Kinetic gait analysis, as assessed on a force plate or pressure mat, has become the gold standard for objectively evaluating limb function in animals. The high cost of the equipment, large amount of space required, and need for specially trained operators for data acquisition make this form of analysis largely unavailable in most clinical settings.1 Several numerical rating and visual analog scales have been validated for subjective evaluation of limb function in canine patients as an alternative to kinetic gait analysis, but little agreement has been found between scoring systems, and the results most accurately refect force plate gait analysis findings only when the lameness is severe.2,3 Gillette and Angle4 reviewed recent developments in locomotor analysis of dogs in 2008 and commented on the validity of both kinetic and kinematic analysis in veterinary medicine, noting again the limitations of cost, space needs, and need for specialized knowledge of locomotor analysis. Rumph et al5 reported multiday variation in clinically normal Greyhounds when trotting on a force plate during 3 consecutive days and suggested that studies evaluating medical or surgical treatments should be interpreted with caution because of the variation in ground reaction forces within and between days.
In practice, many clinicians use a subjective assessment of BW distribution in a standing dog when lameness is not visually evident by manually lifting individual feet and subjectively assessing the amount of weight bearing.6,7 Objectively, the percentage of BW placed on each limb at a stance can be evaluated with force plate analysis.8 A study9 of dogs undergoing hip joint surgery found that the percentage of BW carried by each limb is a valid measurement for differentiating which leg is most affected. As an alternative to the use of force plate analysis, a computerized device to simultaneously measure static quadruped weight distribution has been investigated.10 Placement of bathroom scales under each hind limb has also been used to measure static weight load distribution in dogs; in that investigation, bathroom scales were placed only under the hind limbs because placement under each limb, forelimbs included, was perceived in practice as difficult and unrewarding.11 A platform with 4 separate recording units for measurement of weight bearing has been used for detection of lameness and hoof discomfort in dairy cattle since at least 2006.12,13 Similar devices have been used for lameness evaluation in dogs. In a recent study,a evaluation of static quadruped load distribution and dynamic peak vertical forces derived from force plate gait analysis revealed a greater difference between lame and nonlame limbs on static weight bearing than on trotting gait analysis, suggesting that static weight bearing may be more sensitive than gait analysis during locomotion for detection of small weight-bearing differences.
A newer commercial weight distribution analyzer for small animals has been described as a diagnostic tool for detection of subtle lameness and monitoring of changes during rehabilitation programs following orthopedic and neurologic injuries.14 This device measures the distribution of BW on each limb during stance. Cole and Millis1 have recommended the use of stance analysis to aid veterinary practitioners in evaluating the limb with the largest expected increase in weight bearing following amputation for possible overuse. In the authors' experience, benefits of this type of analyzer, compared with gait analysis on a standard force plate, include the need for less space and time, lower cost, and ease of use and data acquisition. Stance variables collected with force plate gait analysis include peak vertical force and vertical impulse; stride length, velocity, acceleration, and dog size can all influence these values. Static stance analysis eliminates the motion variables associated with gait analysis by force plate measurements; however, deficiencies from a research perspective such as the inability to save individual measurement data (rather than mean data from each trial) within the existing software, as well as the potential for results to be influenced by positioning of the handler, proximity of the closest wall, positioning within an enclosed space, and local environmental factors during testing, have been described.10 The purpose of the study reported here was to assess the single-day and multiday repeatability of stance analysis results for dogs with hind limb lameness as measured with a single commercial system. Our hypothesis was that measurements of BW distribution in lame dogs would have a high degree of repeatability during single-day and multiday trials.
Materials and Methods
Dogs
Dogs evaluated at The Kansas State University Veterinary Health Center Orthopedic Service for unilateral or bilateral hind limb lameness and considered for orthopedic surgery were included in the study. Dogs that met the study criteria were enrolled consecutively until a predetermined number of dogs for each trial type (number selected on the basis of the authors' clinical experience) was met. Dogs of any weight or breed and either sex were eligible for study inclusion. Dogs with forelimb lameness and those with neurologic disease were excluded, but dogs receiving medications were not excluded. There was no overlap of dogs between trial types. Measurements used for stance analysis were performed according to a protocol for clinical research approved by the Institutional Animal Care and Use Committee of The Kansas State University. Owner consent was not required because the analyzer was routinely used for clinical orthopedic evaluation of patients.
Data collection protocols
Data recorded from the medical records included signalment, limb affected (lame or most lame as determined on orthopedic examination), and diagnoses. All measurements were performed with a commercial weight distribution analyzerb that was calibrated by use of a registered known weight in accordance with manufacturer's instructions prior to use each day. The analyzer was placed in the center of a dedicated gait analysis laboratory, and leashed dogs were walked onto the device from behind the analyzer and encouraged to stand in a relaxed position with each foot placed in its respective quadrant. Each dog participated in trials prior to receiving any medications that day. The same 2 handlers were used for each trial. Handler 1 stood directly in front of the dog, and handler 2 stood directly behind the dog. Attempts were made to have the dog stand squarely on the mat with its head facing forward; this was achieved with the use of peanut butter to keep the dog's attention. If a dog was observed to move its head position to the side or to move its feet, the measurements during the motion were considered invalid and removed from analysis. The position of the mat within the room remained the same for all data collections.
Single-day trials—Fifteen dogs were included in single-day trials. Five to 10 valid measurements/limb were collected over a 30-second period for each trial with the dog in a static standing position. The mean of these measurements was calculated as the mean distribution of weight on each limb; BW was measured in the same manner. The dog was then walked out of the room and returned immediately afterward for 4 additional 30-second trials, each at 2-minute intervals, for a total of 5 trials/dog.
Multiday trials—Thirty-one dogs were included in multiday trials. The dogs were placed on the analyzer, and measurements were collected in a manner identical to that used in single-day trials. This process was repeated on the following day for a total of 2 trials/dog (1/dog/d).
Statistical analysis
Data were assessed as normally distributed on the basis of visual assessment of graphed data. For all statistical analyses, values of P ≤ 0.05 were considered significant.
Single-day trials—Measured variables from each trial included BW (in kilograms) and weight load distribution (measured as percentage of BW) on the affected (lame) hind limb, contralateral hind limb, ipsilateral forelimb, and contralateral forelimb. Symmetry indices for the forelimbs and hind limbs were calculated as follows:
where L1 represents the weight load (measured as percentage of BW) on the limb with the higher value and L2 represents the weight load on the contralateral forelimb or hind limb (measured as percentage of BW).15,16 An SI of 0 indicates perfect symmetry with this calculation.
Body weight, weight load distribution on each limb, and calculated SIs were compared by use of repeated-measures ANOVA for the 5 trials with a post hoc Newman-Keuls multiple comparison test. Data analyses were performed with a commercial statistical calculator.c Data are reported as mean ± SD for all dogs across trials. To assess repeatability, a multiple correlation coefficient (r) was determined by multiple regression analysis of each measured or calculated variable for the 5 trials by use of the same calculator.c Additionally, the LCCC (where −1 represents perfect discordance and 1 represents perfect concordance) was calculated with an online calculatord to assess repeatability of measurements. A mean CV was calculated for each measured variable as the SD of repeated trial measurements divided by the mean of repeated trial measurements and was expressed as a percentage.
Multiday trials—Body weight, weight load distribution on each limb, and calculated SIs were compared between trial days by paired t tests performed with a commercial statistical calculator.c Data are reported as the mean ± SD for all dogs across trials on each day. The same calculatorc was used to assess repeatability by calculation of a Pearson correlation coefficient (r) between day 1 and day 2 trials for each measured or calculated variable. The LCCC was also calculated as described for single-day trials. A mean CV was calculated for each measured variable as the SD of paired trial measurements divided by the mean of paired trial measurements and was expressed as a percentage.
Results
Single-day trials
The 15 clinical patients in single-day trials consisted of 4 Labrador Retrievers, 2 Golden Retrievers, and 1 each of the following breeds: Beagle, Bernese Mountain Dog, Greater Swiss Mountain Dog, Great Pyrenees, American Bulldog, and Rottweiler. Two were pit bull–type dogs, and 1 was a Golden Retriever-Poodle cross. Nine were castrated males, and 6 were spayed females; the mean ± SD age was 5.65 ± 2.66 years (range, 1.30 to 11.05 years). Nine of 15 dogs had unilateral left hind limb lameness, and 6 had unilateral right hind limb lameness. Fourteen dogs had unilateral cranial cruciate ligament tears, and 1 dog had bilateral cranial cruciate ligament tears but was visibly lame only on the left hind limb on orthopedic examination.
Mean ± SD measured and calculated variables for the 5 trials were summarized (Table 1). There were no significant differences among trials for BW (P = 0.10) or for weight load distribution (percentage of BW) on the lame hind limb (P = 0.06), contralateral hind limb (P = 0.50), ipsilateral forelimb (P = 0.54), or contralateral forelimb (P = 0.72). The forelimb SI did not differ significantly (P = 0.56) among trials; however, the hind limb SI varied significantly (P = 0.022), with the mean hind limb SI of trial 2 (63.8 ± 69.0) and trial 4 (69.5 ± 63.1) lower than that of trial 3 (94.4 ± 63.1).
Mean ± SD weight distribution variables and results of analysis for repeatability (multiple correlation coefficient [r] and LCCC) and variability (CV) of single-day trial data for 15 dogs with unilateral hind limb lameness that participated in a study to assess stance analysis results as measured with a single commercial system.
| Variable | Mean ± SD | r | P value* | LCCC (95% CI) | CV (%) |
|---|---|---|---|---|---|
| BW (kg) | 39.75 ± 0.37 | 0.999 | 0.001 | 0.863 (0.675 to 0.926)) | 0.93 |
| Weight distribution (% of BW) | |||||
|   Lame hind limb | 10.73 ± 2.25 | 0.915 | 0.001 | 0.682 (0.466 to 0.822) | 20.97 |
|   Contralateral hind limb | 20.68 ± 2.89 | 0.948 | 0.001 | 0.817 (0.675 to 0.901) | 14.00 |
|   Ipsilateral forelimb | 33.85 ± 5.78 | 0.704 | 0.113 | 0.214 (−0.108 to 0.495) | 17.06 |
|   Contralateral forelimb | 34.87 ± 5.64 | 0.751 | 0.060 | 0.176 (−0.145 to 0.463) | 16.18 |
| SI | |||||
|   Forelimb | 33.69 ± 22.72 | 0.640 | 0.218 | 0.190 (−0.133 to 0.477) | 67.44 |
|   Hind limb | 75.61 ± 21.53 | 0.964 | 0.001 | 0.726 (0.531 to 0.847) | 28.48 |
Data represent the results for 5 sequential trials/dog performed in a single day. One dog had bilateral cranial cruciate ligament tears but was deemed lame on the left hind limb only by orthopedic examination. The SIs were calculated as previously described15,16; an SI of 0 represented perfect symmetry.
P value is shown for the multiple correlation coefficient.
CI = Confidence interval.
Patient BW (r = 0.999) as well as weight distribution on the lame hind limb (r = 0.915), contralateral hind limb (r = 0.948), and hind limb SI (r = 0.964) were significantly (P < 0.001 for all comparisons) correlated among multiple single-day trials (Table 1). The forelimb SI was most variable among trials (r = 0.640) and was not significantly correlated among trials. The LCCC was highest for BW and lowest for weight distribution on the contralateral forelimb. The CV was highest for the forelimb SI and lowest for BW; CVs for weight distribution on each limb ranged from 14.00% for the contralateral hind limb to 20.97% for the lame hind limb. The CV for the hind limb SI was substantially smaller than that for the forelimb SI, but the values were not compared statistically.
Multiday trials
The 31 patients in multiday trials included 11 Labrador Retrievers, 4 Golden Retrievers, 2 German Wirehaired Pointers, 2 Australian Shepherds, and 1 of each of the following breeds: English Bulldog, Bernese Mountain Dog, Chihuahua, Bullmastiff, Whippet, and Akita. Two were pit bull–type dogs, and 4 were mixed-breed dogs. There were 18 spayed females, 10 castrated males, 2 sexually intact females, and 1 sexually intact male; mean ± SD age was 6.02 ± 2.59 years (range, 1.71 years to 10.42 years). Sixteen of 31 (52%) and 15 of 31 (48%) had unilateral left and right hind limb lameness, respectively. Twenty-eight (90%) dogs had a diagnosis of unilateral cranial cruciate ligament tear, 2 (6%) had medial patellar luxation combined with a cranial cruciate ligament tear, and 1 (3%) had a hip joint luxation.
Mean ± SD measured and calculated variables were summarized for each trial day (Table 2). There were no significant interday differences for BW (P = 0.33) or for weight distribution on the lame (P = 0.29) or contralateral (P = 0.24) hind limb or the ipsilateral (P = 0.90) or contralateral (P = 0.97) forelimb. There was no significant (P = 0.97) difference in hind limb SI between trial days, but a significant (P = 0.043) increase was observed for the forelimb SI day 2 (mean, 39.28), compared with that on day 1 (26.58). The mean change in weight bearing on the lame hind limb between days was a nonsignificant increase of 1.07% of BW (range, −8% to 13%). Thirteen of 31 dogs had a numerical decrease in symmetry of the hind limbs on day 2, whereas 18 had numerically increased values. Redistribution of weight to the lame hind limb was primarily from the contralateral hind limb, which had a mean change of −1.23% of BW on the second day. The ipsilateral forelimb and contralateral forelimb had considerably smaller mean changes (0.19% and −0.07% of BW, respectively) in weight distribution between days.
Mean ± SD weight distribution variables and results of analysis for repeatability (Pearson correlation coefficient [r] and LCCC) and variability (CV) of multiday trial data for 31 dogs with unilateral hind limb lameness that participated in a study to assess stance analysis results as measured with the same commercial system as in Table 1.
|  | Mean ± SD |  |  |  |  | |
|---|---|---|---|---|---|---|
| Variable | Day 1 | Day 2 | r | P value* | LCCC (95% CI) | CV (%) |
| BW (kg) | 31.13 ± 11.50 | 30.85 ± 11.49 | 0.990 | 0.001 | 0.990 (0.979 to 0.995) | 2.93 |
| Weight distribution (% of BW) | ||||||
|   Lame hind limb | 7.77 ± 4.92 | 8.84 ± 6.42 | 0.552 | 0.001 | 0.524 (0.236 to 0.727) | 37.62 |
|   Contralateral hind limb | 25.0 ± 8.16 | 23.77 ± 7.75 | 0.743 | 0.001 | 0.733 (0.520 to 0.860) | 12.72 |
|   Ipsilateral forelimb | 35.16 ± 7.51 | 35.35 ± 9.15 | 0.455 | 0.010 | 0.446 (0.124 to 0.683) | 13.72 |
|   Contralateral forelimb | 32.10 ± 6.07 | 32.03 ± 8.73 | 0.307 | 0.093 | 0.288 (−0.043 to 0.562) | 15.51 |
| SI | ||||||
|   Forelimb | 26.58 ± 23.34 | 39.28 ± 30.45 | 0.248 | 0.178 | 0.215 (−0.097 to 0.489) | 60.36 |
|   Hind limb | 103.54 ± 59.21 | 103.97 ± 50.20 | 0.473 | 0.007 | 0.467 (0.147 to 0.698) | 29.71 |
Data represent results for 1 trial/dog performed on each of 2 consecutive days.
P value is shown for the Pearson correlation coefficient.
See Table 1 for remainder of key.
Patient BW (r = 0.990) and weight distribution on the lame hind limb (r = 0.552) and contralateral hind limb (r = 0.743) were each significantly (P = 0.001 for all comparisons) correlated between days 1 and 2 (Table 2). Similarly, hind limb SIs were significantly (P = 0.007) correlated between days 1 and 2 (r = 0.473). The LCCC was highest for BW and lowest for forelimb SI. The CV was highest for forelimb SI and lowest for BW. The CVs for weight distribution on each limb ranged from 12.72% for the contralateral forelimb to 37.62% for the lame hind limb.
Discussion
Weight distribution (stance) analysis allows for assessment of lameness when the motion-related variables of kinetic force plate gait analysis are eliminated, but to the authors' knowledge, there are no reports of the degree to which many other common variables associated with force plate gait analysis, such as trial, handler, habituation, and day,5,15,17 may influence stance analysis data. Our study assessed repeatability among multiple trials within 1 day and between 2 different days with the analyzer placed in a static location in 1 room, where handler 1 was positioned at the front of the dog with peanut butter to keep the dog's attention and handler 2 was directly behind the dog. Habituation was not attempted prior to performing measurements in the present study. Given the ease of the task of standing on the mat, we believed that habituation would not be necessary and would not substantially influence results of repeated trials; we also considered that a lack of habituation better represented routine use of the analyzer for assessment of clinical patients.
Our results indicated that, with the device used, stance analysis produced consistent results for measurement of weight distribution (percentage of total BW) on the lame hind limb and contralateral hind limb on 2 consecutive trial days. The Pearson correlation coefficient is a relative repeatability coefficient for test-retest assessment in biologic studies, and in the present study, multiday measurements with several trials performed each day were significantly correlated. The LCCC is used to measure concordance between a new test or measurement and a gold-standard test or measurement and thus quantifies agreement between 2 measures of the same variable. The LCCCs of 0.524 and 0.733 for lame and contralateral hind limbs, respectively, indicated that repeatability of the method between the 2 trial days varied between these 2 limbs. The Pearson correlation coefficients and LCCCs for forelimbs were numerically lower than those of the hind limbs, likely because of greater day-to-day and moment-to-moment forelimb variations in redistribution of weight bearing, including head position variation, by individual dogs with hind limb lameness. The CV for weight distribution between trial days ranged from 12.72% on the contralateral hind limb to 37.62% on the lame hind limb. Although not directly comparable, these results were similar in magnitude to findings in a previous study18 on variability of force plate analysis data for 5 dogs, which found that the percentage of variance attributable to dogs and to repetitions ranged from 14% to 69% and from 29% to 85%, respectively. In the present study, the variation between trial days was most likely attributable to daily changes in the severity of musculoskeletal disease and related pain in individual dogs. Dogs in the multiday trial had a slight but nonsignificant increase (1.07% of BW) in weight distribution on the lame hind limb from days 1 to 2, which was consistent with information from a previous study.19 Hicks et ala detected a greater difference in static weight bearing between lame and nonlame limbs of dogs with hind limb lameness, suggesting that static weight bearing may be more sensitive than trotting gait analysis for detecting small weight-bearing differences. We speculated that larger variation among measurements by stance analysis in the present study may have also represented increased, rather than decreased, sensitivity to detect such changes.
Stance analysis also produced consistent measurements for weight distribution on the lame hind limb and contralateral hind limb during repeated trials on the same day. Significant correlation with coefficients of 0.915 and 0.948 and LCCCs of 0.682 and 0.817 among 5 consecutive trials for the lame hind limb and contralateral hind limb, respectively, indicated the repeatability of the method. Correlation coefficients and LCCCs of the forelimbs in the same-day trials were less consistent, likely because of the same reasons described for multiday trials. Owing to the potential influence of habituation of the dog to the room, handler, and equipment, insufficient trials may have been performed to allow for normalization of measurements. The CVs for weight distribution on limbs ranged from 14.00% for the contralateral hind limb to 20.97% for the lame hind limb, which was consistent with the CVs in a previous study18 for forelimb force plate variability between locomotor trials.
Force plate gait analysis can be influenced by body type or size.17 In the author's opinion, stance analysis performed with the commercial system used in the present study is not limited as much by body size or conformation and is thus easier and faster for assessing vastly different breeds than force plate analysis. Breed and size were not controlled for in our study, likely leading to an increase in variability. Mölsä et al20 found that after controlling for the effects of relative velocity, functional limb length, and BW by use of ANCOVA, there were no significant differences between breeds when assessing for differences in ground reaction forces between healthy Rottweilers and Labrador Retrievers without orthopedic disease.20 The use of standardized normalization methods and inclusion of dogs that have similar conformation and BWs have significant effects in reducing variability of measurements with other devices.5,15,17 It is unknown whether repeatability would be improved for measurement of weight distribution variables in a more homogenous population of dogs.
Various statistical analysis methods have been used to assess continuous variables in attempts to evaluate reproducibility of measurements from trial to trial, including correlation analysis, paired t tests, least squares analysis of the slope and intercept for linear regression data, determination of the CV, and calculation of the interclass correlation coeffocient.18,20–23 No single method fully assesses the desired reproducibility characteristics. The LCCC is a recently developed measurement for repeatability of laboratory data and was chosen as an analysis method in the present study because it avoids the shortcomings associated with the other statistical methods described.24 In the present study, the LCCC data showed that intraday repeatability of weight distribution among trials varied among individual limbs with the analyzer used. Repeatability of total BW measurement was highly consistent between trial days (r = 0.990; LCCC = 0.990), and the CV for this variable was low (2.93%). The multiday CV was numerically higher than that found for single-day weight measurements (0.93%), and we considered this likely attributable to changes in hydration status overnight and withholding of food in preparation for surgery on the second day. Although most of the LCCC values in the study would be considered low for in vitro laboratory procedures,24,25 published values for the relative strength of the associations in biologic systems are lacking in veterinary medicine, and these data may serve as comparisons with correlation coefficients for future studies.
Trial repetition has been reported to lead to variation in ground reaction forces.26 However, Fanchon et al26 found that reliable data can be obtained from a single training session on a treadmill. Between days 1 and 2 in the present study, the only significant difference in measured or calculated variables was forelimb SI. Given the lack of significant changes between trial days for all other weight distribution variables, it appears that a training period is not needed to acclimate dogs to the analyzer used in this study for assessment of hind limb lameness. In addition, a lack of significant changes among trials, with the exception of hind limb SI performed in the single-day assessment, suggested the same. Rumph et al5 reported interday variation in clinically normal Greyhounds trotting on a force plate on 3 different days, suggesting that small variations in ground reaction forces within and between days in studies evaluating medical or surgical treatments should be interpreted with caution. The present study did not evaluate efficacy of treatment, and the magnitude of change in weight distribution or SI needed to detect clinical changes in hind limb lameness remains unknown. Evaluation of dogs with forelimb lameness was also beyond the scope of the study.
Forelimb SIs varied more than hind limb SIs in our study, likely because weight distribution shifts from the lame limb in an inconsistent manner that varies by dog and by many other factors (health of the other limbs, environmental factors, or concurrent systemic disease potentially causing exercise intolerance). The hind limb SI was correlated between trial days (r = 0.473; P = 0.007), although the mean hind limb SI varied significantly in individual dogs over repeated single-day trials.
In a study by Keebaugh et al,17 pressure mat analysis of gait characteristics in small breed dogs at a walk was used to assess the influence of handler and leash side. No significant differences were observed with different handlers; however, leash side significantly influenced SIs of the dogs' forelimbs but not hind limbs. The CVs for each limb were also evaluated in that study,17 with values ranging from 21% to 36% and similar to those in the present study. The forelimb SIs for multiday trials were found to differ in our study, similar to the findings of Keebaugh et al.17 Leash side was not recorded in the present study, but handler 1 was directly in front of the dog and handler 2 was directly behind the dog in each trial, and their positions remained constant for all measurements. It was therefore unknown whether variations in the multiday forelimb SI might have been attributable to leash side. Phelps et al10 assessed the position of a weight distribution analyzer in a gait analysis laboratory and found that positioning the mat in the center of the room resulted in dogs leaning toward the handler with their forelimbs and away from the handler with their hind limbs. When the analyzer was placed along a wall, dogs had a tendency to lean toward the wall.10 The significant increase in forelimb SI between day 1 and day 2 in the present study could have resulted from habituation to the room, handler, and analyzer, consistent with the findings of Fanchon et al26 during measurement of ground reaction forces in dogs trotting on a treadmill on 3 consecutive days. In that study,26 there was a significant difference in vertical force variables between day 1 and subsequent days, with most measurement variations attributable to the factor of dog.
Overall, the analyzer used in the present study provided repeatable results for hind limb weight distribution data with variability similar to that historically reported in force plate analyses. Additional studies to assess changes in weight distribution with changes in head position, position of the mat within a room, or with various handlers and handler positions should be performed to assess the importance of standardization of these features among trials. In addition, studies to assess potential effects of breed and body size on these variables, utility of the analyzer for assessment of treatment response, and repeatability of measurements in dogs with forelimb lameness are recommended.
Acknowledgments
No financial support was received for the purchase of the weight distribution analyzer or for the study methods. The authors declare that there were no conflicts of interest.
ABBREVIATIONS
| BW | Body weight |
| CV | Coefficient of variation |
| LCCC | Lin concordance correlation coefficient |
| SI | Symmetry index |
Footnotes
Hicks DA, Millis DL, Arnold GA, et al. Comparison of weight-bearing at a stance vs. trotting in dogs with rear limb lameness (abstr), in Proceedings. 32nd Annu Conf Vet Orthoped Soc 2005;12.
Stance Analyzer, LiteCure Companion Animal Health, Newark, Del.
Winks SDA, version 7.0.9, Texassoft, Cedar Hill, Tex.
NIWA statistical calculators. Lin's concordance. Available at: www.niwa.co.nz/node/104318/concordance. Accessed Oct 22, 2018.
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