STATISTICAL METHOD ON QUANTITATIVE TESTING THE CHARACTERISTICS OF THE HUMAN SOLID FOOTMARKS

It is very probably for criminals to have their characteristics of footmarks left in the crime scene. But the investigators make little use of it. They simply analysed and compared the features of footmarks by experience. In the references （1）, （2）, and （3）, we had presented successfully four statistical methods for testing characteristics of step magnitude. On the basis of above methods, this paper presented a new statistical method for testing characteristics of solid footmarks, it had gained success in many occasions. At first, in the plaster models of the solid footmark Descartes coordinate system was established. In coordinates, point （0, 12） （length in unit of CM） at the fore sole of the foot （not thumb） was chosen as the centre. Height of the point in the plaster model was measured, and recorded as h₀ （height in unit of MM）. A special instrument was used to measure the height. Then we chose points （0, 13）, （0, 11）, （-1, 12）, （1, 12）, （1, 13）, （-1, 13）, （-1, 11）, （1, 11）, and called them as middle points. Their heights were noted as h’₁,h’₂, h’₃, h’₄, h’₅, h’₆, h’₇, h’₈ respectively. Similarly （0, 15）, （0, 9）, （-3, 12）, （3, 12）, （3, 15）, （-3, 15）, （-3, 9） and （3, 9） were called as marginal points, their heights were noted as h₁, h₂, h₃, h₄, h₅, h₆, h₇, h₈. By testing, it was indicated that h_O, h_j and h’_j （j=1, 2, …, 8） all had normal distribution. Let g_j=h_O-h_j, Then g_j obviously had normal distribution. The values of this variable of the criminal and the suspect were noted as g_Oj, g_ij （i=1, 2,., n, n is number of suspects） respectively. Suppose g_Oj～N (μ_Oj, σ_Oj²), g_ij～N (μ_ij, σ_ij²). The results obtained by testing 2000 footmarks of 20 persons （100 footmarks per person） indicated \sigma_0 f^2=\sigma_i j^2 \triangleq \sigma_1^2, \quad i=1,2, \cdots, n ; j=1,2, \cdots, 8. σ₁²= 1. 12 was obtained from 2000 data. Hence g_Oj-g_ij～N (μ_Oj-μ_ij, 2σ₁², Under hypothesis H_0: \mu_0 j-\mu_8 y=0, \fracg_o j-g_i j\sqrt2 \sigma_1 \sim N(0,1) Therefore \boldsymbolC_16 \triangleq \sum_j=1^8 \frac\left(g_0 j-g_i j\right)^22 \sigma_1^2 \sim \chi^2(8) For \alpha given, there is P\left(C_15>\chi_\alpha^2(8)\right)=\alpha, That is, statistio C_1 s can be used to test hypothesis H_0. Similarly, the statisties C_\text sr and O_3 of characteristios at the fore sole and thumb of the foot are constructed respectively, O_2, O_\mathbf3 i bave Ohi-square distributions with 8 and 5 degrees of freedom respeotively. If C_14 \leqslant \chi_\alpha^2(8), O_24 \leqslant \chi_\alpha^2(8), C_31 \leqslant \chi_\alpha^2(5) happen at the same time, then the suspect and the oriminal have same charaoteristios of the footmark, otherwise, the suspect can be eliminated. At last, this paper gives a practical example.