Indmedica Home | About Indmedica | Medical Jobs | Advertise On Indmedica
Search Indmedica Web
Indmedica - India's premier medical portal

Journal of the Anatomical Society of India

Comparison of Cranial Sex Determination by Univariate and Multivariate Analysis

Author(s): Deshmukh AG, Devershi DB

Vol. 55, No. 2 (2006-07 - 2006-12)

Deshmukh AG, Devershi DB
Govt. Medical College, Nanded


Numerous studies have clearly demonstrated that skeletal characteristics vary in different population. The purpose of this study was to establish population specific standards for sex determination from the cranium by univariate and multivariate analysis and compare the results of them. 16 parameters were studied on 74 adult crania of known sex (male 40 and female 34) in department of Anatomy. Aim was to study sexual dimorphism in adult human cranium by using various parameters and comparing the result of multivariate analysis with that of univariate analysis. By using univariate analysis 32.41% of crania were sexed correctly. Maximum cranial circumference was found to be most reliable. By using multivariate analysis 90% of male crania and 85.29% of female crania were sexed correctly. The overall percentage for sexing crania correctly was 87.84%. When we compare the result of usual statistical methods and multivariate analysis, it becomes obvious that multivariate analysis surpasses former both in reliability and accuracy.

Key words: Sex Determination, Cranium, Discriminant Analysis.


To identify the deceased person from bones is the most common and critical problem faced by anatomist, forensic science experts and anthropologist. Skeletal remains have been used for sexing the individual as bones of the body are last to perish after death, next to enamel of teeth. Almost all bones of the human skeleton show some degree of sexual dimorphism. Sex of the deceased can be determined if cranium is available for study. Earlier traditional studies by nonmetrical methods were centered on morphological traits which were not reliable because more features depends on occupation, nutrition, race, geographical regions and visual impressions change from person to person. Subsequently trends changed to morphometry and statistical methods like univariate analysis, demarcating point and use of indices. In these methods many parameters show overlap between male and female value so the bones cannot be sexed correctly with 100% accuracy. The recent trend is to apply advanced analytical methods to metrical data. Armitage (1971) described such important method, multivariate linear discriminant functional analysis, so sexing can be done with almost 100% accuracy. Hanihara (1959) worked on Japanese skull, Giles and Elliot (1963) worked on American crania and Hong Wei Song (1992) studied Chinese skull by using multivariate linear discriminant functional analysis.

As studies on sexual dimorphism of cranium were very few we have taken this study to enhance the accuracy of sexing the cranium which will be helpful in anthropometric and medico legal studies.

Material and Method:

Total 74 adult human crania of known sex (40 males and 34 females) available in department of Anatomy, were used for present study. All the crania were dry, free of damage or deformity and were fully ossified. Instruments used for the measurements of various parameters of cranium were sliding vernier caliper, spreading caliper, standard flexible steel tape, scientific balance and weight, scale, thread, chalk, marker.

Following measurements were taken of each cranium

  1. Weight (W) in grams.
  2. Maximum cranial length (L) – Glabella to ophisthocranium.
  3. Maximum cranial breadth (B) – Above the level of supramastoid crest at right angle to median sagital plane.
  4. Cranial height (H) – Basion to bregma.
  5. Maximum cranial circumference(C) – circumference of skull at the level of plane passing from Glabella to the most distant projection of occiput.
  6. Maximum Bizygomatic diameter (MBZD) – width between lateral surfaces of two zygomatic arches.
  7. Basion – Prosthion length (BPL)
  8. Basion – Nasion length (BNL)
  9. Biasterionic breadth (BAB)
  10. Nasion – Bregma length (NBL)
  11. Bregma – Lambda length (BLL)
  12. Mastoid length (ML) – upper border of auditory meatus to tip of mastoid process.
  13. Foramina Magnum length (FML) – Basion to Opisthion.
  14. Foramina Magnum breadth (FMB) – Broadest part of foramina magnum.
  15. Palatal length (PL) – Staphylion to Orale.
  16. Palatal breadth (PB) – Between end molare.

As the first part of study, values were tabulated and analysed by routine statistical methods. The values of range, mean, standard deviation (S.D.), were obtained for each parameter. Subsequently ‘t’ test was applied to each parameter. Demarkating points were calculated from mean ± 3 S.D. for each parameter. Percentage of the crania identified by D.P. was calculated.

For second part of study standard computer programme (SPSS) which analyze the values like range, mean, S.D. was prepared according to multivariate linear discriminant function as proposed by Armitage was used. The principle of multivariate linear discriminant function is that measured variables are taken as independent variables where as sex is dependent variable. After feeding the measurements of the study and analyzing the same by computer SPSS programme, co-efficients were obtained. The discriminant functional score (Z) was obtained by summing the independent variables after weighing each of them by appropriate coefficient. The formula was Z = b0 + b1X1 + b2 X2 + – - – - – - – - + b16 X16 (b0 - constant, b1 – b16 are coefficients, X1 – X16 are variable of parameters).

In the above formula mean values of respective male and female variables were used and the functional score was designated as Zm for male and Zf for female respectively. Sectioning point (Z0) was obtained by putting the average value of mean of male and female variables in place of X. Any cranium falling on male side of the sectioning point (Z0) would be categorized as male craniums while that falling on female side as a female cranium.


The parameters maximum cranial length, maximum cranial breadth, cranial height, maximum cranial circumference, maximum bizygomatic diameter, basion – nasion length, biasterionic breadth, bregma lambda length, mastoid length, palatal breadth were found to be significant by univariate analysis with P value < 0.5. (Table no. 1) But by D.P. method very few crania were sexed correctly (32.41%). It was observed that there was a lot of overlap in the values of male and female crania. So the method of D.P. was not found helpful in determining the sex of cranium.

By multivariate analysis the mean functional score for male (Zm – 32.059) and female (Zf – 43.320) was obtained by subjecting mean values of all variable to discriminant function. The arithmetic mean of the mean values of males and females when used in place of variable in the formula gives the sectioning point (Z0 - 37.689). Any cranium falling on male side of sectioning point i.e. < Z0 (37.689) would be categorized as male and falling on female side i.e. > Z0 (37.689) as female cranium. It was observed that 36 Male crania out of 40 were sexed correctly and 29 Female crania out of 34 were sexed correctly. Overall 65 out of 74 crania were sexed correctly. So the percentage of crania sexed correctly for male was 90% and for female was 82.29%. Overall 87.84% of crania were sexed correctly.


In this study we analyze all the crania by using univariate as well as multivariate statistical methods. In univariate analysis only one variable determines the sex of cranium. The parameters maximum cranial length, maximum cranial breadth, cranial height, maximum cranial circumference, maximum bizygomatic diameter, basion – nasion length, biasterionic breadth, bregma lambda length, mastoid length, palatal breadth were found to be significant by univariate analysis with P < 0.5.

Giles and Elliot (1963) worked on 408 American White and Negro crania of known sex and found cranial height, maximum bizygomatic diameter and mastoid length to be statistically significant. Hong Wei Song (1992) studied 30 male and 50 female Chinese skulls. He found maximum cranial length, maximum cranial breadth, cranial height, maximum bizygomatic diameter, biasterionic breadth, basion – nasion length, bregma lambda length, foramina magnum length and foramina magnum breadth to be significant. Maryna Steyn (1998) studied 43 male and 46 female South African White crania and found maximum cranial length, cranial height, maximum bizygomatic diameter, biasterionic breadth, basion – nasion length, mastoid length, basion prosthion length to be statistically significant.

By using demarcating point method only 32.41% crania were sexed correctly. It was observed that there was a lot of overlap in values of male and female crania, so this method of univariate analysis was not found helpful in determining the sex of cranium with almost 100% accuracy.

The road out of the above limitation is multivariate analysis. The amount of information lost in univariate analysis is enormous. Armitage (1971) described one such important method “multivariate linear discriminant functional analysis”. This analysis deals with problem of assigning the individual values to a particular group depending on summation of number of variable characteristics of an individual, giving proper weightage to each character. Discriminant functions are derived from this data which are most efficacious in distinguishing the two groups, there by minimizing errors in classifying individuals. Multivariate discriminant is of course more useful and productive than single discriminant function. In multivariate analysis many measured variables are taken as independent variables where as sex is dependant variable. When many variables are taken some of them are significant in identifying the sex of individual and other variables by themselves may be insignificant to correctly sex the individual. Any one variable may not accurately inform about the sex in 100% cases, there are about 10-15% cases which remain without proper sex determination. Those variables are significant by themselves may potentiate the effect of other insignificant variable. If all the variables are used to determine the sex by discriminant function analysis the percentage of correct sexing still increases.

By multivariate analysis we found 87.84% accuracy in sexing the crania correctly. Hanihara (1959) worked on Japanese skull and found 89.7% accuracy in diagnosing the sex correctly. Giles and Elliot (1963) obtained 85.5% accuracy in sexing the crania correctly. Hong Wei Song (1992) found accurate sex determination in 96.7% of cases. Maryna Steyn (1998) found 86% accuracy in the crania by multivariate analysis. The findings of the present study were similar to those of previous workers.

By comparing the results of usual statistical method and multivariate analysis it was but obvious that multivariate analysis surpasses the former both in reliability and accuracy. Finally we can say that the multivariate analysis is by far the best method for determination of sex of cranium with available resources.

parameters mean S. D P value
male female male female
1 Weight 526 494 74.94 71.09 > 0.05
2 Maximum Cranial Length 173 166 6.04 8.03 < 0.001
3 Maximum Cranial Breadth 131 127 4.96 4.91 < 0.001
4 Cranial Height 132 127 5.59 5.85 < 0.001
5 Maximum Cranial Circumference 496 479 13.32 15.58 < 0.001
6 Maximum Bizygomatic Diameter 126 121 4.82 6.47 < 0.001
7 Basion-Prosthion Length 90 89 4.21 5.08 > 0.05
8 Basion-Nasion Length 99 96 4.19 4.61 <0.001
9 Biasterionic Breadth 101 98 4.53 3.75 < 0.05
10 Nasion-Bregma Length 125 123 7.04 8.17 > 0.05
11 Bregma-Lambda Length 125 120 7.96 8.86 < 0.05
12 Mastoid Length 29 27 3.16 4.02 < 0.05
13 Foramina Magnum Length 34 34 3.09 2.05 > 0.05
14 Foramina Magnum Breadth 29 28 1.97 2.09 > 0.05
15 Palatal Length 45 44 3.08 3.37 > 0.05
16 Palatal Breadth 35 34 1.50 2.73 < 0.05
* Weight was in grams and other parameters were in millimeters.


  1. Armitage P: Statistical methods in medical research. Oxford, Blackwell; 1971, pp 332-335.
  2. Giles E and Elliot G: Sex determination by discriminant function analysis of crania. American Journal of physical anthropology 1963; 21: 53-56.
  3. Hanihara K: Sex diagnosis of Japanese skulls and scapulae by means of discriminant function. J. Anth. Soc. Nippon 1959; 67(722) : 21 – 27.
  4. Hong Wei Song, et. al: Sex diagnosis of Chinese skulls using multiple stepwise discriminant function analysis. Forensic science international 1992; 54: 135 – 140.
  5. Maryna S., Iscan M. Y.: Sexual dimorphism in the crania and mandibles of South African whites. Forensic Science international 1998; 98: 9 – 22.
Access free medical resources from Wiley-Blackwell now!

About Indmedica - Conditions of Usage - Advertise On Indmedica - Contact Us

Copyright © 2005 Indmedica