Allometric Scaling Grip Strength Measurements to Predict Upper Body Strength

Blake J. Surina

Abstract:     The data obtained from 1123 untrained subjects, upon joining a health club, were used in a study examining the relationship between grip strength and upper body strength as represented by the shoulder press and pulldown exercises. Absolute strength values generally classify larger individuals as stronger but this is usually not the case when strength to weight ratio, (relative strength) is taken into account. Allometric scaling research has shown that smaller subjects are favored when strength is examined in relative terms. The purpose of this study was to develop a method of classifying an individual’s strength independent of body weight, and to increase the ability of handgrip dynamometer measurements to predict upper body strength.  The results of this study showed that simple allometric corrections increased the correlation coefficient 49.4% in males and 54.4% in females, when examining the relationship of grip strength to upper body strength.  This method will enable the clinician to more accurately predict and classify a subject’s upper body strength using a hand-grip dynamometer.   

Statement of the Problem:  

     The handgrip dynamometer is often used as a tool for assessing a subject’s upper body strength.  Grip strength measurements are also used for documenting improvement in strength and/or functional ability after disuse or injury.  There has been limited research (Chimes, 2006) that attempted to draw a correlation between objective measurements of grip strength and objective measurements of upper body strength. This limited research is an important consideration for the practical application of using grip strength as a valid indicator of upper body strength.  

   A number of studies have been published suggesting standards to use when assessing normal function, (Schmidt 1970, Corbin 1978, Mathiowetz 1985).  Absolute strength scores are often criticized as being more advantageous for larger subjects.  Corbin (1976) created standards using a relative strength classification model, (i.e. grip strength per unit of body weight).  The creation of relative standards shifted the advantage to smaller subjects who have higher strength to weight ratios compared to their larger, similarly proportioned counterparts.  

     Recent evidence suggests that allometric scaling, based on individual body dimensions, can substantially increase the accuracy of classifying a subject’s upper body strength.  Recent studies have attempted to allometrically scale the subject’s body mass or forearm girth as a means to further increase the accuracy of classifying upper body strength based on grip strength measurements, (Giardina 1997, Amara 2003, Jurimae 2008, Zoeller 2008).  The purpose of this study is to determine the correlation coefficients relating allometrically scaled grip strength to upper body strength measurements.  


     The anthropometric and strength data was collected from the initial assessment of 1123 subjects (491 males, 632 females) upon joining a community wellness and fitness center.  Subject were untrained and ranged in age from 9 to 84 years old.  Variables collected included: body weight, (Befour: Model PS 6600) to the nearest 0.1 kilo, and height using wall-mounted stadiometer (Seca Accu-Height) to the nearest 0.1 centimeter.  Girth measurements were taken with a Gulick fiberglass measuring tape at the maximum circumferences of the forearm, flexed biceps, and calf. Skinfold measurements were taken with a Harpenden Skinfold Caliper (British Limited, UK) at 7 sites, with bone diameter measurements taken with a Lafayette skeletal anthropometer at the elbow and the knee.  All measurements were taken on the right side of the body as described using the procedures outlined by Lohman (1988).

     Subject’s grip strength was assessed with a Jamar handgrip dynamometer, in a seated position, with shoulder adducted and the elbow bent at 90 degrees.  The Jamar dynamometer used a hand setting of “2”, with the occasional larger male subjects using a setting of “3”, and the occasional small child or female subject using a setting of “1” setting as per the recommendation by Montoye (1964). The best of three trials was recorded with each hand, with all measurements having the wrist held in a neutral position.  Right or left hand dominance is also recorded. 

     Upper body strength measurements were obtained with an isokinetic strength testing dynamometer (Ariel Dynamics Inc.) at a fixed velocity of 20 inches per second. All subjects were given a warm up set of 3 to 5 repetitions to familiarize themselves with the machine before actual testing.  The average of 5 repetitions was recorded performing the shoulder press (pushing) and the lat pulldown exercises (pulling) concurrently. 

     Allometric scaling was performed using four different methods, based on subjects’ body weight, forearm girth, BMI, and mesomorphic component from somatotype evaluation, (Heath/Carter method).  Scaling was performed using a -1/3 scaling correction factor, adjusting each score to a relative strength value to the 2/3 power,  (Surina, 2004, White and Seymour 2005).  


     Grip strength means and standard deviations are shown for male and female subjects between 9 and 84 years, (Tables 2a & 2b).  Subject’s ages between 9 and 20 were displayed in yearly increments to examine more closely the changes and relationships with developing strength in children.  Age groups were combined if less that 4 subjects were collected in the age group, (i.e. 10 -12, and 70-84).     

     Five repetitions means and standard deviations of the shoulder press and the lat pulldown are shown for male and female subjects between 9 and 84 years, (Tables 3a & 3b).   Subject’s ages between 9 and 20 are displayed in yearly increments to examine more closely the changes and relationships with developing strength in children.  Age groups are combined if less than 4 subjects were collected in the age group, (i.e. 10 -12, and 70-82).      

     The relationship between grip strength and upper body strength were examined using a correlation analysis incorporating the SPSS 13.0 software package.  The correlation analysis was done on all subjects, and also broken down by male and female separately.  The recorded sum from the combined right and left grip strength values was compared with the five-repetition average for the shoulder press and lat pulldown strength values.   Correlation coefficients compared absolute strength values for all subjects at .794, while broken down by sex, males were r= .603, and females were r= .534.  The observed correlations were substantially higher than the values reported by Chimes (2006) of r= .439 and r= .493 when comparing grip strength values to absolute strength values of internal and external shoulder rotation respectively.

     Relative strength values were evaluated comparing the combined right and left hand grip strength values, and the sum of the five-repetition average of shoulder press and lat pulldown values divided by the subject’s body weight. Correlation coefficients for relative strength for males decreased slightly to r= .572, while the females increased to r= .635 when comparing relative grip strength to relative upper body strength.

     Allometric scaling was performed by taking the subject’s scaled variable^(1/3)) over the reference scaled variable^(1/3).  Reference variables used were constructed from the group means for the male and females of each scaled variable, i.e. weight, forearm girth, BMI and mesomorphic body component score (Table 1).   The correction factor represents the adjustment for relative strength scores needed to compensate for body dimensional differences in strength to weight ratio.   Allometric scaling using the subject’s body weight increased the correlation coefficient to r= .683 in males, and to r= .728 in females when comparing relative grip strength to relative upper body strength.

     The correlation r= values were similar when scaling from the subjects Body Mass Index, for males, r= .671, and females r= .722. Forearm girth measurements, often used in predictive equations for grip strength standards, provided the lowest correlation of the scaling variables examined, at r= .596 and r= .661 for males and females respectively.   The highest correlation coefficient was demonstrated by allometrically scaling the relative strength values by the subject’s mesomorphic somatotype component obtained by the Heath-Carter method at r= .699 and r= .789 for males and females respectively. 


     Allometric scaling provides a more meaningful index of strength performance for individuals of differing body dimensions, (Astrand, 1977).  The most common reason for the lack of widespread use is the units of measurement are often cumbersome, and there has been disagreement as to which scaling exponent that should be used, although most researchers agree that it should fall between the ¾ or 2/3 scaling.  Our research showed that 2/3 scaling was the preferred exponent giving the highest correlations between grip strength and upper body strength.  

     Scaling variables is the simple process of inputting the scaled variable of the subject, selecting the yxfunction on a standard calculator, and inputting a (1/3) exponent.  This would be divided by the reference population’s scaled variable ^(1/3), (Surina, 2004).  The resulting correction factor would be the adjustment to the raw strength scores to account for inherent differences in strength to weight ratios due to body dimensions between individuals.  

                                    Subject’s Scaled Variable^(1/3)

                                  Reference Scaled Variable^(1/3)    =  113.5% adjustment for relative score

Group means and standards can be created for grip strength and upper body strength from the data provided in this paper.  By allometrically scaling raw grip strength data, more appropriate classification of grip strengths can be made by based on sex and age.  For most applications the use of body mass in the scaling exponent provides results similar to scaling the mesomorphic component, which is more complex and involves the use of various anthropometric equipment.  Furthermore the use of allometrically scaled grip strength data greatly increases the prediction of upper body strength in untrained populations.


     The coefficient of determination, i.e. squaring the r=values, shows the fraction of the variance in upper body strength that is accounted for by its linear relationship to grip strength measurements.  The ability to estimate upper body strength based on grip strength is increased 49.4% in males and 54.4% in females, by including allometric scaling adjustment for mesomorphy.  This was further demonstrated to be equally effective with scaling using body weight, (increase of 42.6% for males and 31.4% for females).  Using allometric scaling techniques by other investigators has been shown to be equally effective, although rarely used.   Amara (2003) reported a correlation coefficient of r= .845 for older adults (55 – 86 years) using allometric scaled models to create regression equations using sex, age, forearm girth and demispan in predicting grip strength. Obtaining scaling correction factors to increase in functionality and predictability of strength measurements should not be underestimated.


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