Continuous-variable quantification of dermatoglyphic whorl patterns A statistical study of angular measurements.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 83:161-171 (1990) Continuous-Variable Quantification of Dermatoglyphic Whorl Patterns: A Statistical Study of Angular Measurements CHANCHAL SINGH mun KARL B MCKNIGHT Department of Mathematics i C S i, Department of Biology iK B M), St Lawrence University, Canton, New York 13617 KEY WORDS Base angles, Tangent angles, Core, Triradius, Ridge Count, Dermatoglyphics, Whorl patterns, Sex Discrimination ABSTRACT Core(s) and triradii of dermatoglyphic whorl patterns were joined together to form triangles. Base angles of these triangles were measured (in degrees). The tangent angle at the lower edge of a ridge crossing the core-triradius line was also measured in degrees on each side of the whorl. Significant differences and similarities of these angles were investigated for unrelated Caucasian males and females by the use of Student’s t- and Pearson’s r-tests. Angular findings were related to the corresponding information provided by ridge counts. Similarities and differences between males and females are described. Dermatoglyphic whorl patterns reflect various genetic and environmental traits in human populations and vary in ways that have proved useful in the study of genetics (Holt, 1968; Rostron, 1977; Wertelecki and Plato, 19831, medical disorders (Wertelecki et al., 1973; Schaumann and Alter, 1976; Schaumann et al., 1982; Garruto et al., 19831, criminology (FBI, 1979; Moses, 1987; Hall, 19871, gerontology (Plato, 1978; Wertelecki and Plato, 1983). physical anthropology (Jantz, 1977; Pollitzer and Plato, 1979), and sexual dimorphism (Arrieta et a]., 1987; Dennis and Sunderland, 1979; Janz, 1977; Karev, 1986; Micle and Kobyliansky, 1986, 1988; Goodson and Meier, 1986). However, more extensive use of dermatogly hic atterns has been limited not only by t e in erent genotypic and phenotypic variability of the patterns but by the discontinuous nature of the dermatogly hic variables currently used by most wor ers as well. Dermatoglyphic studies usually use ridge counts, a discrete random variable. Statistical conclusions reached with ridge count data are often questionable, unless large sample sizes permit the use of the central limit theorem. However, in order to maintain the largeness of the sample sizes, ridge counts of loops and whorls have been mostly lumped together. As a result, much of the potential information inherent in the dermatoglyphic patterns K K K 0 1990 WTLEY-IJSS, INC. may have been either obscured or lost. Many powerful statistical techniques such as analysis of variance, principal components, and multiple linear regression assume that variables are distributed normally and that variances are homogeneous (Kleinbaum et al., 1988; Sokal and Rohlf, 1981). Consequently, the validity of many studies using these techniques may be questionable (because of smallness of sample sizes) if pooling of ridge counts of loops and whorls were not done in the hope of gaining more insight by studying these patterns separately. Even though most nonparametric statistical techniques comparable to corresponding parametric techniques assume continuity of the variables under study (Conover, 19711, we are not aware of any digital dermatoglyphic studies using continuous variables. Nor have we any knowledge of dermatoglyphic studies making use of nonparametric statistics, even though nonparametric techniques permit small sample sizes. In the present study, new variables of a continuous type are introduced. Inasmuch as the underlying causes of medical disorders, criminal behavior, gerontology, and so forth, are very complex, we believe that dermatoglyphic studies should Received September 11,1987, accepted September 13,1989. 162 C. SINGH AND K.B. MCKNIGHT not overlook possible variables that may be potentially of greater complexity than ridge counts. We hope this study inspires the reader to explore new dimensions in the study of digtal dermatoglyphics patterns. MATERIALS AND METHODS Fingerprints of 300 unrelated North American Caucasian males and females were obtained using the inked pad method of Cummins and Midlo (1961). Equal numbers of males and females were sampled. The fingerprints were projected onto white paper taped to a wall approximately 2 m away from an opaque projector. Each fingerprint’s image was thus approximately 10 cm x 20 cm. This study presents only the results of finger rints having whorl patterns. AT1 the whorls we examined had two triradii and one or two cores. A straight line connecting a core to the nearest triradius was called a CT (core-triradius) line (Fig. 1). A core-triradius line was drawn the same way as it is done in recording ridge counts. We have followed Holt’s (1968) convention and the CT lines drawn in Figures 1-3 are from her book. A strai ht line joining the two triradii was called a TgR (triradius) line. The two CT lines were extended, if necessary, to form a triangle AABC (Fig. 1).For the left hand, the angles, <ABC and QACB, were called the ulnar and the radial base angles respectively. For the right hand, the angles, QABC and -SACB,were called the radial and ulnar base angles, respectively. A tangent angle of a ridge was defined and measured by the following procedure. A point along the lower edge of a ridge was marked 3 mm above the point of intersection of the ridge with a CT line. A point was also marked along the lower edge of a ridge 3 mm below the point of intersection of a ridge and the CT line. A straight line connecting the two points was then extended to intersect the TR line, this was called a tangent line. Tangent angles were formed by the intersection of tangent lines and the TR line on either side of the pattern. For a left hand some of the radial tangent angles are QR,DC, aR,EC, QR,FC and some of the ulnar tangent angles are QL,ZB, QL2YB as shown in Figures 1-3. For a right hand some of the ulnar tangent angles are QR,DC, QR,EC, QR,FC and some of the radial tangent angles are QL,ZB, 4L2YB as shown in Figures 1-3. Since the tangent angles of adjacent ridges did not seem to vary considerably, measurements of these angles were taken for every third ridge starting from the triradius. If the third ridge did not cross the CT line, the tangent angle of the next ridge was measured. The number of tangent an les is usually different for the two sides o f t e triangle AABC because frequently there are a different number of ridges on the two sides of a whorl pattern. Consequently, arithmetic averages of all the tangent angles on each side of the triangle AABC were computed and were reported as one value for each side for each digt. In a few cases (less than 1%of the entire sample for any digit) a core or cores happened to be below the TR line. These patterns seem to be very important for identification purposes, but their base angles were hard to interpret and behave like “outliers.” Accordingly, they were discarded in this study. Measurements of angles were made in degrees. In order to relate the present study with previous work, we have performed univariate parametric tests (rather than nonparametric) for each digit and for each sex. The paired-t-statistic was used to test for significant differences in arithmetic means between ulnar and radial base angles, ulnar and radial tangent angles, and ulnar and radial ridge counts. We also used the t statistic for univariate tests of sexual dimorphism for each of the preceding six variables. Pearson’s r-test was used to determine significant correlations among the six variables. Statistical significance was assessed at Pc-O.05 unless otherwise noted. Inasmuch as different digits of any given subject do not necessarily have the same dermatoglyphic pattern (Holt, 19681, analysis of variance, discriminant analysis, and many multivariate techniques are inappropriate for sample sizes such as ours. In particular, it is not possible to construct a discriminant analysis based on all digits because not all subjects have whorls on the same digits. This is unlike the numerous such studies done with ridge counts (e.g.,see Micle and Kobyliansky, 1986). However, in order to demonstrate how the new variables described in this paper might compare with already available dermatoglyphic measures of sexual dimorphism, we selected R, (R4 is one of the digits for which we have the most data) for a stepwise discriminant analysis. Ulnar and radial base angles, ulnar and fl CONTINUOUS VARIABLES AND DERMATOGLYPHIC WHORLS 163 males and 150females included in this study is given in Tables 1 and 2, respectively. For males (Table 31, ulnar base angles were significantly higher than radial base angles of digits LI, Lg, and L5 (PS0.064) and RI, R4, and R5 (P~0.013).Radial tangent angles were significantlyhigher than the ulnar tanRESULTS gent angles for digitis LI, LB, and L4 A statistical summary of four angular (P~0.047)and RI, R4, and R5 ( P ~ 0 . 0 0 3 ) . measures and two ridge counts for the 150 Similarly, radial ridge counts were signifi- radial tangent angles, and ulnar and radial ridge counts for males and females of digit R4 were entered into the SAS (Ray,1982)STEPDISC routine. Default significance levels (0.15) for variable entry and retention were used. Fig. 1. Base and tangent angles of a symmetric whorl pattern. The line, TR connects the two triradii. CT, and CT, are core-triradius lines. L,-L, and R,-R, are tangent lines. For a left-hand print, the angles dABC and aACB, are the ulnar and radial base angles. The angles, QR,DC, dR,EC, and QR,FC are some of the radial tangent angles. The angles, QL,ZB, QL,YB are two of the ulnar tangent angles. See methods for a more detailed description ofthe construction ofthis figure. (Modified from Halt (1968),with permission.) 164 C. SINGH AND K.B. MCKNIGHT Fig. 2. Base and tangent angles of a double loop whorl pattern. See Figure 1 for construction details. cantiv higher than ulnar ridge counts for digits R,, R,, R,, (PS0.003)and digits L1, L,, and L, (PS0.004), whereas ulnar ridge counts were significantly higher than radial ridge counts for digit L, (PS0.003). For females (Table 31, ulnar base angles were significantly higher than radial base angles of digit Rl, RB, and R, and L, (PsO.044).Radial tangent angles were significantly higher than ulnar tangent angles for digits R, and R3 (PS0.051) and L,,. L,, and L, (PS0.04). Similarly, radial ridge counts were significantly higher than ulnar ridge counts for digits R,, R3, R4,and R5 (Ps0.0221, and L,, L,, and L, (PS0.053). Digit R3 presented an interesting contrast between males and females. For males none of the three differences was statistically significant, however, for females all three were statistically significant (PS0.051)(Table 3). Similarly, digit L3 of males showed signifi- cant differences only of tangent angles, whereas L, of females presented significant differences in tangent angles and ridge counts (PS0.053).In contrast, R2 showed no significant differences for either males or females. Measurements of new variables, in relationship to sexual dimorphism, differed from ridge counts on digits R,, R,, R,, L1, and L, (Table 4). There were significant differences between males and females on digits R, (with respect to total ridge count) and digit L2 (with respect to ulnar ridge count). However, none of the new variables showed any significant differences on these digits. There were significant differences between males and females on digit R, (with respect to radial tangent angle), on R4 (with respect to ulnar tangent angle), and on L, (with respect to ulnar base angle). For these three digits, none of the ridge count variables showed any CONTINUOUS VARIABLES AND DERMATOGLYPHIC WHORLS 165 Fig. 3. Base and tangent angIes of a spiral whorl pattern. See Figure 1 for construction details. significant differences. It is interesting to note that only L5 presented si ificant differences between males and emales with res ect to both the radial base angle and ra ial ridge count. Correlation analysis brought out more similarities between males and females. For both sexes (Tables 5 and 61, there was a significant negative correlation between the radial tan ent angle and the radial base angle for igits R,, R3, R,, L,, L,, and L,; between the ulnar tangent angle and ulnar P B % base angle for R2,R3, R4,and L2;between the radial ridge count and the radial base angle for digits R2, R4,and L,; between the ulnar ridge count and the ulnar base angle for digits R,, RS, L2,L3, and L4;and between the radial ridge count and the ulnar base angle for digit L,. For both males and females, we observed a significant positive correlation between the radiaI ridge count and the radial tangent angle for digits R,, R,, and Lz; between the ulnar ridge count and the ulnar tangent angle on digits R1, R,, R3,R,, L1, and 166 C. SINGH AND K.B. MCKNIGHT TABLE 1. Means and Standard Deviations of Four Trigonometric Measures and Ridge Counts for the Digits of 150 Unrelated Caucasian Males Digit N R1 56 29 19 42 15 46 40 R2 R3 R4 R5 Ll La I,? L; 16 30 9 L.> Radial base angle Ulnar base angle Radial tangent angle Ulnar tangent angle 28.8 i 8.6 41.8 f 12.1 46.6 i 12.9 41.6 i11.4 36.1 i10.0 33.5 i 9.4 43.9 i15.1 44.9 It 7.8 40.7 i 8.0 :x,4 i s.3 37.8 k 24.0 39.2 i 11.2 46.5 i13.9 53.3 i14.6 50.9 i 17.0 40.5 i11.7 40.3 I 10.5 45.9 i 14.8 54.1 rt 13.6 46.2 L iG.2 80.8 i 8.4 72.2 i 1 4 . 6 71.2 1 1 4 . 9 76.3 -i- 13.7 81.8 i 8.9 69.6 i11.0 75.4 t 15.2 72.7 t 14.0 64.2 i17.1 55.9 i 22.9 62.3 i 12.6 75.2 i14.5 68.4 I 18.1 66.7 -., F 13.9 83.7 i 7.3 68.7 t 14.5 80.5 i10.3 80.5 1 1 0 . 4 61.1 I6.6 Radial no. of ridges __.__.. rh.2 i 3i.7 Ulnar no. of ridges 19.8 i4.2 13.6 i 4.3 15.5 i 5.4 17.4 i- 4.3 16.9 i 3.0 14.8 i 4.8 15.1 i 4.1 14.5 i 5.0 12.5 t 4.4 9.3 I 3.6 18.2 I 3.6 12.8 i4.3 16.4 i 3.7 3.6 18.4 i 4 7 . i i 2.8 13.4 i 4.5 16.0 f 4.4 15.2 + fin 13.0 i 3.6 ~ Y.b ? 4.5 TABLE 2. Means and Standard Deviations of Four Trigonometric Measures and Ridge Counts for the Fingers of 150 1Jnrelated Caucasian Females Digit N Radial base angle R, 47 44 12 37 12 28.6 i- 7.7 41.6 i 9.3 39.3 5 12.3 41.3 i 11.7 38.1 i12.1 33.4 i12.8 38.3 f 12.1 54.8 f 14.2 47.7 i 14.3 46.4 i 16.7 46 31 17 31 33.7 i 8.3 44.7 i 12.6 42.4 i 7.3 40.5 f 10.2 47.3 i 10.3 33.9 i 13.6 41.3 i 9.6 51.2 -t 14.5 55.0 i13.6 43.4 i 6.8 ~. R; R3 R4 R5 L1 L‘i LJ L4 L5 10 Ulnar base angle Radial tangent angle Ulnar tangent angle Radial no. of ridges Ulnar no. of ridges 80.6 i 7.7 70.7 t 13.0 81.6 i11.7 75.4 i 10.6 76.6 f 12.7 82.3 5 7 . 3 67.5 I 17.0 76.8 I 11.0 81.3 i- 9.7 76.6 i 9.7 69.6 i11.6 73.4 t 15.2 63.7 i 20.6 73.2 i 12.1 68.5 i 19.8 19.9 i 3.2 12.6 i- 3.8 17.3 i 3.9 17.3 i- 4.1 17.3 i 4.4 14.0 i 5 . 2 13.3rt 5.0 13.0 i- 5.6 14.0 i 4.3 11.3 i 3.7 66.3 i 13.8 72.6 i 11.7 66.9 i 13.0 66.9 i 13.7 74.6 F 9.7 18.8 i4.0 12.9 i 4.4 15.8 i 3.5 18.2 F 4.2 12.7 i 2.3 14.7 i5.4 13.9 i 4.0 13.8 i- 4.6 13.0 i 4.3 12.0 i 3.6 TABLE 3. Student’s Paired t-Test with Associated P Values between Ulnar Base Angle (UBA)and Radial Base Angle (RBAj, the Ulnar Tangent Angle (UTAj and the Radial Tangent Angle (RTA), and the U h a r Ridge Count (URC) and the Radial Ridge Count (RRCj Males REP, Sampie size (h’) R1 Rz R3 R4 R,j L1 Lz L3 I,4 LS 56 29 19 42 15 41 40 16 30 9 .T. 1 % UBA t P ...____ ___. nT A RRC YS. VS. LlLil UTA t _- P -2.70/0.009 5.58/0.000 0.85/0.400 -0.73/0.470 0.02/0.980 -0.26/0.800 -4.10/0.000 3.21/0.003 -2.83/0.013 3.73/0.002 --3.32/0.002 9.22/0.000 1.21/0.240 -1.64/0.110 -0.25/0.810 2.17/0.047 -4.80/0.000 4.14/0.000 0.42/0.690 -2.15/0.064 URC t P Females RTA Sampie size (N) RBA vs. UBA t P 47 44 12 37 12 46 31 17 31 10 -2.70/0.010 1.27/0.210 -2.39/0.036 -2.09/0.044 --1.60/0.140 -0.07/0.950 1.05/0.300 --1.82/0.087 -5.90/0.000 1.26/0.240 VS. UTA t P ~~~ 7.20/0.000 -1.16/0.250 0.65/0.320 7.41/0.000 9.66/0.000 5.93/0.000 -3.11/0.003 0.90/0.380 7.35/0.000 4.05/0.004 L,; between the radial ridge count and the ulnar ridge count for digits R1 and L4. Males and females differed most notably in the correlation analyses (Tables 5 and 6) when the radial base angles were compared with ulnar base angles (significantly posi- 5.14/0.000 -0.76/0.450 2.19/0.051 0.74/0.460 1.17/0.270 6.20/0.000 -1.11/0.270 2.23/0.040 4.11/0.000 0.46/0.660 RRC vs. URC t P- 7.68/0.000 -0.90/0.370 2.651’0.022 3.98/0.000 3.49/0.005 4.84/0.000 -0.90/0.380 2.09/0.053 7.32/0.000 0.47/0.650 tive for digits R1 and Lq of females but not of males, significantly negative for L, of females but not of males). Radial base angles were positively correlated with ulnar tangent angles for digits R,, R3 of females but not of males. Ulnar base angles and radial 167 CONTINUOUS VARIABLES AND DERMATOGLYPHIC WHORLS TABLE 4. C o m m r i s o n s (Studenti; t-Testi between Males and Females for Seven DematodvDhic Measures.’,2 RBA t RTA UBA P Ri R:, R:] -0.12/0.900 -0.10/0.920 K4 -0.12/0.910 - 1.5$/0.130 t P -1.19l0.240 -0.34/0.730 1.59/0.130 -1.87/0.066 Rr, 0.45/0.650 -0.69/0.490 Li O.OXI’0.930 L:! L:I -0.95/0.350 -2.43/0.017* 0.44/0.660 1.04/0.310 0.27/0.790 L1 Lz 0.23l0.820 --0.11/0.920 2.24/0.039* -0.70/0.500 t RRC UTA P t -0.11/0.920 P 0.02/0.980 -0.57/0.570 -0.45/0.660 2.16/0.040* -0.32/0.7!3 -1.20/0.240 t 0.09/0.930 -1.03/0.310 -1.32/0.200 2.71/0.008* 1.541’0.140 --0.86/0.390 1.4 lI’0.160 -0.32/0.750 -0.85/0.400 -0.99/0.330 -0.28/0.780 0.08/0.940 0.29/0.770 --1.05/0.310 -1.18i0.860 URC -____ P 1.07/0.290 - 0.06/0.950 0.31/0.760 0.67/0.500 0.07/0.940 -0.49/0.630 -0.24/0.810 --3.71/0.002* t P -0.85/0.400 -1.69/0.096 0.77/0.450 1.55l0.120 1.35l0.190 1.23/0.220 -2.07/0.043* -0.73l0.470 O.OOI’O.999 1.31/0.210 TRC t P --0.55/0.580 ---2.11/0.038* 0.09/0.930 0.92/0.360 1.08l0.290 1.24/0.220 --1.40/0.170 -0.73/0.470 -0.14/0.890 --0.97/0.350 ‘Uinar base angir ~l;r)X,.iadS!iasc 3ng!. (RR4’ xlnw tanwnt, angle (UTA),radialtangent angle (RTA),ulnarridge count (URC),radial gdge count (RRC), and total (ulnar + radial! ridge count (TRC). See Tables 1 and 2 for sample sizes and average values and standard deviations for each sex. *Comparisons significant a t P 5 0.05. tangent angles were positively correlated for digit L, of females but not of males. We also observed a si ificant negative correlation: between the u nar tangent angle and the ulnar base angle on digit L3 for males but not of females, between the radial ridge count and the radial base angle on digit R3 of males but not of females, between the radial ridge count and the radial base angle on di ‘t R, of females but not of males; between t e radial ridge count and the ulnar tangent angle on digit L, of males but not of females; between the ulnar ridge count and the radial tangent angle on digits RI and R, of females but not of males (Tables 5 and 6). Our data also differed significant1 between the sexes for the correlation of ra ial ridge count and ulnar base angle of digit R1 and for the correlation of ulnar ridge count and radial base angle of digit L,. Similar differences were exhibited by digit R, for the correlation of radial ridge count and ulnar tan ent an le and the correlation between the u nar ri ge count and radial tangent angle of digit L,. A significant positive correlation between ulnar ridge count and radial base angle on digits R1 and R5 of males was not shared by the females. The stepwise discriminant analysis of the R4 data showed that of the six variables possible (radial and ulnar base angles, radial and ulnar tangent angles and radial and ulnar ridge counts) for the discriminant function, the ulnar tangent angle was the only significant variable to be entered and retained (Wilks h = 0.92, P<0.0098, average squared canonical correlation = 0.08). Q f B Eif DISCUSSION There is inevitably some measurement error associated with the measurement of tangent angles and base angles. However, such error is present during the measurement of almost any continuous variable such as weight, height, income, and so forth, due to the im recision of the measurin instrument. Following the technique dgescribed above, we believe that the amount of error due to measurement is not significant enough to obscure many important relationships among and between these new dermatoglyphic variables and ridge counts. The positive correlation we observed for most digits between the ulnarkadial tangent angle and ulnariradial ridge counts and the radiaYulnar tangent angle and the radial/ ulnar rid e counts suggests that for both males an females, the hi her the tangent angles, the higher will be t e ridge count of the same side. Intuitively, this makes sense, since the hi her the tangent angle, the farther away t e core will be located from the TR line. Consequently, there will be more ridges between the core and the triradius. Thus, tangent angles throw light on ridge counts in an indirect way. The negative correlation we observed for most digits between the ulnarkadial base angle and the ulnariradial ridge counts, and the radiavulnar base angle and the radiaY fi fl a 168 C. SINGH AND K.B. MCKNIGHT TABLE 5. Pearson's Coefficient o f Correlation (r) Expressing the Relationships for Each Digit antorig Sir I)erm.atoglypkic Measures' N Parameter 56 UBA KTA UTA RRC URC UBA RTA UTA RRC URC 29 ia 42 15 41 40 16 30 9 RBA -UBA RTA UTA RRC -. 0.221 0.5611. 0.339* 0.055 ---0.126 0.051 -0.036 0.328* -0.039 -0.608t 0.341 -0.4031 0.303 0.142 - 0.246 -0.205 -0.150 -0.192 -0.026 -0.246 0.078 -0.510t 0.236 -0.50ot -0.256 0.426* -0.234 -0.5731. 0.6631 Tq?4 n 125 RTA UTA RRC IJRC UBA RTA UTA RRC URC UBA RTA UTA RRC URC RBA UTA RTA URC RRC RBA UTA RTA URC RRC RBA UTA H A I iRC RRC -0.755t 0.252 -0.7'241 0.021 --(]..51ia: -0.U77 0.133 -0.200 -U.179 0.6941. 0.304 RBA UTA RTA URC RRC RBA UTA RTA URC RRC 0.073 -0.240 -0.004 -0.691t -0.461* 0.049 -0.6161 -0.028 -0.662t -0.126 0.171 -0.075 -0.092 0.4851 0.179 0.8921 -0.436 -0.143 0.206 -0.fi99* 0.609 -0.676* -0.213 -0.165 0.402 -0.547 0.155 -0.087 -0.6301. 0.256 -0.fiost 0.069 -0.066 -0.330 0.510 -0.094 0.553* 0.205 -0,010 0.145 -0.013 0.236 -0.068 -0.4731 0.308 -0.4871 0.229 0.015 -0.6701 -0.013 0.179 -0.767t 0.040 -0.692t -0.340 -0.380 0.849t 0.057 -0.133 0.7271 0.248 0.098 0.7021 0.5141- 0.346* -0.488i 0.131 -0.159 -0.250 0.6051 0.009 -0.059 -0.623* -0.426 -0.393 -0.305 0.170 -0.211 0.387* -0.045 0.5281 0.043 -0.042 0.6261. -0.184 0.146 -0.4731 0.127 -0.243 0.572* 0.6521 -0.009 0.213 0.5971- 0.187 -0.482t 0.5sst -0.4811. -0.240 0.7231 -0.058 0.391 -0.7001- -0.122 ij.274 0.371* 0.006 -0.134 'The suhjtacts were North American Caucasian males. *Correlations significant at PI-:0.05. ?Correlations significant a t P 5 0.01. a pattern, the more the tilt of the triradius on that side towards the core, thus producing a smaller number of ridges. Here again we learn something (in an indirect way) about ridge counts from the magnitude of base angles. Holt (1961)reported a slightly smaller, but nevertheless statistically significant, aver- 169 CONTINUOUS VARIABLES AND DERMATOGLYPHIC WHORLS TABLE 6. Pearson's Coefficient o f Correlation (r) Expressing the Relationships for Each Digit among Six Dermatoglvahic Measures' Digit N Parameter RBA Ri 47 UBA RTA IJTA RRC URC UBA RTA IJTA RRC URC 0.3831 -0.225 44 R4 R5 L1 37 12 46 31 17 31 10 UTA RRC URC UBA RTA UTA RRC URC UBA RTA UTA RRC URC RBA UTA RTA URC RRC RBA IJTA RTA URC RRC RBA UTA RTA URC RRC RBA UTA RTA URC RRC RBA UTA RTA URC RRC _ - RTA IJTA -0.184 .409t -0.058 -0.097 0.087 -0.295" 0.046 -0.370* -0.094 -0.134 0.091 -0.357" -0.278 --0.5741. 0.364* -0.4061. 0.194 0.357* -0.5881. 0.215 -0.4957 -0.294 0.5701. -0.4031. -n.430 -0.762i R3 ~UBA _ _ 0.606" -0.534 0.533 -0.027 -0.4677 0.201 --0.413" 0.184 0.236 -0.422 0.037 -0.7271. 0.300 -0.204 -0.214 0.147 -0.034 0.207 -0.227 -0.5191. 0.5121. -0.382" 0.307 -0.641t -0.451 -0.202 -0.6YZt -0.379 RRC 0.300" 0.075 0.627-! 0.098 0.465 -0.7757 -0.374 -0.8131 0.461 -0.243 0.189 0.8241. 0.354 0.375* -0.577i 0.059 -0.4961 -0.354" 0.4831 -0.253 0.093 0.6651. 0.245 0.130 -0.370 -0.269 -0.437 -0.071 0.669" -0.392 --0.123 -0.260 0.087 0.036 -0.328* 0.5751. -0.069 -0.360* -0.089 0.109 -0.426" 0.306 -0.299 -0.5421. 0.5547 -0.315 -0.355 0.7191 - 0.490 0.287 0.309 -0.094 0.291* -0.004 -0.121 0.082 0,338 0.1% -0.168 0.478 0.054 ~ 0.359" -0.4751 -0.069 -0.433* -0.586t 0.026 -0.413* -0.068 -0.6431. -0.345 0.5841. 0.4837 -0.275 0.104 0.408 -0.380 -0.328 0.078 -0.169 0.450 -0.634" 0.586 -0.482 -0.479 0.655* -0.341 -0.527 0.649* 0.5721. -0.262 'The subjects were North American Caucasian females *Correlations significant at P 5 0.06. iCorrelations significant at P 5 0.01. age ridge count for 825 British females when compared with 825 British males. Similar results were observed by Arrieta et al. (1987),Dennis and Sunderland (1979), Janz (1977), Karev (1986), and Micle and Ko- byliansky (1986, 1988). Our data likewise reinforce the notion that sex discrimination with individual variables is hazardous. However, the sex differences reported here for R3 and L3 suggest that multivariate combina- 170 C. SINGH AND K.B. MCKNIGHT tions of variables may effectively discriminate between sexes or other groups of individuals. Sample sizes may have to be much larger than ours to do multivariate analyses, especially if its necessary to make comparisons across digits. Because our intent was not to try to describe average values for Caucasian tangent angles or base angles, but rather to describe how these new variables may be measured and utilized, we did not perform discriminant anal ses for digits other than R4. However, we t ink it may be significant that for the analysis of R4,uiie 0:' the ~ e variables w described here provided more information about sexual dimorphism than ridge counts. We expect that studies utilizing larger sample sizes may be able to analyze variables across digits or combine raw data for base and tangent angles into useful new variables, such as the differences between ulnar and radial base angles or ulnar and radial tangent angles. There appears to be an untapped storehouse of information in dermal prints. We have only begun to examine the angular aspect of whorl patterns. We hope that there may be other kinds of information that other workers might uncover. We also believe that the contribution of dermatoglyphics to future medical, sociological, and anthropological studies will be strengthened if eontinuous-variable measurements such as those described here are included in the investigations. K ACKVnWXDGMENTS We are extremely grateful to the anonymous reviewers and the editor-in-chief, Dr. Matt Cartmill, for helping us to improve the quality of the manuscript. The contribution of the first author is dedicated to Dr. William J. Ash, formerly professor of biology at St. Lawrence University, who introduced this author to the study of dermatoglyphics. LITERATURE CITED Arrieta MI, Ibarrondo MA, and Lostao CM (1987)Digital Dermatoglyphics in the Basque Population: Univariate and Multivariate Comparison With Other Spanish Populations, Am. J . Phys. Anthropol. 73339-98. Bansel IJS (ed) (1980) Human Biology: Recent Advances. Vol. 2. Proceedings of the International Symposium on Dermatoglyphics, Department of Human Biology, Punjabi University, Patiala, India. New Delhi, India: Today and Tomorrow's Printers and Publishers. Conover WJ (1971) Practical Nonparametric Statistics. New York: John Wiley & Sons. 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