Abstract:
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
hO,
hj and
h’j (
j=1, 2, …, 8) all had normal distribution. Let
gj=
hO-
hj, Then
gj obviously had normal distribution. The values of this variable of the criminal and the suspect were noted as
gOj,
gij (
i=1, 2,.,
n,
n is number of suspects) respectively. Suppose
gOj~
N (
μOj,
σOj2),
gij~N (
μij,
σij2). 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. σ
12= 1. 12 was obtained from 2000 data. Hence
gOj-
gij~
N (
μOj-
μij, 2σ
12, 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.