Comparing Log-based and Exponent-based Functions to Predict Human Height by Foot Length

Abstract

Background: Human height estimation is critical in medicolegal cases. This anthropometric measurement not only reveals racial differences but also aids police investigation to narrow down. Foot size varies in different races and ethnic groups, because of genetic influence on development height. The present study aimed to explore the relationship between foot size and the height of a person in a particular context. The current research also compared log-based function and exponent-based function to explore which best fits the relation between age, foot size, and height. Methods: This cross-sectional study included foot measurements from 240 participants of 6 different age groups in the age range of 2-21 years. Foot length and height were recorded as per standard methods after obtaining ethical approval from the Institutional Review Board of COMSATs University Islamabad Pakistan and gaining consent from the study participants. Correlation and regression analyses were performed using SPSS V 23. In this study, two mathematical functions of log-based and exponent-based were compared to more accurately predict the behavior of two variables. The appropriateness of these candidate functions was evaluated using statistical parameters, including the Sum of Squared Errors (SSE), R2, adjusted R2, and Root Mean Square Error (RMSE). Results: The mean height of male participants of the age group of 3-5 years was higher than that of the female participants. Among 6-10-year-olds and 11-15-year-olds, female participants presented a greater height than males. In the age groups of 16-20 and ≥21 years, males were taller than females. The average foot size of males and females of all age groups was 22.09 cm and 20.44 cm, respectively. The exponent-based candidate functions best fitted the relationship between age, foot size, and height, compared to the log-based candidate function. Conclusion: Foot size indicated the highest correlation with height and minimum standard error in the estimation of stature. Therefore, foot size provided the highest reliability and accuracy in estimating height.