Open Access

ISSN: 2161-0940

Research Article - (2013) Volume 3, Issue 1

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**Keywords:**
Anthropometry; Correlation coefficient; Regression equation; Maximal tibial length; Supine length; Medicolegal aspect; Forensic medicine

Human bones just lie in the ground slowly degrading to atoms from which they were originally created, often the only reminder of past life. Height of a person, which itself is a sum of the length of certain bones and appendages of the body represent certain relationship with form of proportions to the total stature. It takes a very important role both in anthropological research and identification necessitated by medico legal experts. Height estimation by measurement of various long bones has been attempted by several workers with variable degree of success. One exhaustive work was done by Pan for estimation of stature from long bones including tibia. However the work was done more than a century ago and a more recent study is felt necessary due to various reasons. Any particular population gets reformed by the process of migration, invasion and sometimes also by natural ways such as famines, disaster that lead to natural auto selection. The region in which the present author has worked remains a testimony to many such past unfortunate incidents. There are indications that mobility in general has declined between European Mesolithic and late Neolithic, and that body size and shape may have become more variable throughout the continent following the Upper Paleolithic (The strange Horizon, a journal of Anthropology: 1996-1997). Stature prediction from measurement of long bones with the help of correlational calculus was first introduced by Professor Pearson [4]. Telkka [5] studied 115 male and 39 female dry skeletons. He took the maximum length of tibia for the purpose of finding out the stature of Finnish population; he opined about the need of a separate formula for estimation of stature of different racial population. Dupertius and Hadden [6] summarized that long bones of inferior extremity usually gives a closer estimate of stature than long bones of upper extremities. Allbrook [7] attempted to measure percutaneous tibial lengths from the medial condyle to the tip of medial malleolus with knee semi-flexed and foot partly everted and deduced the following formulae: 88.78 + 2.30 T (where, T=Tibial length). Lundy [8] concluded that length of the lower extremity provides the best estimate to measure stature of an individual. Nineteenth century was nearing its end when anthropologists convened an international meeting in Geneva [9] and promulgated the need of measuring oblique length of bones for correct estimation of stature. Mohanty [10] attempted to correlate percutaneous tibial lengths (from the medial condyle to the tip of medial malleolus) and stature of 1000 adult individuals belonging to the state of Orissa.

The present study was undertaken to deduce a regression equation formulae for prediction of stature from tibial length and vice versa; the authors also wanted to make a comparison (test of significance) of stature and dry tibial length separately for males and females.

23 years was selected as the lower limit of age group of the cadaver samples; this was done to eliminate the influence of the epiphyseal growth factor in formulation of the regression equations. The upper age limit was taken as 75 years. The maximum length of Tibia, a bone of inferior extremity was measured obliquely in the present study.

A busy morgue was chosen to obtain a sizeable number of fresh samples. The study was undertaken at the Department of Forensic Medicine at Calcutta Medical College, Calcutta Police morgue; the cadavers were from different parts of Eastern India, mostly from districts of Kolkata, 24 Parganas and Midnapore of West Bengal and also from adjoining states of Jharkhand and Orissa. Out of a total of 550 samples, 32 were rejected due to skeletal deformities in limbs and pelvis. The present study was made up of 294 male cadavers (56.76%) and 224 female cadavers (43.24%).

Maximum convexity of lateral condylar profile was determined and it was taken as one of the two reference points. The oblique length of tibia (Geneva conference) of left side was measured from the former point to the lowest point of medial malleolus of the corresponding side. The supine length was measured by steel tape in centimeters and the maximal tibial length was taken with the help of oblique calipers. The error of both the steel tapes and calipers was not more than 1 mm in 100 centimeters. The supine length of cadavers was taken after fixing the head in Frankfurt plane and the foot was kept at right angles to the table by a right angled wooden block. Left tibia was chosen arbitrarily for measurements of tibia to maintain uniformity. All the measurements were taken only by the first author to avoid interpersonal variation of measurements. With subtraction of 5 mm from the wet bone length, dry tibial length was obtained [11]. All the statistical values like mean, range, sample standard deviation, population standard deviation, regression coefficient, intercept, regression equation, standard error of estimate and correlation co efficient were calculated by using the software named MAT-LAB 7.1.

For Males**→** S=71.2333+2.5792 T

For Females**→**S=65.345+2.6914 T

Where, S= Stature (in centimeters); T= Dry Tibial length (in centimeters)

To test the reliability of the sample equations, the relevant formulae was used to calculate the‘t’ value. The‘t’ value calculated for males and females was much higher than the critical values of ‘t’_{(0.05)} with 40 degree of freedom (n-2) and ‘t’_{(0.05)} with 30 degree of freedom (n-2) respectively. Hence the null hypothesis was rejected. Thus, it is not realistic to assume that the regression coefficient of the population is zero. The square of standard error of estimate of male and female sample was compared using an “F test”. The F value was calculated to be 2.223. From the statistical tables (**Tables 1**-**4**) it was found that the [{critical F value} – {F_{0.05 (40,30)}}] was 2.011; since the computed F exceeded the critical F value, the null hypothesis was rejected and it was concluded that the regression coefficient b_{male} is significantly different from b_{female}. Thus, the same formulae cannot be used and separate formulae for males and females have to be used for correct estimation of stature Z.

Statistical Parameters | Males | Females |
---|---|---|

1.Sample size | 294 | 224 |

2. Cadaver supine length (Y) Mean Range Sample standard deviation Population S. D. |
164.0602 146.4-176.7 7.6120 ± 7.593 |
156.38 142.0-167.7 6.0263 ± 6.011 |

3. Dry tibial length (X) Mean Range Sample standard deviation Population S. D. |
35.9905 29.2-40.7 2.7341 ± 2.730 |
33.825 28.9-38.2 2.1224 ± 2.118 |

4. Correlation coefficient | 0.9264 | 0.9479 |

5. Standard error of estimate | 1.6664 | 1.6829 |

**Table 1**: Descriptive Statistics of the Samples (N=518).

For Males : •Regression coefficient (b) •Constant/intercept (a) •Regression equation •SE of estimate •Correlation coefficient (ryx) |
= 2.5792 = 71.2333 = 71.2333+2.5792x = ± 1.6664 = 0.9264 |

For females: •Regression coefficient (b) •Constant/intercept (a) •Regression equation •SE of estimate •Correlation coefficient (ryx) |
= 2.6914 = 65.3450 = 65.3450+2.6914x = ± 1.6829 = 0.9479 |

**Table 2**: Formulation of new regression equation of stature from tibial length.

Study | Male | Female | Sex Combined |
---|---|---|---|

Present study | S=71.2333+2.5792 T | S=65.345+2.6914 T | S=64.052+2.756 T |

Pearson (99) | S=78.664+3.378T | S=74.744+2.532T | |

Tr.Glesser^{1} |
S=78.62+2.52T | S=61.53+2.9T | |

Tr.Glesser^{2} |
S=86.02+2.19T | S=72.65+2.45T | |

Patel (64) | S=65.51+2.203T | ||

Joshi (65) | S=80.97+2.206T |

**Table 3**: Different regression equations popularly used to calculate stature (s) from tibial length (t).

Study | Male | Female |
---|---|---|

Nat (1931) | 4.48 | - |

Pan (1924) | 4.49 | 4.46 |

Lal (1972) | 4.268 | 4.109 |

Siddique and Shah (1944) | 4.2 | - |

Singh and Sohal (1952) | 4.18 | - |

**Table 4**: Different multiplication factors (inches) popularly used to calculate stature (s) from tibial length (t).

The mean age of the whole sample of subjects (n=518) was 36.081 years; 56% (287 Out of 518) were of age group 25 to 35 years. Hence, younger age group contributed mostly to form the present regression equation.

The standard error of estimate for males was calculated to be (± 1.6664) and that of the females to be (± 1.6829). This indicates that in two thirds of cases, the stature computed from this equation will correspond with the observed values within +1.6664 and -1.6664 for males and within + 1.6829 and - 1.6829 for females. The standard error of estimate of the regression equations are quite low, especially that of females. Hence the scatter of data along the regression lines is minimal and this achieves goodness of fit (**Figures 1** and **2**).

Most Indian researchers have formulated multiplying factors rather than regression coefficient, by assuming a constant proportionality of the tibia with stature. However, this assumption is not always correct as Meadows and Jantz [12] had shown that tibia was positively allometric with stature (**Figures 3** and **4**).

Patel et al. [13] and Joshi et al. [14], amongst many others derived a common regression equation. Nat [1], Siddique and Shah [15] and Singh and Sohal [16] derived a multiplying factor applicable only for males. It may also be noted that the difference between the multiplying factors for males between Nat and Pan is only 0.36 cm.

The estimated stature as calculated by applying the present regression equation was compared with that of derived from popularly used formulae; the result has been tabulated in **table 5**.

Study | Male | Female | Sex Combined | Difference From Present Study |
---|---|---|---|---|

Present Study | 164.0602 | 156.38 | 160.74 | 0.0 |

Patel | - | - | 145.06 | -15.68 |

Joshi | - | - | 158.29 | -2.45 |

Nat | 161.24 | - | - | -2.8202 |

Pan | 163.84 | 153.11 | - | (-0.2202, -3.27) |

Siddique and Shah | 151.16 | - | - | -12.9002 |

Singh and Sohal | 150.44 | - | - | -13.621 |

Pearson | 200.24 | 154.38 | - | (+36.24, +2.42) |

Tr. Gl. | 169.32 | 159.64 | - | (+5.32, +3.26) |

Tr. Gl. | 164.84 | 154.87 | - | (+0.84, -1.27) |

**Table 5**: Comparison of estimated stature (cm) from different formulae.

For the valid comparison with those who have formulated a common regression, it was very pertinent to formulate a common regression equation from the pooled data of males and females; the formula stands as follows: S (Stature)=64.052+2.756 T

As can be seen from **table 5**, the regression equation of Patel underestimated the stature by 15.68 cm. Multiplying factors of Siddique and Shah [15] underestimated the stature by 12.9002 cm and that of Singh and Sohal [16] underestimated the stature by 13.621 cm. Thus, clearly, their formulae or multiplication factors cannot be applied for the population of Eastern India.

The difference between the estimated stature of males by application of the present regression equation and that of Nat [1] or Pan [2] was much less (underestimation of 2.8202 cm and 0.2202 cm respectively). However for Females, Nat did not offer any multiplying factor and applying the Pan’s factor and adjusting for the wet tibia, an underestimation of 3.27 cm was obtained. Thus, while Pan’s factor for males closely followed the present regression estimations that for females yielded a wider difference.

Considering the regression equations for Westerners, it was found that the application of Pearson’s male formulae was not at all feasible for estimation of stature of this part of the country as it overestimated the stature by a wide margin of 36.24 cm, though its equation for females was quite close (overestimation by 2.42 cm). This is quite in contrast to Trotter and Gleser’s [3] regression equation for Black Negroes whose formula for males overestimated the stature by only 0.84 cm and its formula for female underestimated stature by 1.27 cm. Thus, the Trotter’s and Gleser’s [3] regression equation for Black Negroes was the closest approximation (apart form the Pan’s multiplication factor for male) of our regression equation and applicable for the population of Eastern India.

This work was carried out in the Department of Forensic Medicine at Calcutta Medical College and Calcutta Police Morgue. We are thankful to the Head of the Department of Anatomy, Calcutta Medical College and the Director of Calcutta Police Morgue for carrying out the research work.

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