distributed and do not show any associations with the average GS, limits of the LoA_{95} are computed as

$$ {\mathrm{LoA}}_{95}={\mathrm{mean}}_{\mathrm{difference}}\pm 1.96\ {\mathrm{SD}}_{\mathrm{difference}} $$

(3)

where mean_{difference} is the mean of differences between the two tests, and SD_{difference} is the standard deviation of the differences. This implies that 95% of the differences will lie between the upper and lower limits.

In injured upper extremities, the Spearman’s correlation coefficient *ρ* between the observed differences, which were not normally distributed, and the average GS was 0.118 (*p* = 0.310). Therefore, residuals were defined as the differences between observed differences and the mean of differences. It was observed that the absolute values of residuals (|*R*|), which were the distances between the observed differences and mean_{difference}, tended to increase as the average GS increased in upper extremities with poor GS. However, in upper extremities with high GS, this trend was not distinct. To identify the most appropriate cutoff point on the average GS to separate the above two conditions, the Spearman’s correlation coefficient *ρ* between the |*R*| and the average GS lower than each possible cutoff point on the average GS was calculated. This was because the |*R*| was not normally distributed. The cutoff was defined as the point where the relationship between the |*R*| and the average GS had the highest Spearman’s correlation coefficient. The Bland-Altman plots were then constructed again for the two conditions according to Bland and Altman’s recommendations [13]. First, we regressed the |*R*| on the average GS to derive

$$ \left|R\right|=c0+c1\times \mathrm{average}\ \mathrm{GS} $$

(4)

Second, the LoA_{95} was calculated using the following formula:

$$ {\mathrm{LoA}}_{95}={\mathrm{mean}}_{\mathrm{difference}}\pm 1.96\times \sqrt{\pi \div 2}\times \mid R\mid $$

(5)

Once upper and lower limits of the LoA_{95} were calculated, one-to-one matches between integral GS scores and transformed ranges of random errors with 95% certainty were created for convenience in clinical application. The transformed lower and upper limits of the ranges of random errors were calculated using the integral GS scores plus the upper and lower limits of LoA_{95}, respectively.

All statistical analyses were performed with the IBM SPSS Statistics 20. The level of significance was set at *p* < 0.05 for all statistical analyses performed.