

ORIGINAL ARTICLE 

Year : 2016  Volume
: 57
 Issue : 4  Page : 226232 


Evaluation of sexual dimorphism by discriminant function analysis of toe length (1T5T) of adult Igbo populace in Nigeria
Stephen A Alabi^{1}, Blessing C Didia^{2}, Gabriel Sunday Oladipo^{2}, Eric O Aigbogun^{2}
^{1} Department of Human Anatomy, Faculty of Basic Medical Sciences, University of Ilorin, Ilorin; Department of Human Anatomy, Faculty of Basic Medical Sciences, University of Port Harcourt, Port Harcourt, Nigeria ^{2} Department of Human Anatomy, Faculty of Basic Medical Sciences, University of Port Harcourt, Port Harcourt, Nigeria
Date of Web Publication  12Aug2016 
Correspondence Address: Stephen A Alabi Department of Human Anatomy, Faculty of Basic Medical Sciences, University of Ilorin, Ilorin Nigeria
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/03001652.188351
Abstract   
Background: Sex determination is an important and one of the foremost criteria in establishing the identity of an individual, and this is achieved by investigating various anatomical structures to establish sex discriminatory features. The present study conducted baseline data for the toe with a view of finding discriminatory sex characteristics. Materials and Methods: A total of 420 subjects were studied by direct linear measurements of the toe length (big toe [1T] to the fifth toes [5T]) of both feet using a digital Vernier caliper with accuracy of 0.01 mm. Statistical Package for Social Sciences (IBM, version 23, Armonk, New York, USA), Levene's ANOVA outcome informed the use of ttests to compare mean differences. Discriminant function analysis (DFA) was used to evaluate the possibility of sex categorization. The significance level was set at 95%. Results: The mean ± standard deviation values of the right (R) toes for the males were 49.63 ± 4.43 mm (1T), 36.92 ± 5.14 mm (2T), 30.35 ± 4.95 mm (3T), 25.55 ± 3.97 mm (4T) and 22.21 ± 2.94 mm (5T), whereas the female values were 45.73 ± 4.07 mm (1T), 33.31 ± 4.66 mm (2T), 26.63 ± 4.02 mm (3T), 22.89 ± 3.43 mm (4T), and 19.77 ± 2.70 mm (5T). The left male values were 49.16 ± 4.32 mm (1T), 36.82 ± 5.16 mm (2T), 30.88 ± 4.91 mm (3T), 26.13 ± 3.99 mm (4T), and 22.46 ± 3.24 mm (5T), whereas the female values were 45.33 ± 4.05 mm (1T), 33.05 ± 4.70 mm (2T), 27.27 ± 4.29 mm (3T), 23.10 ± 3.36 mm (4T), 19.81 ± 2.59 mm (5T). From the results, males displayed significantly higher mean values than females in all measured parameters (t = 2.405, P = 0.018) with no asymmetry (P > 0.05); although T3 and T4 were larger on the left foot. The DFA model when tested with the present data derived a significant "F" likelihood ratio test (P < 0.001), a Wilks' lambda predictability value of 0.759 having a model accuracy of 69.5% with a better prediction for female (70%) than males (69%). Conclusion: The use of toe length alone may not be effective for sex differentiation; however, it can serve as an adjunct in forensic investigation involving sex identification. Keywords: Discriminant function analysis, Igbo, sexual dimorphism, toe length
How to cite this article: Alabi SA, Didia BC, Oladipo GS, Aigbogun EO. Evaluation of sexual dimorphism by discriminant function analysis of toe length (1T5T) of adult Igbo populace in Nigeria. Niger Med J 2016;57:22632 
How to cite this URL: Alabi SA, Didia BC, Oladipo GS, Aigbogun EO. Evaluation of sexual dimorphism by discriminant function analysis of toe length (1T5T) of adult Igbo populace in Nigeria. Niger Med J [serial online] 2016 [cited 2022 Jan 19];57:22632. Available from: https://www.nigeriamedj.com/text.asp?2016/57/4/226/188351 
Introduction   
The application of somatometry (a significant aspect of anthropometry) in the identification of human remains led to the formation of term "forensic anthropometry." The ultimate aim of using anthropometry in forensic medicine/science is to assist the law enforcement agencies achieve "personal identity" in cases of unknown human remains; ^{[1]} which involves the combination of different procedures. However, those set of physical characteristics, functional or psychic, normal or pathological that defines an individual can be regarded as identity. ^{[2]}
In establishing the identity of an individual, sex determination is an important and one of the foremost requirement; ^{[3]} as it statistically excludes approximately half of the population under innvestigation ^{[4]} and narrows down the search for the identity of an individual. ^{[5]} Sex is considered one of the easiest discriminants from skeletal material and the most reliable if essential parts of the skeleton are available in good condition. ^{[5],[6]} However, identification of dismembered or scattered human remains; frequently found in case of mass disasters and criminal mutilation still remains a challenge to medicolegal experts. ^{[3]} Supportively, some characteristics such as weight, height, and body mass index gives a better imaginable pictorial view of the individual, and aid anthropological studies. ^{[6]}
Various studies have established sexual differences from different human bones such as the skull, pelvis, ^{[7],[8]} long bones, scapula, ^{[9],[10]} clavicle, and smaller bones such as metatarsals, metacarpals, phalanges, ^{[3]} patella, vertebrae, ribs, and other vital structures such as dentition. ^{[11]} The most widely applied statistical model in sex determination is the discriminant function analysis (DFA) established by Fisher. ^{[12],[13]} This model encouraged many forensic scientists to assess their anthropometric data accordingly and critically. ^{[6],[11]}
Materials and methods   
A total of 420 subjects within the age range; 1865 years, equally distributed into males and females of Igbo descent, traced to paternal and maternal grandparents were selected. The Igbo population was estimated from the percentage contribution of the various ethnic groups to the Nigerian population, while the sample size was determined by proportion using Fisher's formula for large population (>10,000) or infinite population; ^{[14],[15]}
Subjects were selected by multistage stratified sampling technique. Structured questionnaires were used to determine sociodemographical status of the subjects and written informed consent was obtained from each participant. All subjects were healthy individuals free of deformity, injury, fracture, amputation or any surgical procedures carried out on the toes. Ethical clearance was obtained from the University of Port Harcourt Ethical Committee prior to the commencement of the study.
Anthropometric determination of toe length was carried out using a digital Vernier caliper with precision of 0.01 mm. The following toe measurements were taken; 1Tgreat toe (hallux), 2Tlong toe (second toe), 3Tmiddle toe (third toe), 4Tring toe (fourth toe), and 5Tlittle toe (fifth toe) for both foot. The toe length was defined by the distance from the tip of the toe till the proximal metatarsophalangeal crease of that toe; when fully extended [Figure 1]. Measurements were taken trice and the average tabulated as the value for the measured length.  Figure 1: (a) Landmark for first (big) toe length (b) actual measurement using digital vernier caliper
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Statistical analysis
Statistical Package for Social Sciences (IBM, version 23, Armonk, New York, USA) ANOVA and unpaired ttest was used in assessing the sex differences in the measured parameters, and univariate DFA was used to ascertain the possibility of classifying the parameters into group membership. Only statistically significant or close to significant variables were selected for DFA. The confidence level was set at 95%; hence, P ≤ 0.05 was considered to be statistically significant.
Data Analysis   
The results were presented based on the anthropometric measurements of toes length (1T5T) for both feet. Continuous data were represented as mean (standard deviation [SD]), whereas frequency (%) for other categorical data. The sociodemographic characteristics of the subjects were represented in [Table 1]. The values observed from the anthropometric measurements were tabulated and the mean (SD) values, and range (minimum  maximum) were determined for the sex (male and female) [Table 2] with side specific differences (left and right) evaluated. The Levene's ANOVA; prompting specific ttest was used to compare the mean difference (MD) in the values obtained for sex with 95% confidence interval for observed MDs [Table 3] and [Table 4]. The DFA was presented in tables using foot parameters. The models are described in [Table 5],[Table 6],[Table 7],[Table 8],[Table 9] and [Table 10] with it summary membership classification in [Table 11].  Table 2: Anthropometric characteristics of the measured foot dimension (toe length)
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 Table 4: Comparative (ttest) analysis of measured toe length (by gender)
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 Table 6: Table tests of equality in population covariance matrices and canonical correlation
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 Table 8: Canonical discriminant function coefficient structured, standardized, and unstandardized
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Results   
The study comprised 420 subjects, of equal proportion of males (50%) with mean (SD) age of 25.26 ± 6.06 years and females (50%) with mean age of females 24.55 ± 5.79. A larger proportion of males (197; 51.4%) and females (186; 48.6%) were single while the rest, married (22.77%) at the time of the study. Moreover, 86.9% (365) of the population had above secondary education [Table 1].
The mean ± SD values of the right (R) toes (big toe or fist toe [1T] to the fifth toes [5T]) for the male were 49.63 ± 4.43 mm (1T), 36.92 ± 5.14 mm (2T), 30.35 ± 4.95 mm (3T), 25.55 ± 3.97 mm (4T), and 22.21 ± 2.94 mm (5T), whereas the female values were 45.73 ± 4.07 mm (1T), 33.31 ± 4.66 mm (2T), 26.63 ± 4.02 mm (3T), 22.89 ± 3.43 mm (4T), and 19.77 ± 2.70 mm (5T).
The mean ± SD of the left (L) toes (big [1T] to the fifth toes [5T]) for males 49.16 ± 4.32 mm (1T), 36.82 ± 5.16 mm (2T), 30.88 ± 4.91 mm (3T), 26.13 ± 3.99 mm (4T), and 22.46 ± 3.24 mm (5T), whereas the female values were 45.33 ± 4.05 mm (1T), 33.05 ± 4.70 mm (2T), 27.27 ± 4.29 mm (3T), 23.10 ± 3.36 mm (4T), 19.81 ± 2.59 mm (5T) [Table 3].
The right toe values for the 1T and 2T were larger than those left in both sexes with MD ± standard error of T1 = 0.719 ± 0.487 mm for males and 0.404 ± 0.396 mm for females, T2 = 0.102 ± 0.502 mm for males and 0.257 ± 0.457 mm for females, whereas the left side of T3 and T4 were larger than the right in both sexes (T3 = 0.529 ± 0.481 mm for males, 0.642 ± 0.406 mm for females). The male left side was larger than the right for T5 (T4 = 0.125 ± 0.319 mm), whereas female had a relatively equal length for 5T (0.051 ± 0.294 mm) [Table 4].
Levene's analysis of variance in mean showed that R.3T (F > 3.363, P = 0.067), R.4T (F > 5.704; P = 0.017) [Figure 1], and L.4T (F > 5.888; P = 0.016) had varied significantly in both sex which prompted the assumption of unequal variance analysis of MD for the aforementioned variables, whereas for others, equal variances were assumed. The ttest analysis of MD revealed significantly higher mean values for males when compared to females for all measured toe length (t > 7.00; P < 0.01) [Table 5]. Graphical illustration of the changes in mean values of the toe in both sexes is highlighted in [Figure 2].  Figure 2: Plot of mean difference of right and left side (RL) of the toe length (for male and female, only T1 and T2 had a right dominance with 3T, 4T having left dominance, whereas 5T in male was dominant in left and almost equal in females; the differences observed was not significant; P > 0.05)
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The DFA was carried out using parameters that exhibited significant difference. The test of equality of group means in [Table 5] indicates significant difference in the mean values of males and female (P < 0.001). [Table 6 Box's M tests null hypothesis of equal population covariance matrices. The canonical correlation is the multiple correlations between the predictors and the discriminant function. With only one function, it provides an index of overall model fit, which is interpreted as being the proportion of variance explained (R ^{[2]}). A canonical correlation of 0.491 suggests the model explains 23.24% of the variation in the grouping variable (that is; whether a value is male or female). [Table 7] reveals that all the predictors add some predictive power to the discriminant function as all are statistically significant with P < 0.001.
These unstandardized coefficients (b) in [Table 8] are used to create the discriminant function (equation). It operates just like a regression equation. In this case, we have [Table 8]: D = (0.097 Χ R.1T) + (0.137 Χ R.5T) + (0.076 Χ R.3T) + (0.032 Χ L.4T) +0.080 Χ L.5T) + (0.022 Χ L.3T) + (0.020 Χ L.1T) + (0.001 Χ R.2T) + (−0.108 Χ R.4T) + (−0.017 Χ R.4T) − 10.572. The discriminant function coefficients or standardized form beta both indicate the partial contribution of each variable to the discriminate function controlling for all other variables in the equation. These values are used to assess each individual variable's unique contribution to the discriminate function and therefore provide information on the relative importance of each variable. In [Table 9], the interpretation of the DFA results of each group can further be described in terms of its profile using the group means of the predictor variables. These group means are called centroids. These are displayed in the group centroids [Table 9]. In this study, the males have a mean of 0.562, whereas female produce a mean of0.562. Cases with scores near to a centroid are predicted as belonging to that group.
The coefficients of linear discriminant function which is also called "classification functions," in [Table 10] interprets the Fisher's theory for each observation, have following form P_{k} = P_{k0} + P_{k1} Χ _{1} + P_{k2} Χ _{2} +… + P_{km} X_{m} . Where; P_{k} is the classification score for group k and P's are the coefficients in [Table 10]. For one observation, we can compute its score for each group by the coefficients according to equation (above).
[Table 5 shows the level of difference in the observed values of males and females with P < 0.01 indicating a statistically significant difference. The Box's M covariance matrix showed inequality in the group variance did not meet the assumption of equal group variance, which indicates a larger discrepancy in the predictor variables. The magnitude of the actual effect of the predictors (canonical coefficient) and the outcome is the square of the coefficient (0.491); ^{[2]} this indicates that the relationship between the predictor variable and the prediction outcome is 0.232 which suggests the model explains 23.24% of the variation in the grouping variable, that is, whether the values are male or female [Table 6]. However, the group of predictor variables (R.1T, R.2T, R.3T, R.4T, R.5T, L.1T, L.2T, L.3T, L.4T, and L.5T) will make predictions that are statistically significant in their outcomes (Wilk's lambda = 0.759, P < 0.001) [Table 7], as the variables that seems to have the highest predictor capability which can be used to classify into group membership are R.1T (0.82), R.5T (0.77), R.3T (0.74) with other values falling between 0.70 and 0.66 [Table 8].
The classification results [Table 11] reveal that 72.6% of toe measurements were classified correctly into "male" or "female" groups using the various parameters; upon cross validation, accurate prediction fell to 69.5%. This overall predictive accuracy of the discriminant function is called the "hit ratio." Upon reclassification, what is an acceptable hit ratio? You must compare the calculated hit ratio with what you could achieve by chance. If two samples are equal in size, then you have a 50/50 chance anyway. This research would accept a "hit ratio" that is 30% larger than that due to chance.
Discussion   
Forensic anthropometry will require series of systematized measuring techniques that express quantitatively the dimensions of the human body and skeleton ^{[16]} in order to present findings as evidences in the course of any investigation. Some authors have used fragments of the long bones; upper or lower end to evaluate sex. ^{[1],[3]} Most of the time, long bones have been used in the determination of stature because they relatively give more accurate prediction. ^{[1]}
Sex is considered as one of the easiest determinations from the skeletal material and one of the most reliable if essential parts of the skeleton are available in good condition. ^{[5],[6]} The most often chosen bones for the determination of sex are the pelvis and the skull although the round heads of the ball joints also provide very reliable means of determining sex. ^{[7],[8]} Sex determination is also supposed to be reliable when up to 95% accuracy can be achieved. ^{[6],[7],[8]}
There are remarkable scholarly publications on the sexual dimorphic characteristics of the hand bones; ^{[17],[18]} noteworthy is the use of the 2 ^{nd} digit: 4 ^{th} digit ratio ^{[19],[20],[21]} with its dimorphic characteristics attributed to hormonal difference. ^{[22],[23]} However, such cannot be said about the toe as successive decrease in toe length was observed (1T5T).
Research on the use of toe length to differentiate sex is rather scarce; thus, making this study a pioneer one. Indications from the analysis highlights nonasymmetric difference in toe length with significant sexrelated anthropometric difference in all toes (1T5T). From the difference observed in toe measurements, there may be indication of foot dominance correlating with big toe length in association with foot length; as the right big toe (1T) was larger than the left in most subjects, whereas the reverse was observed for the third toe (3T), fourth toe (4T); and small toe (5T) in males. The graphical illustration shows how the MDs in both sex changes with toe; indicating sex discrimination.
The use of DFA was to evaluate the accurateness and predictability of the model using the observed significant measured variables. The strength of such model is the ability to classify above 80% of the measured parameters into groups (sex) although a 95% accuracy bench mark have been established. ^{[6],[7],[8]}
The model accuracy for discriminant model for sex categorization in this study seems quite low; although with a better prediction for female (70%) than males (69%). This result indicates cautious prediction into group membership using this model taking into consideration; errors (e) which may have occurred that resulted in the deviation from high discrimination.
Conclusion   
Evidence from this study clearly indicates sexassociated difference in foot parameters. DFA successfully predicted 69.5% of the data into groups (sex) and the prediction statistically significant; thus suggestive of forensic attributes. However, such predictive value seems quite low; hence, the use of toe dimensions alone may not be effective for sex differentiation. The findings argue that a single set of foot dimensions may not be applicable in sex grouping. Therefore, toe length can serve as adjunct in sex identification.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8], [Table 9], [Table 10], [Table 11]
