Sage Journals: Discover world-class research

Abstract

Sex estimation from skeletal remains is an important component of personal identification in forensic anthropology. The different rates of skeletal growth and development pertaining to age, ethnicity and sex form the basis of such identification. The present study has been conducted on the contemporary North Indian Haryanvi population to ascertain the cephalometric measurements and the best machine learning algorithm to study sexual dimorphism. A cross-sectional study was conducted on 200 individuals (M: 100: F:100) aged between 18 and 40 years and 12 cephalometric measurements were obtained using spreading and sliding callipers. Statistical analysis was done using Statistical Package for Social Science (SPSS) version 21.00. All 12 variables showed sexual dimorphism and the sexing accuracy ranged between 62% and 93.5% in univariate analysis. Bizygomatic breadth and bi-gonial width (BiGoW) showed an accuracy of 99% in multivariate analysis. The receiver operating curve (ROC) analysis also depicted BiGoW to have the highest area under the curve (AUC) (1.00) and sexing accuracy of 95.5%. Principal component analysis (PCA) also revealed a similar result with BiGoW, nasal height (NH) and ZyBr having the highest communalities. However, it was concluded that discriminant function analysis (DFA) and ROC analysis showed more promising results in studying sexing accuracy as compared to PCA.

Keywords

Sexual dimorphism cephalometry forensic anthropology discriminant function analysis (DFA)receiver operating curve (ROC) analysis principal component analysis (PCA)

Introduction

Sex estimation is one of the major parameters which help in personal identification from skeletal remains. Furthermore, in cases of mass disasters, charred, mutilated and highly decomposed skeletal remains, identification pose a difficult task for the forensic anthropologists.^{1, 2} Hence, a systematic approach to determine sex from the morphometric differences of the skeleton is important. Modern humans are found to exhibit a lower level of sexual dimorphism as compared to other primates.³ Sexual dimorphism in the skull is mostly attributed to a larger size in males as compared to females due to an extended growth period in males during puberty, effects of androgens leading to higher bone deposition in the craniofacial region and increased masticatory forces exerted on the masseter muscles. Most of the sexual differences in the skull are related to physiological and functional features such as muscle mass, volume of oxygen intake, metabolic system and bone development.⁴ Cephalometric measurements have also shown statistically significant results in establishing sexual dimorphism among various populations.^5–9 The discriminant functions developed are individual to each population. However, a rise in immigration and population inter-mixing is one of the most important genetic factors, along with other epigenetic factors, that have prompted the development of new and updated cephalometric sexual discriminant formulas.^{10, 11} With the inclusion of advanced imaging tools such as computed tomography (CT), cone-based CT, magnetic resonance imaging (MRI) and digital radiography, the accuracy of analysis has increased, but the expense and trained personnel can be challenging.¹² Further, machine learning algorithms have also shown promising results while analysing huge volumes of data.¹³ Therefore, the present study aims to provide the updated discriminant functions of cephalometric variables for the contemporary North Indian Haryanvi population and compare different machine learning techniques to ascertain the best tool for observing sexual dimorphism among the same.

Material and Methodology

A total of 200 (100 M/100 F) Haryanvi adults aged between 18 and 40 years were included in the study. Informed consent with the approval of the Institutional Ethics Committee in both English and Hindi languages was obtained from all the participants. The inclusion criteria were: (a) Participants belonging to the Haryanvi origin and (b) participants who gave their consent for the study. The exclusion criteria were: (a) Any participant with traumatic or congenital deformities of the head or face and (b) any transgender individual belonging to Haryana.

The participants were asked to sit with their backs straight and feet touching the ground in the Frankfurt Horizontal Plane while taking the measurements. Digital vernier callipers and spreading callipers were used to obtain the measurements. After the measurements were made, all the data were analysed statistically using Statistical Package for Social Science (SPSS) version 21.00. The following frequently used measurements were obtained by the first author at two different time intervals to avoid intra-observer error: Maximum head length (MxHL), maximum head breadth (MxHBr), bi-gonial width (BiGoW), minimum frontal width (MnFW), zygomatic breadth (ZyBr), physiognomic facial height (PhyFH), morphological facial height (MorFH), nasal length (NL), nasal breadth (NBr), nasal height (NH), maximum orbital width (MxOW) and minimum orbital width (MnOW).

Statistical Analysis

Descriptive statistics with the independent t-test were performed using IBM SPSS version 21.0. A t-test measures the variation between two groups. The sexual dimorphism index (SDI) has been calculated for all the variables. A paired t-test has also been done to evaluate the intra-observer error. Stepwise discriminant analysis, univariate and multivariate direct discriminant function analysis (DFA) were also performed to obtain the highest separation between the sexes. The receiver operating curve (ROC) analysis has been used to identify the cut-off points for each variable. These points were determined by analysing the optimum sensitivity (true positive rate) and 1-specificity (true negative rate) values, which are closest to the area under the curve (AUC) for each variable. Principal component analysis (PCA), discovered by Karl Pearson in 1901, is a statistical tool that is used to explore the interrelationships among variables. The loading of the variables on PC1, PC2 and PC3 has been used to distinguish between both sexes.

Results

Table 1 shows the descriptive statistics, including the mean, standard deviation, t value, p value, SDI and sexing accuracy ranging from 62% to 93.5% after cross-validating the results. All the variables have shown significantly larger dimensions in males (p < .05).

Table 1.

Descriptive Statistics of the North Indian Population.

Variable (in cm)	Male (n = 100)	Female (n = 100)	t Value	p Value	SDI	Sexing Accuracy (%)
Variable (in cm)	Mean ± SD	Mean ± SD	t Value	p Value	SDI	Sexing Accuracy (%)
MxHL	18.38 ± 0.49	17.06 ± 0.57	17.22	<.001	7.73	87
MxHBr	13.63 ± 0.59	12.36 ± 0.82	12.46	<.001	10.27	82.5
BiGoW	9.46 ± 0.18	8.49 ± 0.29	27.71	<.001	11.42	91
MnFW	9.16 ± 0.33	8.57 ± 0.75	7.18	<.001	6.88	82
ZyBr	13.31 ± 0.49	11.93 ± 0.64	17.08	<.001	11.56	87.5
PhyFH	17.15 ± 0.65	16.27 ± 0.87	8.12	<.001	5.40	78.5
MorFH	11.43 ± 0.59	10.18 ± 0.59	14.88	<.001	12.27	89
NL	4.66 ± 0.27	4.22 ± 0.39	9.10	<.001	10.42	70.5
NBr	3.34 ± 0.23	3.12 ± 0.25	6.26	<.001	7.05	62
NH	5.31 ± 0.20	4.51 ± 0.29	22.27	<.001	17.73	93.5
MxOW	10.07 ± 0.15	9.83 ± 0.53	4.30	<.001	2.44	67.5
MnOW	1.35 ± 0.28	1.15 ± 0.06	7.19	<.001	17.39	74

Table 2 depicts the results of the paired t-test, which has been used to determine the extent of intra-observer error. The correlation values depict a strong correlation between the first and second measurements. The p value also exhibits a non-significant difference between the measurements taken at two different times.

Table 2.

Paired t-test for Intra-observer Error.

Variables	Correlation	t Values	Significance (Two-tailed)
MxHL	0.996	1.523	0.144
MxHBr	0.996	1.000	0.330
BiGoW	1.000	0.224	0.825
MnFW	0.996	−0.900	0.379
ZyBr	0.998	−0.040	0.969
PhyFH	0.999	1.000	0.330
MorFH	0.998	1.512	0.147
NL	1.000	2.423	0.026
NBr	0.998	1.231	0.233
NH	0.999	1.467	0.159
MxOW	0.990	0.698	0.494
MnOW	1.000	2.979	0.008

Table 3 shows the results of stepwise DFA, where seven variables were selected, which showed maximum classification accuracy. In stepwise DFA, the SPSS system automatically chooses those variables which provide maximum classification.

Table 3.

Stepwise DFA.

Variables	Wilk’s Lambda	Equivalent F. Ratio	Degree of Freedom
BiGoW	0.205	768.211	1,198
NH	0.146	577.091	2,197
MxHBr	0.122	468.918	3,196
MxHL	0.108	403.413	4,195
MorFH	0.100	348.131	5,194
NL	0.095	304.767	6,193
ZyBr	0.092	271.741	7,192

Table 4 shows the canonical discriminant coefficients and sexing accuracy for stepwise and direct discriminant functions. In stepwise analysis, seven variables that are MxHL, BiGoW, MxHBr, ZyBr, MorFH, NL and NH were selected and provided 100% sexing accuracy after cross-validation. Direct DFA showed the highest sexing accuracy of 99% (M = 100%, F = 98%) using the variables BiGoW and ZyBr. A combination of ZyBr and BiGoW shows a minimum of 98.5% accuracy with the addition of any one of the remaining 10 variables. Keeping in view the fragmentary condition of the skull, we created functions using MnOW and MorFH in combination with NH.

Table 4.

Canonical Discriminant Coefficients.

Stepwise DFA
Variables and Functions	Unstandardised/Raw Co-efficient	Standardised Co-efficient	Structured Co-efficient	Centroids	Males (n = 100) (%)	Females (n = 100) (%)	Accuracy
Variables and Functions	Unstandardised/Raw Co-efficient	Standardised Co-efficient	Structured Co-efficient	Centroids	Males (n = 100) (%)	Females (n = 100) (%)	Original (%)	Cross-validated
F1 MxHL	0.586	0.316	0.389	M = 3.132	100	100	100	100
BiGoW	2.465	0.616	0.626	F = −3.132
ZyBr	0.384	0.220	0.386	SP = 0
MxHBr	0.438	0.314	0.281
MorFH	0.369	0.220	0.336
NL	0.664	0.225	0.205
NH	1.556	0.394	0.503
(Constant)	−57.698
Direct Discriminant Analysis
F2 MxHL	0.765	0.413	0.735	M = 2.668	100	100	100	100
BiGoW	2.936	0.733	0.456	F = −2.668
ZyBr	0.681	0.390	0.453	SP = 0
MxHBr	0.406	0.291	0.330
(Constant)	−53.803
F3 MxHL	0.802	0.433	0.766	M = 2.559	100	99	99.5	99.5
BiGoW	2.975	0.743	0.476	F = −2.559
ZyBr	0.832	0.477	0.472	SP = 0
(constant)	−51.435
F4 BiGoW	3.412	0.852	0.849	M = 2.308	100	98	99	99
ZyBr	0.922	0.528	0.523	F = −2.308
				SP = 0
F5 MorFH	0.436	0.26	0.331	M = 2.201	98	98	98	98
NH	1.515	0.382	0.495	F = −2.201
				SP = 0
F6 MnOW	0.505	0.253	0.401	M = 2.052	98	94	96	96
NH	1.515	0.387	0.486	F = −2.052
				SP = 0

Note: SP, sectioning point.

Table 5 provides the results of ROC analysis, depicting the cut-off points along with the sensitivity and specificity of each variable. The highest AUC was shown by BiGoW with a sexing accuracy of 95.5% (M = 100%, F = 91%). Figure 1 shows the ROC plot along with the reference line, where most of the variables occupy the top left corner of the plot, thereby depicting a model with high sensitivity and specificity.

Figure 1.

Shows the ROC Plot for all Cephalometric Variables.

Table 5.

ROC Analysis Depicting AUC, Cut-off Values and Sexing Accuracy of Each Variable.

Variables	AUC	Cut-off Value	Sensitivity	1-Specificity	Male Identified (n = 100)	Females identified (n = 100)	Total (n = 200)
Variables	AUC	Cut-off Value	Sensitivity	1-Specificity	%	%	%
MxHL	0.957	♂ ≥ 16.7 < ♀	1	0.70	100	70	85
MxHBr	0.898	♂ ≥ 11.5 < ♀	1	0.84	100	84	92
BiGoW	1.000	♂ ≥ 8.15 < ♀	1	0.91	100	91	95.5
MnFW	0.782	♂ ≥ 7.95 < ♀	1	0.90	100	90	95
ZyBr	0.952	♂ ≥ 11.35 < ♀	1	0.84	100	84	92
PhyFH	0.831	♂ ≥ 15.75 < ♀	0.96	0.79	96	79	87.5
MorFH	0.912	♂ ≥ 9.81 < ♀	0.98	0.71	98	71	84.5
NL	0.838	♂ ≥ 4.03 < ♀	0.98	0.72	98	72	85
NBr	0.719	♂ ≥ 3.04 < ♀	0.96	0.70	96	70	83
NH	0.993	♂ ≥ 4.13 < ♀	1	0.90	100	90	95
MxOW	0.684	♂ ≥ 9.45 < ♀	0.99	0.78	99	78	88.5
MnOW	0.829	♂ ≥ 1.125 < ♀	0.88	0.76	88	76	82

Table 6 depicts the Kaiser–Meyer–Olkin measure of sampling adequacy, which ranges from 0 to 1 and is a measure to provide the minimum standard before conducting a PCA. A minimum value of 0.6 or more is suggested to be optimum for the analysis. It also shows Bartlett’s Test of Sphericity that the correlation between the variables does not form an identity matrix. PCA cannot be conducted if the correlation matrix forms an identity matrix.

Table 6.

PCA–KMO and Bartlett’s Test.

Kaiser–Meyer–Olkin Measure of Sampling Adequacy	Bartlett’s Test of Sphericity
Kaiser–Meyer–Olkin Measure of Sampling Adequacy	Approx. Chi-Square	df	Sig.
0.927	1,288.170	78	<0.001

Table 7 shows the communalities, eigenvalues, percentage of variance and loading of each variable on the principal components, which is the correlation between the variable and principal components for both sexes. The communalities depict the proportion of each variable’s variance that can be explained by the principal components. BiGoW has depicted the highest communality for both sexes (M = 0.765, F = 0.738). The first principal component for both sexes has accounted for the most variance (M = 33.24%, F = 32.26%), followed by the second component and so on. Three principal components have been extracted and the correlation of BiGoW, followed by NH and ZyBr, has depicted the highest correlation with the principal component 1(PC 1) for both males and females (Figures 2 and 3).

Figure 2.

The Scree Plot Depicts the Distribution of Variances (Eigenvalues) of the Principal Components.

Figure 3.

Shows the Plot for Factors in Rotated Space for Only PC1 and PC2, as all the Variables Showed a Positive Loading on these Two Components.

Table 7.

Communalities, Eigenvalues and Loading of Factors.

Variables	Males				Females
	Principal Components			Communality	Principal Components			Communality
	1	2	3	Communality	1	2	3
BigoW	0.856	0.09	0.24	0.765	0.876	0.308	0.576	0.738
NH	0.844	0.05	0.262	0.733	0.832	0.303	0.327	0.696
ZyBr	0.827	0.321	0.246	0.692	0.829	0.607	0.422	0.681
MxHL	0.804	0.421	0.19	0.572	0.801	0.638	0.396	0.656
MorFH	0.784	0.021	0.258	0.424	0.743	0.656	−0.349	0.638
MxHBr	0.716	0.393	0.32	0.413	0.606	0.585	−0.392	0.604
MnFW	0.521	0.629	0.342	0.445	0.602	0.561	−0.342	0.539
PhyFH	0.604	0.483	−0.07	0.396	0.593	0.535	0.337	0.611
NL	0.570	0.452	0.302	0.228	0.574	0.577	0.308	0.574
NBr	0.532	0.626	0.351	0.338	0.539	0.529	−0.381	0.681
MnOW	0.519	0.421	0.408	0.291	0.407	0.446	−0.436	0.596
MxOW	0.441	0.576	0.392	0.331	0.426	0.395	0.323	0.554
Eigenvalues	5.610	2.179	1.048		5.388	3.30	1.81
% of variance	33.24	28.17	19.06		32.26	29.79	21.04

The scree plot (Figure 2) depicts the distribution of variances (eigenvalues) of the principal components. PC 1 shows the highest variance. The plot peaks at the first principal component and eventually falls flat, depicting that each successive principal component accounts for gradually smaller variances.

In Figure 3, the plot for factors in rotated space has been obtained for only PC1 and PC2, as all the variables showed a positive loading on these two components, while some variables which show no correlation with sex loaded negatively on the third component.

Discussions

Population Variability in Sexual Dimorphism

The study of sexual dimorphism from percutaneous measurements can play an imperative role in forensic facial reconstruction and personal identification. The growth and development of the craniofacial region is affected by a plethora of factors, such as nutrition, environmental stress and masticatory forces influenced by dietary habits.¹⁴ The anatomical and morphological variations are a result of the different ontogenetic trajectories in males and females.^{15, 16} However, sexual dimorphism is typically found in the adult craniofacial measurements. This explains the age group of 18–40 years for the present study. The viscerocranium is responsible for the development of facial features and undergoes a slower growth rate as compared to the neurocranium. The later-developing areas of the craniofacial region, such as the mandible, maxilla, upper face, cranial base and head height, have a higher likelihood of showing greater classification accuracy.¹⁷

Univariate Discriminant Analysis

This study depicts that all cephalometric variables are significantly larger among males and have a sexing accuracy ranging between 62% and 93.5%. NH showed the highest classification accuracy (93.5%), as the nasal bone and piriform aperture are sexually dimorphic.¹⁸ Bhargava and Sharma (1959) found that variation is higher within the nasal region compared to the cranium.¹⁹ The findings of the present study are in accordance with the previous literature, where NH provided a sexing accuracy of 70.8% in males and 68% in females in the Ladakhi population, 64.96% in the European population and 77.2% in males and 68.4% in females within the Dehradun population.^20–22 The nasal organ plays a key role in regulating air pressure and temperature before it reaches the lungs. A study by Noback et al. (2011) revealed a strong correlation between the shape of the nasal cavity and two climatic variables, namely temperature and humidity. The nasal cavities of populations living in cold-dry climates tend to be relatively narrower and longer compared to those living in hot-humid regions. This adaptation helps to optimise the warming and humidification of air in colder climates, whereas wider nasal passages are advantageous in hot-humid climates for efficient cooling and moisture management.²³ However, this explanation may not be sufficient in explaining the sexual dimorphism of the NH among the North Indian Haryanvi population. The nasal morphology is a complex trait influenced by multiple factors, including genetics, evolutionary history and adaptation to environmental conditions, which should additionally be considered.

The human mandible is the most durable cranial-facial bone and depicts functional morphological variation due to higher masticatory forces in males. A sexing accuracy of 91% has been obtained in the present study using univariate DFA of BiGoW. This is also, in accordance with other studies depicting a sex accuracy of 92% in the Croatian archaeological samples, 86% in the Brazilian population and 70.7% in the Central Indian population.^24–26

The sample size, unequal number of male and female participants and secular and temporal variations may lead to different sexing accuracy percentages across different population groups.²⁷

Multivariate Sex Discriminant Analysis

We achieved very exceptionally high sexing accuracy using multivariate direct discriminant analysis by a combination of four variables, that is MxHL, BiGoW, ZyBr and MxHBr provided an accuracy of 100% and a little less (99%) by combining two variables, that is BiGoW and ZyBr. The extra-wide curvature of the zygomatic arch can be associated with the robustness of the male skull and increased development of the masseter muscle, which also affects the development of the mandible.^{17, 28} Multivariate analysis, including bizygomatic width, NH and nasal width, has provided high sexing accuracy also in other population groups, that is, 96.7% in the Chinese crania, 91.7% in North West Indians, 90.3% in Australian skulls, 89.7% in Japanese skulls, 88.2% and 81.5% in the Tibetan and South Indian crania, respectively.^{9, 29–32}

Best Machine Learning Algorithm for Sex Estimation

In the present study, we have used a combination of machine learning techniques, including ROC analysis, PCA and DFA, to determine the best tool for obtaining accurate sex determination from craniofacial skeleton data. ROC analysis has depicted a sexing accuracy of 82%–95.5% with an AUC of 1.00 for BiGoW. It is in accordance with the other studies that is AUC was 0.809 with 71.7% sex classification in the Central Chinese population, 0.764 with 79% in the Brazilian population²⁵ and 0.684 with 79.6% in the Portuguese population.^{33, 34}

This study has also drawn a comparison between a supervised learning algorithm, namely DFA and an unsupervised technique, that is, PCA, to obtain sexing accuracy of the metric parameters and morphological features. The PCA results focused on identifying differences in the shape and size of cephalometric variables, without considering sex, whereas DFA identified the variables that can best differentiate between males and females. PC1 accounted for 33.24% in males and 32.26% in females. These results concur with the findings of a PCA-based study on sex estimation from skeletal collections containing American white crania, where the principal component explained 38% of the variation in males and 34% in females.³⁵ This study has thus provided an updated discriminant function for sex estimation and deduced a novel combination of the above-mentioned algorithms to enhance the accuracy of estimation from these metric and morphological features of the North Indian population. The results of this research will also be beneficial in facial reconstruction for forensic anthropology and reconstructive orthognathic surgery. However, the results may be slightly varied due to larger population sizes and an unequal number of males and females. The data collection technique (CT scan, geometric morphometric or direct measurement) also affects the results while assessing sexual dimorphism within the same population.³⁶

Footnotes

Acknowledgements

We would like to extend our gratitude to the Department of Forensic Science, SGT University, Gurugram, for their laboratory infrastructure and research support.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Ethical Approval

Informed consent, along with approval from the Institutional Ethics Committee, was obtained (Ref. No. SGTU/FOSC/2023/1481).

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Informed Consent

As mentioned in the manuscript, an informed consent in both English and Hindi languages were obtained from the participants prior to obtaining their measurements. This was in accordance with the approval of the Institutional Ethical Committee.

ORCID iD

Vineeta Saini

References

Johnson

, Hoggard

, Singh

, . Investigating sexual dimorphism of the human mandible in Indian population using geometric morphometric method. J Indian Acad Forensic Med 2025; 46(4): 467–473.

Kiran

, Shetty

, . Morphometric sex estimation using mastoid triangle: A prospective study. J Indian Acad Forensic Med 2021; 43(2): 108–113.

Del Bove

, Menéndez

, Manzi

, . Mapping sexual dimorphism signal in the human cranium. Sci Rep 2023; 13(1): 16847.

Toneva

, Nikolova

, Tasheva-Terzieva

, . A geometric morphometric study on sexual dimorphism in viscerocranium. Biology (Basel) 2022; 11(9): 1333.

Keche

, Keche

, Sahoo

, . Study of cephalic index and its correlation with sex and race in central India. J Indian Acad Forensic Med 2024; 46(1): 63–66.

Shirpure

, Mendpara

and Dhenge

A digital retrospective study: Evaluating the reliability of mandibular parameters as sex predictors in the Maharashtra Population. J Indian Acad Forensic Med 2025; 46(3): 319–324.

Christoloukas

, Mitsea

, Kovatsi

, . Sex determination using linear anthropometric measurements relative to the mandibular reference plane on CBCT 3D images. J Imaging 2025; 11(7): 224.

Bhanarkar

and Koley

Study of cephalic index in medical students of West Bengal. J Indian Acad Forensic Med 2020; 42(1): 44–45.

Battan

, Sharma

, Gakhar

, . Cranio-facial bones evaluation based on clinical CT data for sex determination in Northwest Indian population. Leg Med 2023; 64: 102292.

10.

Ceballos

, Deana

and Alves

Sex estimation in a Chilean population by mandibular analysis in cone beam computed tomography images. BMC Oral Health 2025; 25(1): 122.

11.

Chaudhary

, Kaore

, Kashyap

, . Study of mandibular ramus morphology as a tool for sex determination in Indian population. CME J Ger Med 2025; 17(1): 79–82.

12.

Jangid

, Dalal

, Kumari

, . From traditional to virtual: The evolving landscape of autopsy techniques in forensic science. J Indian Acad Forensic Med 2025; 46(4): 545–552.

13.

Patil

, Vineetha

, Vatsa

, . Artificial neural network for gender determination using mandibular morphometric parameters: A comparative retrospective study. Cogent Eng 2020; 7(1): 1723783.

14.

Kemkes

and Göbel

Metric assessment of the “mastoid triangle” for sex determination: A validation study. J Forensic Sci 2006; 51(5): 985–989.

15.

Bastir

, Rosas

and O’Higgins

Craniofacial levels and the morphological maturation of the human skull. J Anat 2006; 209(5): 637–654.

16.

Noble

JME.

Morphometrics of the juvenile skull: Analysis of ontogenetic growth patterns. Master’s thesis. University of Western Australia; Perth, Australia, 2015.

17.

Parlak

, Etli

, Beyhan

, . Sex estimation with ensemble learning: An analysis using anthropometric measurements of piriform aperture. Egypt J Forensic Sci 2025; 15(1): 10.

18.

Kim

, Park

, . Differences in nasal shapes and the degree of changes over a decade or more: A paired analysis. Clin Exp Otorhinolaryngol 2024; 17(1): 56–63.

19.

Bhargava

and Sharma

JC.

The nose in relation to head and face-an anthropometric study. Indian J Otolaryngol 1959; 11(2): 213–218.

20.

Ali

, Sehrawat

and Sehrawat

Sex determination from discriminant function analysis of cephalometric measurements of Brokpas and Purigpas of Ladakh (UT): A forensic anthropological study. Rom J Leg Med 2020; 28: 178–188.

21.

Scendoni

, Kelmendi

, Arrais Ribeiro

, . Anthropometric analysis of orbital and nasal parameters for sexual dimorphism: New anatomical evidences in the field of personal identification through a retrospective observational study. Plos One 2023; 18(5): e0284219.

22.

Barwa

and Singh

Nasal height as a parameter for stature estimation & sex differentiation in Dehradun region. Med-Leg Update 2020; 20(1): 116–121.

23.

Noback

, Harvati

and Spoor

Climate-related variation of the human nasal cavity. Am J Phys Anthropol 2011; 145(4): 599–614.

24.

Vodanović

, Dumančić

, Demo

, . Determination of sex by discriminant function analysis of mandibles from two Croatian archaeological sites. Acta Stomatol Croat 2006; 40(3): 263–277.

25.

Lopez-Capp

, Rynn

, Wilkinson

, . Discriminant analysis of mandibular measurements for the estimation of sex in a modern Brazilian sample. Int J Legal Med 2018; 132(3): 843–851.

26.

Wankhede

, Bardale

, Chaudhari

, . Determination of sex by discriminant function analysis of mandibles from a Central Indian population. J Forensic Dental Sci 2015; 7(1): 37–43.

27.

Inskip

, Constantinescu

, Brinkman

, . The effect of population variation on the accuracy of sex estimates derived from basal occipital discriminant functions. Archaeol Anthropol Sci 2018; 10(3): 675–683.

28.

Franklin

, Freedman

, Milne

, . A geometric morphometric study of sexual dimorphism in the crania of indigenous southern Africans. S Afr J Sci 2006; 102(5): 229–238.

29.

Song

, Lin

and Jia

JT.

Sex diagnosis of Chinese skulls using multiple stepwise discriminant function analysis. Forensic Sci Int 1992; 54(2): 135–140.

30.

Swift

, Obertova

, Flavel

, . Estimation of sex from cranial measurements in an Australian population. Aust J Forensic Sci 2023; 55(6): 755–770.

31.

Hanihara

Sex diagnosis of Japanese skulls and scapulae by means of discriminant functions. J Anth Soc Nippon 1959; 67: 21–27.

32.

Naikmasur

, Shrivastava

and Mutalik

Determination of sex in South Indians and immigrant Tibetans from cephalometric analysis and discriminant functions. Forensic Sci Int 2010; 197(1–3): 122. e1–6.

33.

Deng

, Bai

, Dong

, . Sexual determination of the mandible breadth in a central Chinese population sample: A three-dimensional analysis. Aust J Forensic Sci 2017; 49(3): 332–343.

34.

Pereira

, Bernardo

, Pestana

, . Contribution of teeth in human forensic identification–discriminant function sexing odontometrical techniques in Portuguese population. J Forensic Leg Med 2010; 17(2): 105–110.

35.

Jantz

, Mahfouz

, Shirley

, . Improving sex estimation from crania using 3-dimensional CT scans. US Department of Justice. 2013; 1–71. https://www.ojp.gov/pdffiles1/nij/grants/240688.pdf

36.

Roy

, Verma

and Bhutia

Morphometric analysis of foramen magnum and occipital condyles for sexual dimorphism: Exploring reliability through computed tomography investigation. J Indian Acad Forensic Med 2024; 46(2): 259–266.

A Comparative Study on Different Machine Learning Algorithms to Explore Sexual Dimorphism in Cephalometric Measurements of North Indian Population